// Write
void cohesiveLawFvPatchVectorField::write(Ostream& os) const
{
fvPatchVectorField::write(os);
traction_.writeEntry("traction", os);
os.writeKeyword("cohesiveLaw") << law().type()
<< token::END_STATEMENT << nl;
os.writeKeyword("relaxationFactor") << relaxationFactor_
<< token::END_STATEMENT << nl;
law().writeDict(os);
writeEntry("value", os);
}
int main(void)
{
Form paper("Piece of paper", 150, 150);
Bureaucrat barneyStinson("Barney Stinson", 2);
std::cout << "Printing \"paper(\"Piece of paper\", 150, 150);\": " << paper;
barneyStinson.signForm(paper);
std::cout << "Printing \"paper(\"Piece of paper\", 150, 150);\": " << paper;
Form law("Law", 1, 1);
std::cout << "Printing \"paper(\"Law\", 1, 1);\": " << law;
barneyStinson.signForm(law);
std::cout << "Printing \"paper(\"Law\", 1, 1);\": " << law;
try {
std::cout << "Trying to create \"something(\"something\", 151, 151);\"" << std::endl;
Form something("something", 151, 151);
} catch (Form::GradeTooLowException & e) {
std::cout << "Exception: " << e.what() << std::endl;
}
try {
std::cout << "Trying to create \"something(\"something\", 0, 0);\"" << std::endl;
Form something("something", 0, 0);
} catch (Form::GradeTooHighException & e) {
std::cout << "Exception: " << e.what() << std::endl;
}
}
// with stretch (and stretch-rate) independent contraction models the implicit and explicit schemes
// are identical
void TestCompareImplicitAndExplicitWithStretchIndependentContractionModel() throw(Exception)
{
QuadraticMesh<2> mesh(0.25, 1.0, 1.0);
MooneyRivlinMaterialLaw<2> law(1);
std::vector<unsigned> fixed_nodes
= NonlinearElasticityTools<2>::GetNodesByComponentValue(mesh,0,0.0);
ElectroMechanicsProblemDefinition<2> problem_defn(mesh);
problem_defn.SetMaterialLaw(INCOMPRESSIBLE,&law);
problem_defn.SetZeroDisplacementNodes(fixed_nodes);
problem_defn.SetContractionModel(NONPHYSIOL1,0.01);
problem_defn.SetMechanicsSolveTimestep(0.01); //This is only set to make ElectroMechanicsProblemDefinition::Validate pass
//The following lines are not relevant to this test but need to be there
TetrahedralMesh<2,2>* p_fine_mesh = new TetrahedralMesh<2,2>();//unused in this test
p_fine_mesh->ConstructRegularSlabMesh(0.25, 1.0, 1.0);
TetrahedralMesh<2,2>* p_coarse_mesh = new TetrahedralMesh<2,2>();//unused in this test
p_coarse_mesh->ConstructRegularSlabMesh(0.25, 1.0, 1.0);
FineCoarseMeshPair<2>* p_pair = new FineCoarseMeshPair<2>(*p_fine_mesh, *p_coarse_mesh);//also unused in this test
p_pair->SetUpBoxesOnFineMesh();
/////////////////////////////////////////////////////////////////////
// NONPHYSIOL 1 - contraction model is of the form sin(t)
IncompressibleExplicitSolver2d expl_solver(mesh,problem_defn,""/*"TestCompareExplAndImplCardiacSolvers_Exp"*/);
p_pair->ComputeFineElementsAndWeightsForCoarseQuadPoints(*(expl_solver.GetQuadratureRule()), false);
p_pair->DeleteFineBoxCollection();
expl_solver.SetFineCoarseMeshPair(p_pair);
expl_solver.Initialise();
IncompressibleImplicitSolver2d impl_solver(mesh,problem_defn,""/*"TestCompareExplAndImplCardiacSolvers_Imp"*/);
impl_solver.SetFineCoarseMeshPair(p_pair);
impl_solver.Initialise();
double dt = 0.25;
for(double t=0; t<3; t+=dt)
{
expl_solver.Solve(t,t+dt,dt);
impl_solver.Solve(t,t+dt,dt);
// computations should be identical
TS_ASSERT_EQUALS(expl_solver.GetNumNewtonIterations(), impl_solver.GetNumNewtonIterations());
for(unsigned i=0; i<mesh.GetNumNodes(); i++)
{
TS_ASSERT_DELTA(expl_solver.rGetDeformedPosition()[i](0), impl_solver.rGetDeformedPosition()[i](0), 1e-9);
TS_ASSERT_DELTA(expl_solver.rGetDeformedPosition()[i](1), impl_solver.rGetDeformedPosition()[i](1), 1e-9);
}
}
//in need of deletion even if all these 3 have no influence at all on this test
delete p_fine_mesh;
delete p_coarse_mesh;
delete p_pair;
}
void TestWithSimpleContractionModel() throw(Exception)
{
QuadraticMesh<2> mesh(0.25, 1.0, 1.0);
MooneyRivlinMaterialLaw<2> law(1);
std::vector<unsigned> fixed_nodes
= NonlinearElasticityTools<2>::GetNodesByComponentValue(mesh,0,0.0);
ElectroMechanicsProblemDefinition<2> problem_defn(mesh);
problem_defn.SetMaterialLaw(INCOMPRESSIBLE,&law);
problem_defn.SetZeroDisplacementNodes(fixed_nodes);
problem_defn.SetContractionModel(NONPHYSIOL1,0.01);
problem_defn.SetMechanicsSolveTimestep(0.01); //This is only set to make ElectroMechanicsProblemDefinition::Validate pass
// NONPHYSIOL1 => NonphysiologicalContractionModel 1
IncompressibleExplicitSolver2d solver(mesh,problem_defn,"TestExplicitCardiacMech");
//The following lines are not relevant to this test but need to be there
TetrahedralMesh<2,2>* p_fine_mesh = new TetrahedralMesh<2,2>();//unused in this test
p_fine_mesh->ConstructRegularSlabMesh(0.25, 1.0, 1.0);
TetrahedralMesh<2,2>* p_coarse_mesh = new TetrahedralMesh<2,2>();//unused in this test
p_coarse_mesh->ConstructRegularSlabMesh(0.25, 1.0, 1.0);
FineCoarseMeshPair<2>* p_pair = new FineCoarseMeshPair<2>(*p_fine_mesh, *p_coarse_mesh);//also unused in this test
p_pair->SetUpBoxesOnFineMesh();
p_pair->ComputeFineElementsAndWeightsForCoarseQuadPoints(*(solver.GetQuadratureRule()), false);
p_pair->DeleteFineBoxCollection();
solver.SetFineCoarseMeshPair(p_pair);
///////////////////////////////////////////////////////////////////////////
solver.Initialise();
// coverage
QuadraturePointsGroup<2> quad_points(mesh, *(solver.GetQuadratureRule()));
std::vector<double> calcium_conc(solver.GetTotalNumQuadPoints(), 0.0);
std::vector<double> voltages(solver.GetTotalNumQuadPoints(), 0.0);
solver.SetCalciumAndVoltage(calcium_conc, voltages);
// solve UP TO t=0. So Ta(lam_n,t_{n+1})=5*sin(0)=0, ie no deformation
solver.Solve(-0.01,0.0,0.01);
TS_ASSERT_EQUALS(solver.GetNumNewtonIterations(),0u);
solver.Solve(0.24,0.25,0.01);
TS_ASSERT_DELTA(solver.rGetDeformedPosition()[4](0), 0.9732, 1e-2);
TS_ASSERT_DELTA(solver.rGetDeformedPosition()[4](1), -0.0156, 1e-2);
//in need of deletion even if all these 3 have no influence at all on this test
delete p_fine_mesh;
delete p_coarse_mesh;
delete p_pair;
}
/* == Sliding boundary conditions ==
*
* It is common to require a Dirichlet boundary condition where the displacement/position in one dimension
* is fixed, but the displacement/position in the others are free. This can be easily done when
* collecting the new locations for the fixed nodes, as shown in the following example. Here, we
* take a unit square, apply gravity downward, and suppose the Y=0 surface is like a frictionless boundary,
* so that, for the nodes on Y=0, we specify y=0 but leave x free (Here (X,Y)=old position, (x,y)=new position).
* (Note though that this wouldn't be enough to uniquely specify the final solution - an arbitrary
* translation in the Y direction could be added a solution to obtain another valid solution, so we
* fully fix the node at the origin.)
*/
void TestWithSlidingDirichletBoundaryConditions() throw(Exception)
{
QuadraticMesh<2> mesh;
mesh.ConstructRegularSlabMesh(0.1 /*stepsize*/, 1.0 /*width*/, 1.0 /*height*/);
ExponentialMaterialLaw<2> law(1.0, 0.5); // First parameter is 'a', second 'b', in W=a*exp(b(I1-3))
/* Create fixed nodes and locations... */
std::vector<unsigned> fixed_nodes;
std::vector<c_vector<double,2> > locations;
/* Fix node 0 (the node at the origin) */
fixed_nodes.push_back(0);
locations.push_back(zero_vector<double>(2));
/* For the rest, if the node is on the Y=0 surface.. */
for (unsigned i=1; i<mesh.GetNumNodes(); i++)
{
if ( fabs(mesh.GetNode(i)->rGetLocation()[1])<1e-6)
{
/* ..add it to the list of fixed nodes.. */
fixed_nodes.push_back(i);
/* ..and define y to be 0 but x is fixed */
c_vector<double,2> new_location;
new_location(0) = SolidMechanicsProblemDefinition<2>::FREE;
new_location(1) = 0.0;
locations.push_back(new_location);
}
}
/* Set the material law and fixed nodes, add some gravity, and solve */
SolidMechanicsProblemDefinition<2> problem_defn(mesh);
problem_defn.SetMaterialLaw(INCOMPRESSIBLE,&law);
problem_defn.SetFixedNodes(fixed_nodes, locations);
c_vector<double,2> gravity = zero_vector<double>(2);
gravity(1) = -0.5;
problem_defn.SetBodyForce(gravity);
IncompressibleNonlinearElasticitySolver<2> solver(mesh,
problem_defn,
"ElasticitySlidingBcsExample");
solver.Solve();
solver.CreateCmguiOutput();
/* Check the node at (1,0) has moved but has stayed on Y=0 */
TS_ASSERT_LESS_THAN(1.0, solver.rGetDeformedPosition()[10](0));
TS_ASSERT_DELTA(solver.rGetDeformedPosition()[10](1), 0.0, 1e-3);
}
// Update the coefficients associated with the patch field
void cohesiveLawFvPatchVectorField::updateCoeffs()
{
if (updated())
{
return;
}
// Looking up rheology
const fvPatchField<scalar>& mu =
patch().lookupPatchField<volScalarField, scalar>("mu");
const fvPatchField<scalar>& lambda =
patch().lookupPatchField<volScalarField, scalar>("lambda");
vectorField n = patch().nf();
const fvPatchField<tensor>& gradU =
patch().lookupPatchField<volTensorField, tensor>("grad(U)");
// Patch displacement
const vectorField& U = *this;
// Patch stress
tensorField sigma = mu*(gradU + gradU.T()) + I*(lambda*tr(gradU));
// Normal stress component
scalarField sigmaN = (n & (n & sigma));
scalarField delta = -(n & U);
label sizeByTwo = patch().size()/2;
for(label i = 0; i < sizeByTwo; i++)
{
scalar tmp = delta[i];
delta[i] += delta[sizeByTwo + i];
delta[sizeByTwo + i] += tmp;
}
forAll (traction_, faceI)
{
if (delta[faceI] < 0)
{
// Return from traction to symmetryPlane??
traction_[faceI] = law().sigmaMax().value()*n[faceI];
}
else if(delta[faceI] > law().deltaC().value())
{
// Traction free
traction_[faceI] = vector::zero;
}
else
{
// Calculate cohesive traction from cohesive zone model
traction_[faceI] = law().traction(delta[faceI])*n[faceI];
}
}
gradient() =
(
traction_
- (n & (mu*gradU.T() - (mu + lambda)*gradU))
- n*lambda*tr(gradU)
)/(2.0*mu + lambda);
fixedGradientFvPatchVectorField::updateCoeffs();
}
/* == Incompressible deformation: non-zero displacement boundary conditions, functional tractions ==
*
* We now consider a more complicated example. We prescribe particular new locations for the nodes
* on the Dirichlet boundary, and also show how to prescribe a traction that is given in functional form
* rather than prescribed for each boundary element.
*/
void TestIncompressibleProblemMoreComplicatedExample() throw(Exception)
{
/* Create a mesh */
QuadraticMesh<2> mesh;
mesh.ConstructRegularSlabMesh(0.1 /*stepsize*/, 1.0 /*width*/, 1.0 /*height*/);
/* Use a different material law this time, an exponential material law.
* The material law needs to inherit from `AbstractIncompressibleMaterialLaw`,
* and there are a few implemented, see `continuum_mechanics/src/problem/material_laws` */
ExponentialMaterialLaw<2> law(1.0, 0.5); // First parameter is 'a', second 'b', in W=a*exp(b(I1-3))
/* Now specify the fixed nodes, and their new locations. Create `std::vector`s for each. */
std::vector<unsigned> fixed_nodes;
std::vector<c_vector<double,2> > locations;
/* Loop over the mesh nodes */
for (unsigned i=0; i<mesh.GetNumNodes(); i++)
{
/* If the node is on the Y=0 surface (the LHS) */
if ( fabs(mesh.GetNode(i)->rGetLocation()[1])<1e-6)
{
/* Add it to the list of fixed nodes */
fixed_nodes.push_back(i);
/* and define a new position x=(X,0.1*X^2^) */
c_vector<double,2> new_location;
double X = mesh.GetNode(i)->rGetLocation()[0];
new_location(0) = X;
new_location(1) = 0.1*X*X;
locations.push_back(new_location);
}
}
/* Now collect all the boundary elements on the top surface, as before, except
* here we don't create the tractions for each element
*/
std::vector<BoundaryElement<1,2>*> boundary_elems;
for (TetrahedralMesh<2,2>::BoundaryElementIterator iter = mesh.GetBoundaryElementIteratorBegin();
iter != mesh.GetBoundaryElementIteratorEnd();
++iter)
{
/* If Y=1, have found a boundary element */
if (fabs((*iter)->CalculateCentroid()[1] - 1.0)<1e-6)
{
BoundaryElement<1,2>* p_element = *iter;
boundary_elems.push_back(p_element);
}
}
/* Create a problem definition object, and this time calling `SetFixedNodes`
* which takes in the new locations of the fixed nodes.
*/
SolidMechanicsProblemDefinition<2> problem_defn(mesh);
problem_defn.SetMaterialLaw(INCOMPRESSIBLE,&law);
problem_defn.SetFixedNodes(fixed_nodes, locations);
/* Now call `SetTractionBoundaryConditions`, which takes in a vector of
* boundary elements as in the previous test. However this time the second argument
* is a ''function pointer'' (just the name of the function) to a
* function returning traction in terms of position (and time [see below]).
* This function is defined above, before the tests. It has to take in a `c_vector` (position)
* and a double (time), and returns a `c_vector` (traction), and will only be called
* using points in the boundary elements being passed in. The function `MyTraction`
* (defined above, before the tests) above defines a horizontal traction (ie a shear stress, since it is
* applied to the top surface) which increases in magnitude across the object.
*/
problem_defn.SetTractionBoundaryConditions(boundary_elems, MyTraction);
/* Note: You can also call `problem_defn.SetBodyForce(MyBodyForce)`, passing in a function
* instead of a vector, although isn't really physically useful, it is only really useful
* for constructing problems with exact solutions.
*
* Create the solver as before */
IncompressibleNonlinearElasticitySolver<2> solver(mesh,
problem_defn,
"IncompressibleElasticityMoreComplicatedExample");
/* Call `Solve()` */
solver.Solve();
/* Another quick check */
TS_ASSERT_EQUALS(solver.GetNumNewtonIterations(), 6u);
/* Visualise as before.
*
* '''Advanced:''' Note that the function `MyTraction` takes in time, which it didn't use. In the above it would have been called
* with t=0. The current time can be set using `SetCurrentTime()`. The idea is that the user may want to solve a
* sequence of static problems with time-dependent tractions (say), for which they should allow `MyTraction` to
* depend on time, and put the solve inside a time-loop, for example:
*/
//for (double t=0; t<T; t+=dt)
//{
// solver.SetCurrentTime(t);
// solver.Solve();
//}
/* In this the current time would be passed through to `MyTraction`
*
* Create Cmgui output
*/
solver.CreateCmguiOutput();
/* This is just to check that nothing has been accidentally changed in this test */
TS_ASSERT_DELTA(solver.rGetDeformedPosition()[98](0), 1.4543, 1e-3);
TS_ASSERT_DELTA(solver.rGetDeformedPosition()[98](1), 0.5638, 1e-3);
}
/* == Compressible deformation, and other bits and pieces ==
*
* In this test, we will show the (very minor) changes required to solve a compressible nonlinear
* elasticity problem, we will describe and show how to specify 'pressure on deformed body'
* boundary conditions, we illustrate how a quadratic mesh can be generated using a linear mesh
* input files, and we also illustrate how `Solve()` can be called repeatedly, with loading
* changing between the solves.
*
* Note: for other examples of compressible solves, including problems with an exact solution, see the
* file `continuum_mechanics/test/TestCompressibleNonlinearElasticitySolver.hpp`
*/
void TestSolvingCompressibleProblem() throw (Exception)
{
/* All mechanics problems must take in quadratic meshes, but the mesh files for
* (standard) linear meshes in Triangles/Tetgen can be automatically converted
* to quadratic meshes, by simply doing the following. (The mesh loaded here is a disk
* centred at the origin with radius 1).
*/
QuadraticMesh<2> mesh;
TrianglesMeshReader<2,2> reader("mesh/test/data/disk_522_elements");
mesh.ConstructFromLinearMeshReader(reader);
/* Compressible problems require a compressible material law, ie one that
* inherits from `AbstractCompressibleMaterialLaw`. The `CompressibleMooneyRivlinMaterialLaw`
* is one such example; instantiate one of these
*/
CompressibleMooneyRivlinMaterialLaw<2> law(1.0, 0.5);
/* For this problem, we fix the nodes on the surface for which Y < -0.9 */
std::vector<unsigned> fixed_nodes;
for ( TetrahedralMesh<2,2>::BoundaryNodeIterator iter = mesh.GetBoundaryNodeIteratorBegin();
iter != mesh.GetBoundaryNodeIteratorEnd();
++iter)
{
double Y = (*iter)->rGetLocation()[1];
if(Y < -0.9)
{
fixed_nodes.push_back((*iter)->GetIndex());
}
}
/* We will (later) apply Neumann boundary conditions to surface elements which lie below Y=0,
* and these are collected here. (Minor, subtle, comment: we don't bother here checking Y>-0.9,
* so the surface elements collected here include the ones on the Dirichlet boundary. This doesn't
* matter as the Dirichlet boundary conditions to the nonlinear system essentially overwrite
* an Neumann-related effects).
*/
std::vector<BoundaryElement<1,2>*> boundary_elems;
for (TetrahedralMesh<2,2>::BoundaryElementIterator iter
= mesh.GetBoundaryElementIteratorBegin();
iter != mesh.GetBoundaryElementIteratorEnd();
++iter)
{
BoundaryElement<1,2>* p_element = *iter;
if(p_element->CalculateCentroid()[1]<0.0)
{
boundary_elems.push_back(p_element);
}
}
assert(boundary_elems.size()>0);
/* Create the problem definition class, and set the law again, this time
* stating that the law is compressible
*/
SolidMechanicsProblemDefinition<2> problem_defn(mesh);
problem_defn.SetMaterialLaw(COMPRESSIBLE,&law);
/* Set the fixed nodes and gravity */
problem_defn.SetZeroDisplacementNodes(fixed_nodes);
/* The elasticity solvers have two nonlinear solvers implemented, one hand-coded and one which uses PETSc's SNES
* solver. The latter is not the default but can be more robust (and will probably be the default in later
* versions). This is how it can be used. (This option can also be called if the compiled binary is run from
* the command line (see ChasteGuides/RunningBinariesFromCommandLine) using the option "-mech_use_snes").
*/
problem_defn.SetSolveUsingSnes();
/* This line tells the solver to output info about the nonlinear solve as it progresses, and can be used with
* or without the SNES option above. The corresponding command line option is "-mech_verbose"
*/
problem_defn.SetVerboseDuringSolve();
c_vector<double,2> gravity;
gravity(0) = 0;
gravity(1) = 0.1;
problem_defn.SetBodyForce(gravity);
/* Declare the compressible solver, which has the same interface as the incompressible
* one, and call `Solve()`
*/
CompressibleNonlinearElasticitySolver<2> solver(mesh,
problem_defn,
"CompressibleSolidMechanicsExample");
solver.Solve();
/* Now we call add additional boundary conditions, and call `Solve() again. Firstly: these
* Neumann conditions here are not specified traction boundary conditions (such BCs are specified
* on the undeformed body), but instead, the (more natural) specification of a pressure
* exactly in the ''normal direction on the deformed body''. We have to provide a set of boundary
* elements of the mesh, and a pressure to act on those elements. The solver will automatically
* compute the deformed normal directions on which the pressure acts. Note: with this type of
* BC, the ordering of the nodes on the boundary elements needs to be consistent, otherwise some
* normals will be computed to be inward and others outward. The solver will check this on the
* original mesh and throw an exception if this is not the case. (The required ordering is such that:
* in 2D, surface element nodes are ordered anticlockwise (looking at the whole mesh); in 3D, looking
* at any surface element from outside the mesh, the three nodes are ordered anticlockwise. (Triangle/tetgen
* automatically create boundary elements like this)).
*/
double external_pressure = -0.4; // negative sign => inward pressure
problem_defn.SetApplyNormalPressureOnDeformedSurface(boundary_elems, external_pressure);
/* Call `Solve()` again, so now solving with fixed nodes, gravity, and pressure. The solution from
* the previous solve will be used as the initial guess. Although at the moment the solution from the
* previous call to `Solve()` will be over-written, calling `Solve()` repeatedly may be useful for
* some problems: sometimes, Newton's method will fail to converge for given force/pressures etc, and it can
* be (very) helpful to ''increment'' the loading. For example, set the gravity to be (0,-9.81/3), solve,
* then set it to be (0,-2*9.81/3), solve again, and finally set it to be (0,-9.81) and solve for a
* final time
*/
solver.Solve();
solver.CreateCmguiOutput();
}
/* == Incompressible deformation: 2D shape hanging under gravity with a balancing traction ==
*
* We now repeat the above test but include a traction on the bottom surface (Y=0). We apply this
* in the inward direction so that is counters (somewhat) the effect of gravity. We also show how stresses
* and strains can be written to file.
*/
void TestIncompressibleProblemWithTractions() throw(Exception)
{
/* All of this is exactly as above */
QuadraticMesh<2> mesh;
mesh.ConstructRegularSlabMesh(0.1 /*stepsize*/, 0.8 /*width*/, 1.0 /*height*/);
MooneyRivlinMaterialLaw<2> law(1.0);
c_vector<double,2> body_force;
body_force(0) = 0.0;
body_force(1) = -2.0;
std::vector<unsigned> fixed_nodes = NonlinearElasticityTools<2>::GetNodesByComponentValue(mesh, 1, 1.0);
/* Now the traction boundary conditions. We need to collect all the boundary elements on the surface which we want to
* apply non-zero tractions, put them in a `std::vector`, and create a corresponding `std::vector` of the tractions
* for each of the boundary elements. Note that the each traction is a 2D vector with dimensions of pressure.
*
* First, declare the data structures:
*/
std::vector<BoundaryElement<1,2>*> boundary_elems;
std::vector<c_vector<double,2> > tractions;
/* Create a constant traction */
c_vector<double,2> traction;
traction(0) = 0;
traction(1) = 1.0; // this choice of sign corresponds to an inward force (if applied to the bottom surface)
/* Loop over boundary elements */
for (TetrahedralMesh<2,2>::BoundaryElementIterator iter = mesh.GetBoundaryElementIteratorBegin();
iter != mesh.GetBoundaryElementIteratorEnd();
++iter)
{
/* If the centre of the element has Y value of 0.0, it is on the surface we need */
if (fabs((*iter)->CalculateCentroid()[1] - 0.0) < 1e-6)
{
/* Put the boundary element and the constant traction into the stores. */
BoundaryElement<1,2>* p_element = *iter;
boundary_elems.push_back(p_element);
tractions.push_back(traction);
}
}
/* A quick check */
assert(boundary_elems.size() == 8u);
/* Now create the problem definition object, setting the material law, fixed nodes and body force as
* before (this time not calling `SetDensity()`, so using the default density of 1.0,
* and also calling a method for setting tractions, which takes in the boundary elements
* and tractions for each of those elements.
*/
SolidMechanicsProblemDefinition<2> problem_defn(mesh);
problem_defn.SetMaterialLaw(INCOMPRESSIBLE,&law);
problem_defn.SetZeroDisplacementNodes(fixed_nodes);
problem_defn.SetBodyForce(body_force);
problem_defn.SetTractionBoundaryConditions(boundary_elems, tractions);
/* Create solver as before */
IncompressibleNonlinearElasticitySolver<2> solver(mesh,
problem_defn,
"IncompressibleElasticityWithTractionsTutorial");
/* In this test we also output the stress and strain. For the former, we have to tell the solver to store
* the stresses that are computed during the solve.
*/
solver.SetComputeAverageStressPerElementDuringSolve();
/* Call `Solve()` */
solver.Solve();
/* If VTK output is written (discussed above) strains can be visualised. Alternatively, we can create text files
* for strains and stresses by doing the following.
*
* Write the final deformation gradients to file. The i-th line of this file provides the deformation gradient F,
* written as 'F(0,0) F(0,1) F(1,0) F(1,1)', evaluated at the centroid of the i-th element. The first variable
* can also be DEFORMATION_TENSOR_C or LAGRANGE_STRAIN_E to write C or E. The second parameter is the file name.
*/
solver.WriteCurrentStrains(DEFORMATION_GRADIENT_F,"deformation_grad");
/* Since we called `SetComputeAverageStressPerElementDuringSolve`, we can write the stresses to file too. However,
* note that for each element this is not the stress evaluated at the centroid, but the mean average of the stresses
* evaluated at the quadrature points - for technical cardiac electromechanics reasons, it is difficult to
* define the stress at non-quadrature points.
*/
solver.WriteCurrentAverageElementStresses("2nd_PK_stress");
/* Another quick check */
TS_ASSERT_EQUALS(solver.GetNumNewtonIterations(), 4u);
/* Visualise as before by going to the output directory and doing
* `x=load('solution.nodes'); plot(x(:,1),x(:,2),'m*')` in Matlab/octave, or by using Cmgui.
* The effect of the traction should be clear (especially when compared to
* the results of the first test).
*
* Create Cmgui output
*/
solver.CreateCmguiOutput();
/* This is just to check that nothing has been accidentally changed in this test */
TS_ASSERT_DELTA(solver.rGetDeformedPosition()[8](0), 0.8561, 1e-3);
TS_ASSERT_DELTA(solver.rGetDeformedPosition()[8](1), 0.0310, 1e-3);
}
/* In the first test we use INCOMPRESSIBLE nonlinear elasticity. For incompressible elasticity, there
* is a constraint on the deformation, which results in a pressure field (a Lagrange multiplier)
* which is solved for together with the deformation.
*
* All the mechanics solvers solve for the deformation using the finite element method with QUADRATIC
* basis functions for the deformation. This necessitates the use of a `QuadraticMesh` - such meshes have
* extra nodes that aren't vertices of elements, in this case midway along each edge. (The displacement
* is solved for at ''each node'' in the mesh (including internal [non-vertex] nodes), whereas the pressure
* is only solved for at each vertex - in FEM terms, quadratic interpolation for displacement, linear
* interpolation for pressure, which is required for stability. The pressure at internal nodes is computed
* by linear interpolation).
*
*/
void TestSimpleIncompressibleProblem() throw(Exception)
{
/* First, define the geometry. This should be specified using the `QuadraticMesh` class, which inherits from `TetrahedralMesh`
* and has mostly the same interface. Here we define a 0.8 by 1 rectangle, with elements 0.1 wide.
* (`QuadraticMesh`s can also be read in using `TrianglesMeshReader`; see next tutorial/rest of code base for examples of this).
*/
QuadraticMesh<2> mesh;
mesh.ConstructRegularSlabMesh(0.1 /*stepsize*/, 0.8 /*width*/, 1.0 /*height*/);
/* We use a Mooney-Rivlin material law, which applies to isotropic materials and has two parameters.
* Restricted to 2D however, it only has one parameter, which can be thought of as the total
* stiffness. We declare a Mooney-Rivlin law, setting the parameter to 1.
*/
MooneyRivlinMaterialLaw<2> law(1.0);
/* Next, the body force density. In realistic problems this will either be
* acceleration due to gravity (ie b=(0,-9.81)) or zero if the effect of gravity can be neglected.
* In this problem we apply a gravity-like downward force.
*/
c_vector<double,2> body_force;
body_force(0) = 0.0;
body_force(1) = -2.0;
/* Two types of boundary condition are required: displacement and traction. As with the other PDE solvers,
* the displacement (Dirichlet) boundary conditions are specified at nodes, whereas traction (Neumann) boundary
* conditions are specified on boundary elements.
*
* In this test we apply displacement boundary conditions on one surface of the mesh, the upper (Y=1.0) surface.
* We are going to specify zero-displacement at these nodes.
* We do not specify any traction boundary conditions, which means that (effectively) zero-traction boundary
* conditions (ie zero pressures) are applied on the three other surfaces.
*
* We need to get a `std::vector` of all the node indices that we want to fix. The `NonlinearElasticityTools`
* has a static method for helping do this: the following gets all the nodes for which Y=1.0. The second
* argument (the '1') indicates Y . (So, for example, `GetNodesByComponentValue(mesh, 0, 10)` would get the nodes on X=10).
*/
std::vector<unsigned> fixed_nodes = NonlinearElasticityTools<2>::GetNodesByComponentValue(mesh, 1, 1.0);
/*
* Before creating the solver we create a `SolidMechanicsProblemDefinition` object, which contains
* everything that defines the problem: mesh, material law, body force,
* the fixed nodes and their locations, any traction boundary conditions, and the density
* (which multiplies the body force, otherwise isn't used).
*/
SolidMechanicsProblemDefinition<2> problem_defn(mesh);
/* Set the material problem on the problem definition object, saying that the problem, and
* the material law, is incompressible. All material law files can be found in
* `continuum_mechanics/src/problem/material_laws`. */
problem_defn.SetMaterialLaw(INCOMPRESSIBLE,&law);
/* Set the fixed nodes, choosing zero displacement for these nodes (see later for how
* to provide locations for the fixed nodes). */
problem_defn.SetZeroDisplacementNodes(fixed_nodes);
/* Set the body force and the density. (Note that the second line isn't technically
* needed, as internally the density is initialised to 1)
*/
problem_defn.SetBodyForce(body_force);
problem_defn.SetDensity(1.0);
/* Now we create the (incompressible) solver, passing in the mesh, problem definition
* and output directory
*/
IncompressibleNonlinearElasticitySolver<2> solver(mesh,
problem_defn,
"SimpleIncompressibleElasticityTutorial");
/* .. and to compute the solution, just call `Solve()` */
solver.Solve();
/* '''Visualisation'''. Go to the folder `SimpleIncompressibleElasticityTutorial` in your test-output directory.
* There should be 2 files, initial.nodes and solution.nodes. These are the original nodal positions and the deformed
* positions. Each file has two columns, the x and y locations of each node. To visualise the solution in say
* Matlab or Octave, you could do: `x=load('solution.nodes'); plot(x(:,1),x(:,2),'k*')`. For Cmgui output, see below.
*
* To get the actual solution from the solver, use these two methods. Note that the first
* gets the deformed position (ie the new location, not the displacement). They are both of size
* num_total_nodes.
*/
std::vector<c_vector<double,2> >& r_deformed_positions = solver.rGetDeformedPosition();
std::vector<double>& r_pressures = solver.rGetPressures();
/* Let us obtain the values of the new position, and the pressure, at the bottom right corner node. */
unsigned node_index = 8;
assert( fabs(mesh.GetNode(node_index)->rGetLocation()[0] - 0.8) < 1e-6); // check that X=0.8, ie that we have the correct node,
assert( fabs(mesh.GetNode(node_index)->rGetLocation()[1] - 0.0) < 1e-6); // check that Y=0.0, ie that we have the correct node,
std::cout << "New position: " << r_deformed_positions[node_index](0) << " " << r_deformed_positions[node_index](1) << "\n";
std::cout << "Pressure: " << r_pressures[node_index] << "\n";
/* HOW_TO_TAG Continuum mechanics
* Visualise nonlinear elasticity problems solutions, including visualisng strains
*/
/* One visualiser is Cmgui. This method can be used to convert all the output files to Cmgui format.
* They are placed in `[OUTPUT_DIRECTORY]/cmgui`. A script is created to easily load the data: in a
* terminal cd to this directory and call `cmgui LoadSolutions.com`. (In this directory, the initial position is given by
* solution_0.exnode, the deformed by solution_1.exnode).
*/
solver.CreateCmguiOutput();
/* The recommended visualiser is Paraview, for which Chaste must be installed with VTK. With paraview, strains (and in the future
* stresses) can be visualised on the undeformed/deformed geometry). We can create VTK output using
* the `VtkNonlinearElasticitySolutionWriter` class. The undeformed geometry, solution displacement, and pressure (if incompressible
* problem) are written to file, and below we also choose to write the deformation tensor C for each element.
*/
VtkNonlinearElasticitySolutionWriter<2> vtk_writer(solver);
vtk_writer.SetWriteElementWiseStrains(DEFORMATION_TENSOR_C); // other options are DEFORMATION_GRADIENT_F and LAGRANGE_STRAIN_E
vtk_writer.Write();
/* These are just to check that nothing has been accidentally changed in this test.
* Newton's method (with damping) was used to solve the nonlinear problem, and we check that
* 4 iterations were needed to converge.
*/
TS_ASSERT_DELTA(r_deformed_positions[node_index](0), 0.7980, 1e-3);
TS_ASSERT_DELTA(r_deformed_positions[node_index](1), -0.1129, 1e-3);
TS_ASSERT_EQUALS(solver.GetNumNewtonIterations(), 4u);
}
// Solve a problem where some pressure is applied in the outward direction on the bottom (Z=0) surface
//
// Returns the number of newton iterations taken
unsigned SolvePressureOnUnderside(QuadraticMesh<3>& rMesh, std::string outputDirectory,
std::vector<double>& rSolution,
bool useSolutionAsGuess,
double scaleFactor = 1.0)
{
MooneyRivlinMaterialLaw<3> law(1.0, 0.0);
std::vector<unsigned> fixed_nodes = NonlinearElasticityTools<3>::GetNodesByComponentValue(rMesh, 0, 0.0);
std::vector<BoundaryElement<2,3>*> boundary_elems;
double pressure = 0.001;
for (TetrahedralMesh<3,3>::BoundaryElementIterator iter
= rMesh.GetBoundaryElementIteratorBegin();
iter != rMesh.GetBoundaryElementIteratorEnd();
++iter)
{
BoundaryElement<2,3>* p_element = *iter;
double Z = p_element->CalculateCentroid()[2];
if(fabs(Z)<1e-6)
{
boundary_elems.push_back(p_element);
}
}
SolidMechanicsProblemDefinition<3> problem_defn(rMesh);
problem_defn.SetMaterialLaw(INCOMPRESSIBLE,&law);
problem_defn.SetZeroDisplacementNodes(fixed_nodes);
problem_defn.SetApplyNormalPressureOnDeformedSurface(boundary_elems, pressure*scaleFactor);
problem_defn.SetVerboseDuringSolve();
IncompressibleNonlinearElasticitySolver<3> solver(rMesh,problem_defn,outputDirectory);
solver.SetWriteOutputEachNewtonIteration();
// cover the SetTakeFullFirstNewtonStep() method, and the SetUsePetscDirectSolve() method
solver.SetTakeFullFirstNewtonStep();
solver.SetUsePetscDirectSolve();
if(useSolutionAsGuess)
{
if(solver.rGetCurrentSolution().size()!=rSolution.size())
{
EXCEPTION("Badly-sized input");
}
for(unsigned i=0; i<rSolution.size(); i++)
{
solver.rGetCurrentSolution()[i] = rSolution[i];
}
}
if(scaleFactor < 1.0)
{
try
{
solver.Solve();
}
catch (Exception& e)
{
// not final Solve, so don't quit
WARNING(e.GetMessage());
}
}
else
{
solver.Solve();
solver.CreateCmguiOutput();
VtkNonlinearElasticitySolutionWriter<3> vtk_writer(solver);
vtk_writer.SetWriteElementWiseStrains(DEFORMATION_TENSOR_C);
vtk_writer.Write();
}
rSolution.clear();
rSolution.resize(solver.rGetCurrentSolution().size());
for(unsigned i=0; i<rSolution.size(); i++)
{
rSolution[i] = solver.rGetCurrentSolution()[i];
}
return solver.GetNumNewtonIterations();
}
// cover all other contraction model options which are allowed but not been used in a test so far
void TestCoverage() throw(Exception)
{
QuadraticMesh<2> mesh(1.0, 1.0, 1.0);
MooneyRivlinMaterialLaw<2> law(1);
std::vector<unsigned> fixed_nodes
= NonlinearElasticityTools<2>::GetNodesByComponentValue(mesh,0,0.0);
ElectroMechanicsProblemDefinition<2> problem_defn(mesh);
problem_defn.SetMaterialLaw(INCOMPRESSIBLE,&law);
problem_defn.SetZeroDisplacementNodes(fixed_nodes);
problem_defn.SetContractionModel(NONPHYSIOL3,0.01);
problem_defn.SetMechanicsSolveTimestep(0.01); //This is only set to make ElectroMechanicsProblemDefinition::Validate pass
TS_ASSERT_THROWS_THIS(problem_defn.SetApplyAnisotropicCrossFibreTension(true,1.0,1.0),
"You can only apply anisotropic cross fibre tensions in a 3D simulation.");
TetrahedralMesh<2,2>* p_fine_mesh = new TetrahedralMesh<2,2>();
p_fine_mesh->ConstructRegularSlabMesh(1.0, 1.0, 1.0);
TetrahedralMesh<2,2>* p_coarse_mesh = new TetrahedralMesh<2,2>();
p_coarse_mesh->ConstructRegularSlabMesh(1.0, 1.0, 1.0);
FineCoarseMeshPair<2>* p_pair = new FineCoarseMeshPair<2>(*p_fine_mesh, *p_coarse_mesh);
p_pair->SetUpBoxesOnFineMesh();
TetrahedralMesh<2,2>* p_coarse_mesh_big = new TetrahedralMesh<2,2>();
p_coarse_mesh_big->ConstructRegularSlabMesh(1.0, 3.0, 3.0);
FineCoarseMeshPair<2>* p_pair_wrong = new FineCoarseMeshPair<2>(*p_fine_mesh, *p_coarse_mesh_big);
// Some strange memory thing happens if we don't have the test with the
// exceptions below in a separate block. I have no idea why.
{
IncompressibleExplicitSolver2d expl_solver(mesh,problem_defn,"");
p_pair->ComputeFineElementsAndWeightsForCoarseQuadPoints(*(expl_solver.GetQuadratureRule()), false);
p_pair->DeleteFineBoxCollection();
expl_solver.SetFineCoarseMeshPair(p_pair);
expl_solver.Initialise();
// Prevent an assertion being thrown about setting the cell factory more than once.
delete problem_defn.mpContractionCellFactory;
problem_defn.mpContractionCellFactory = NULL;
problem_defn.SetContractionModel(NASH2004,0.01);
IncompressibleExplicitSolver2d expl_solver_with_nash(mesh,problem_defn,"");
expl_solver_with_nash.SetFineCoarseMeshPair(p_pair);
expl_solver_with_nash.Initialise();
// Prevent an assertion being thrown about setting the cell factory more than once.
delete problem_defn.mpContractionCellFactory;
problem_defn.mpContractionCellFactory = NULL;
problem_defn.SetContractionModel(KERCHOFFS2003,0.01);
IncompressibleExplicitSolver2d expl_solver_with_kerchoffs(mesh,problem_defn,"");
expl_solver_with_kerchoffs.SetFineCoarseMeshPair(p_pair);
expl_solver_with_kerchoffs.Initialise();
}
{
// bad contraction model
ElectroMechanicsProblemDefinition<2> problem_defn2(mesh);
problem_defn2.SetMaterialLaw(INCOMPRESSIBLE,&law);
problem_defn2.SetContractionModel(NHS,0.01);
IncompressibleExplicitSolver2d solver(mesh,problem_defn2,"");
TS_ASSERT_THROWS_THIS(solver.SetFineCoarseMeshPair(p_pair_wrong),
"When setting a mesh pair into the solver, the coarse mesh of the mesh pair must be the same as the quadratic mesh");
solver.SetFineCoarseMeshPair(p_pair);
TS_ASSERT_THROWS_THIS(solver.Initialise(),
"stretch-rate-dependent contraction model requires an IMPLICIT cardiac mechanics solver.");
}
delete p_fine_mesh;
delete p_coarse_mesh;
delete p_pair;
delete p_coarse_mesh_big;
delete p_pair_wrong;
}
// with stretch-dependent contraction models the implicit and explicit schemes can be similar
void TestCompareImplicitAndExplicitWithStretchDependentContractionModel() throw(Exception)
{
QuadraticMesh<2> mesh(0.25, 1.0, 1.0);
MooneyRivlinMaterialLaw<2> law(1);
std::vector<unsigned> fixed_nodes
= NonlinearElasticityTools<2>::GetNodesByComponentValue(mesh,0,0.0);
ElectroMechanicsProblemDefinition<2> problem_defn(mesh);
problem_defn.SetMaterialLaw(INCOMPRESSIBLE,&law);
problem_defn.SetZeroDisplacementNodes(fixed_nodes);
problem_defn.SetContractionModel(NONPHYSIOL2,0.01);
problem_defn.SetMechanicsSolveTimestep(0.01); //This is only set to make ElectroMechanicsProblemDefinition::Validate pass
//The following lines are not relevant to this test but need to be there
TetrahedralMesh<2,2>* p_fine_mesh = new TetrahedralMesh<2,2>();//unused in this test
p_fine_mesh->ConstructRegularSlabMesh(0.25, 1.0, 1.0);
TetrahedralMesh<2,2>* p_coarse_mesh = new TetrahedralMesh<2,2>();//unused in this test
p_coarse_mesh->ConstructRegularSlabMesh(0.25, 1.0, 1.0);
FineCoarseMeshPair<2>* p_pair = new FineCoarseMeshPair<2>(*p_fine_mesh, *p_coarse_mesh);//also unused in this test
p_pair->SetUpBoxesOnFineMesh();
/////////////////////////////////////////////////////////////////////
// NONPHYSIOL 2 - contraction model is of the form lam*sin(t)
IncompressibleExplicitSolver2d expl_solver(mesh,problem_defn,"TestCompareExplAndImplCardiacSolversStretch_Exp");
p_pair->ComputeFineElementsAndWeightsForCoarseQuadPoints(*(expl_solver.GetQuadratureRule()), false);
p_pair->DeleteFineBoxCollection();
expl_solver.SetFineCoarseMeshPair(p_pair);
expl_solver.Initialise();
IncompressibleImplicitSolver2d impl_solver(mesh,problem_defn,"TestCompareExplAndImplCardiacSolversStretch_Imp");
impl_solver.SetFineCoarseMeshPair(p_pair);
impl_solver.Initialise();
expl_solver.WriteCurrentSpatialSolution("solution","nodes",0);
impl_solver.WriteCurrentSpatialSolution("solution","nodes",0);
unsigned counter = 1;
double t0 = 0.0;
double t1 = 0.25; // to be quite quick (min stretch ~=0.88), make this 5/4 (?) say for min stretch < 0.7
double dt = 0.025;
for(double t=t0; t<t1; t+=dt)
{
//std::cout << "\n **** t = " << t << " ****\n" << std::flush;
expl_solver.SetWriteOutput(false);
expl_solver.Solve(t,t+dt,dt);
expl_solver.SetWriteOutput();
expl_solver.WriteCurrentSpatialSolution("solution","nodes",counter);
impl_solver.SetWriteOutput(false);
impl_solver.Solve(t,t+dt,dt);
impl_solver.SetWriteOutput();
impl_solver.WriteCurrentSpatialSolution("solution","nodes",counter);
// the solutions turn out to be very close to each other
for(unsigned i=0; i<mesh.GetNumNodes(); i++)
{
TS_ASSERT_DELTA(expl_solver.rGetDeformedPosition()[i](0), impl_solver.rGetDeformedPosition()[i](0), 2e-3);
TS_ASSERT_DELTA(expl_solver.rGetDeformedPosition()[i](1), impl_solver.rGetDeformedPosition()[i](1), 2e-3);
}
// visualisation in matlab or octave
// run from CHASTETESTOUTPUT
//
// close all; figure; hold on
// for i=0:10, x1 = load(['TestCompareExplAndImplCardiacSolversStretch_Exp/solution_',num2str(i),'.nodes']); plot(i,x1(5,1),'b*'); end
// for i=0:10, x2 = load(['TestCompareExplAndImplCardiacSolversStretch_Imp/solution_',num2str(i),'.nodes']); plot(i,x2(5,1),'r*'); end
//
// close all; figure; hold on
// for i=0:10, x2 = load(['TestCompareExplAndImplCardiacSolversStretch_Imp/solution_',num2str(i),'.nodes']); plot(x2(:,1),x2(:,2),'r*'); end
counter++;
}
// check there was significant deformation - node 4 is (1,0)
TS_ASSERT_DELTA(mesh.GetNode(4)->rGetLocation()[0], 1.0, 1e-12);
TS_ASSERT_LESS_THAN(impl_solver.rGetDeformedPosition()[4](0), 0.9);
//in need of deletion even if all these 3 have no influence at all on this test
delete p_fine_mesh;
delete p_coarse_mesh;
delete p_pair;
}
/**
* Solve a problem in which the traction boundary condition is a normal pressure
* applied to a surface of the deformed body.
*
* The initial body is the unit cube. The deformation is given by x=Rx', where
* R is a rotation matrix and x'=[X/(lambda^2) lambda*Y lambda*Z], ie simple stretching
* followed by a rotation.
*
* Ignoring R for the time being, the deformation gradient would be
* F=diag(1/lambda^2, lambda, lambda).
* Assuming a Neo-Hookean material law, the first Piola-Kirchoff tensor is
*
* S = 2c F^T - p F^{-1}
* = diag ( 2c lam^{-2} - p lam^2, 2c lam - p lam^{-1}, 2c lam - p lam^{-1}
*
* We choose the internal pressure (p) to be 2clam^2, so that
*
* S = diag( 2c (lam^{-2} - lam^4), 0, 0)
*
* To obtain this deformation as the solution, we can specify fixed location boundary conditions
* on X=0 and specify a traction of t=[2c(lam^{-2} - lam^4) 0 0] on the X=1 surface.
*
* Now, including the rotation matrix, we can specify appropriate fixed location boundary conditions
* on the X=0 surface, and specify that a normal pressure should act on the *deformed* X=1 surface,
* with value P = 2c(lam^{-2} - lam^4)/(lambda^2) [divided by lambda^2 as the deformed surface
* has a smaller area than the undeformed surface.
*
*/
void TestWithPressureOnDeformedSurfaceBoundaryCondition3d() throw (Exception)
{
double lambda = 0.85;
unsigned num_elem_each_dir = 5;
QuadraticMesh<3> mesh(1.0/num_elem_each_dir, 1.0, 1.0, 1.0);
// Neo-Hookean material law
double c1 = 1.0;
MooneyRivlinMaterialLaw<3> law(c1, 0.0);
// anything will do here
c_matrix<double,3,3> rotation_matrix = identity_matrix<double>(3);
rotation_matrix(0,0)=1.0/sqrt(2.0);
rotation_matrix(0,1)=-1.0/sqrt(2.0);
rotation_matrix(1,0)=1.0/sqrt(2.0);
rotation_matrix(1,1)=1.0/sqrt(2.0);
// Define displacement boundary conditions
std::vector<unsigned> fixed_nodes;
std::vector<c_vector<double,3> > locations;
for (unsigned i=0; i<mesh.GetNumNodes(); i++)
{
double X = mesh.GetNode(i)->rGetLocation()[0];
double Y = mesh.GetNode(i)->rGetLocation()[1];
double Z = mesh.GetNode(i)->rGetLocation()[2];
// if X=0
if ( fabs(X)<1e-6)
{
fixed_nodes.push_back(i);
c_vector<double,3> new_position_before_rotation;
new_position_before_rotation(0) = 0.0;
new_position_before_rotation(1) = lambda*Y;
new_position_before_rotation(2) = lambda*Z;
locations.push_back(prod(rotation_matrix, new_position_before_rotation));
}
}
assert(fixed_nodes.size()==(2*num_elem_each_dir+1)*(2*num_elem_each_dir+1));
// Define pressure boundary conditions X=1 surface
std::vector<BoundaryElement<2,3>*> boundary_elems;
double pressure_bc = 2*c1*((pow(lambda,-2.0)-pow(lambda,4.0)))/(lambda*lambda);
for (TetrahedralMesh<3,3>::BoundaryElementIterator iter
= mesh.GetBoundaryElementIteratorBegin();
iter != mesh.GetBoundaryElementIteratorEnd();
++iter)
{
if (fabs((*iter)->CalculateCentroid()[0]-1)<1e-6)
{
BoundaryElement<2,3>* p_element = *iter;
boundary_elems.push_back(p_element);
}
}
assert(boundary_elems.size()==2*num_elem_each_dir*num_elem_each_dir);
SolidMechanicsProblemDefinition<3> problem_defn(mesh);
problem_defn.SetMaterialLaw(INCOMPRESSIBLE,&law);
problem_defn.SetFixedNodes(fixed_nodes, locations);
problem_defn.SetApplyNormalPressureOnDeformedSurface(boundary_elems, pressure_bc);
IncompressibleNonlinearElasticitySolver<3> solver(mesh,
problem_defn,
"nonlin_elas_3d_pressure_on_deformed");
solver.Solve();
// Compare
std::vector<c_vector<double,3> >& r_solution = solver.rGetDeformedPosition();
for (unsigned i=0; i<mesh.GetNumNodes(); i++)
{
double X = mesh.GetNode(i)->rGetLocation()[0];
double Y = mesh.GetNode(i)->rGetLocation()[1];
double Z = mesh.GetNode(i)->rGetLocation()[2];
c_vector<double,3> new_position_before_rotation;
new_position_before_rotation(0) = X/(lambda*lambda);
new_position_before_rotation(1) = lambda*Y;
new_position_before_rotation(2) = lambda*Z;
c_vector<double,3> new_position = prod(rotation_matrix, new_position_before_rotation);
TS_ASSERT_DELTA(r_solution[i](0), new_position(0), 1e-2);
TS_ASSERT_DELTA(r_solution[i](1), new_position(1), 1e-2);
TS_ASSERT_DELTA(r_solution[i](2), new_position(2), 1e-2);
}
// test the pressures
std::vector<double>& r_pressures = solver.rGetPressures();
for (unsigned i=0; i<r_pressures.size(); i++)
{
TS_ASSERT_DELTA(r_pressures[i], 2*c1*lambda*lambda, 0.05);
}
}
/**
* Solve 3D nonlinear elasticity problem with an exact solution.
*
* For full details see Pathmanathan, Gavaghan, Whiteley "A comparison of numerical
* methods used in finite element modelling of soft tissue deformation", J. Strain
* Analysis, to appear.
*
* We solve a 3d problem on a cube with a Neo-Hookean material, assuming the solution
* will be
* x = X+aX^2/2
* y = Y+bY^2/2
* z = Z/(1+aX)(1+bY)
* with p=2c (c the material parameter),
* which, note, has been constructed to be an incompressible. We assume displacement
* boundary conditions on X=0 and traction boundary conditions on the remaining 5 surfaces.
* It is then possible to determine the body force and surface tractions required for
* this deformation, and they are defined in the above class.
*/
void TestSolve3d() throw(Exception)
{
unsigned num_runs=4;
double l2_errors[4];
unsigned num_elem_each_dir[4] = {1,2,5,10};
for(unsigned run=0; run<num_runs; run++)
{
QuadraticMesh<3> mesh(1.0/num_elem_each_dir[run], 1.0, 1.0, 1.0);
// Neo-Hookean material law
MooneyRivlinMaterialLaw<3> law(ThreeDimensionalModelProblem::c1, 0.0);
// Define displacement boundary conditions
std::vector<unsigned> fixed_nodes;
std::vector<c_vector<double,3> > locations;
for (unsigned i=0; i<mesh.GetNumNodes(); i++)
{
double X = mesh.GetNode(i)->rGetLocation()[0];
double Y = mesh.GetNode(i)->rGetLocation()[1];
double Z = mesh.GetNode(i)->rGetLocation()[2];
// if X=0
if ( fabs(X)<1e-6)
{
fixed_nodes.push_back(i);
c_vector<double,3> new_position;
new_position(0) = 0.0;
new_position(1) = Y + Y*Y*ThreeDimensionalModelProblem::b/2.0;
new_position(2) = Z/((1+X*ThreeDimensionalModelProblem::a)*(1+Y*ThreeDimensionalModelProblem::b));
locations.push_back(new_position);
}
}
assert(fixed_nodes.size()==(2*num_elem_each_dir[run]+1)*(2*num_elem_each_dir[run]+1));
// Define traction boundary conditions on all boundary elems that are not on X=0
std::vector<BoundaryElement<2,3>*> boundary_elems;
for (TetrahedralMesh<3,3>::BoundaryElementIterator iter
= mesh.GetBoundaryElementIteratorBegin();
iter != mesh.GetBoundaryElementIteratorEnd();
++iter)
{
if (fabs((*iter)->CalculateCentroid()[0])>1e-6)
{
BoundaryElement<2,3>* p_element = *iter;
boundary_elems.push_back(p_element);
}
}
assert(boundary_elems.size()==10*num_elem_each_dir[run]*num_elem_each_dir[run]);
SolidMechanicsProblemDefinition<3> problem_defn(mesh);
problem_defn.SetMaterialLaw(INCOMPRESSIBLE,&law);
problem_defn.SetFixedNodes(fixed_nodes, locations);
problem_defn.SetBodyForce(ThreeDimensionalModelProblem::GetBodyForce);
problem_defn.SetTractionBoundaryConditions(boundary_elems, ThreeDimensionalModelProblem::GetTraction);
IncompressibleNonlinearElasticitySolver<3> solver(mesh,
problem_defn,
"nonlin_elas_3d_10");
solver.Solve(1e-12); // note newton tolerance of 1e-12 needed for convergence to occur
solver.CreateCmguiOutput();
// Compare
l2_errors[run] = 0;
std::vector<c_vector<double,3> >& r_solution = solver.rGetDeformedPosition();
for (unsigned i=0; i<mesh.GetNumNodes(); i++)
{
double X = mesh.GetNode(i)->rGetLocation()[0];
double Y = mesh.GetNode(i)->rGetLocation()[1];
double Z = mesh.GetNode(i)->rGetLocation()[2];
double exact_x = X + X*X*ThreeDimensionalModelProblem::a/2.0;
double exact_y = Y + Y*Y*ThreeDimensionalModelProblem::b/2.0;
double exact_z = Z/((1+X*ThreeDimensionalModelProblem::a)*(1+Y*ThreeDimensionalModelProblem::b));
c_vector<double,3> error;
error(0) = r_solution[i](0) - exact_x;
error(1) = r_solution[i](1) - exact_y;
error(2) = r_solution[i](2) - exact_z;
l2_errors[run] += norm_2(error);
if(num_elem_each_dir[run]==5u)
{
TS_ASSERT_DELTA(r_solution[i](0), exact_x, 1e-2);
TS_ASSERT_DELTA(r_solution[i](1), exact_y, 1e-2);
TS_ASSERT_DELTA(r_solution[i](2), exact_z, 1e-2);
}
}
l2_errors[run] /= mesh.GetNumNodes();
std::vector<double>& r_pressures = solver.rGetPressures();
for (unsigned i=0; i<r_pressures.size(); i++)
{
TS_ASSERT_DELTA(r_pressures[i]/(2*ThreeDimensionalModelProblem::c1), 1.0, 2e-1);
}
}
//for(unsigned run=0; run<num_runs; run++)
//{
// std::cout << 1.0/num_elem_each_dir[run] << " " << l2_errors[run] << "\n";
//}
TS_ASSERT_LESS_THAN(l2_errors[0], 0.0005)
TS_ASSERT_LESS_THAN(l2_errors[1], 5e-5);
TS_ASSERT_LESS_THAN(l2_errors[2], 2.1e-6);
TS_ASSERT_LESS_THAN(l2_errors[3], 4e-7);
}
/**
* This time we will make x (fibres) and z (sheet-normal) contract,
* and y will not contract (so nodes will expand out for y, shrink in for x,z).
*/
void TestAnisotropicCrossFibreTensions() throw(Exception)
{
/*
* Expected resulting deformed location of Nodes 4, 24, 104, 124:
* 4: 1, 0, 0
* 24: 1, 1, 0
* 104: 1, 0, 1
* 124: 1, 1, 1
*/
c_vector<double, 4> x;
c_vector<double, 4> y;
c_vector<double, 4> z;
x[0] = 0.9905;
x[1] = 0.9908;
x[2] = 0.9904;
x[3] = 0.9907;
y[0] = -0.0113;
y[1] = 1.0105;
y[2] = -0.0113;
y[3] = 1.0105;
z[0] = 0.0056;
z[1] = 0.0056;
z[2] = 0.9946;
z[3] = 0.9946;
QuadraticMesh<3> mesh(0.25, 1.0, 1.0, 1.0);
MooneyRivlinMaterialLaw<3> law(1,1);
std::vector<unsigned> fixed_nodes
= NonlinearElasticityTools<3>::GetNodesByComponentValue(mesh,0,0.0);
ElectroMechanicsProblemDefinition<3> problem_defn(mesh);
problem_defn.SetMaterialLaw(INCOMPRESSIBLE,&law);
problem_defn.SetZeroDisplacementNodes(fixed_nodes);
problem_defn.SetContractionModel(NONPHYSIOL1,0.01);
problem_defn.SetMechanicsSolveTimestep(0.01); //This is only set to make ElectroMechanicsProblemDefinition::Validate pass
double sheet_tension_fraction=0;
double sheet_normal_tension_fraction=1;
problem_defn.SetApplyAnisotropicCrossFibreTension(true,sheet_tension_fraction, sheet_normal_tension_fraction);
// NONPHYSIOL1 => NonphysiologicalContractionModel 1
IncompressibleExplicitSolver3d solver(mesh,problem_defn,"TestAnisotropicCrossFibreExplicit");
// The following lines are not relevant to this test but need to be there
// as the solver is expecting an electrics node to be paired up with each mechanics node.
TetrahedralMesh<3,3>* p_fine_mesh = new TetrahedralMesh<3,3>();//electrics ignored in this test
p_fine_mesh->ConstructRegularSlabMesh(0.25, 1.0, 1.0, 1.0);
FineCoarseMeshPair<3>* p_pair = new FineCoarseMeshPair<3>(*p_fine_mesh, mesh);
p_pair->SetUpBoxesOnFineMesh();
p_pair->ComputeFineElementsAndWeightsForCoarseQuadPoints(*(solver.GetQuadratureRule()), false);
p_pair->DeleteFineBoxCollection();
solver.SetFineCoarseMeshPair(p_pair);
///////////////////////////////////////////////////////////////////////////
solver.Initialise();
// coverage
QuadraturePointsGroup<3> quad_points(mesh, *(solver.GetQuadratureRule()));
std::vector<double> calcium_conc(solver.GetTotalNumQuadPoints(), 0.0);
std::vector<double> voltages(solver.GetTotalNumQuadPoints(), 0.0);
solver.SetCalciumAndVoltage(calcium_conc, voltages);
// solve UP TO t=0. So Ta(lam_n,t_{n+1})=5*sin(0)=0, ie no deformation
solver.Solve(-0.01,0.0,0.01);
TS_ASSERT_EQUALS(solver.GetNumNewtonIterations(),0u);
solver.Solve(0.24,0.25,0.01);
std::vector<unsigned> nodes;
nodes.push_back(4);
nodes.push_back(24);
nodes.push_back(104);
nodes.push_back(124);
for (unsigned node=0; node<4; node++)
{
std::cout << "Node: " << nodes[node] << "\n";
TS_ASSERT_DELTA(solver.rGetDeformedPosition()[nodes[node]](0), x[node], 1e-3);
TS_ASSERT_DELTA(solver.rGetDeformedPosition()[nodes[node]](1), y[node], 1e-3);
TS_ASSERT_DELTA(solver.rGetDeformedPosition()[nodes[node]](2), z[node], 1e-3);
}
// tidy up memory
delete p_fine_mesh;
delete p_pair;
}
void TestCrossFibreTensionWithSimpleContractionModel() throw(Exception)
{
QuadraticMesh<2> mesh(0.25, 1.0, 1.0);
MooneyRivlinMaterialLaw<2> law(1);
std::vector<unsigned> fixed_nodes
= NonlinearElasticityTools<2>::GetNodesByComponentValue(mesh,0,0.0);
ElectroMechanicsProblemDefinition<2> problem_defn(mesh);
problem_defn.SetMaterialLaw(INCOMPRESSIBLE,&law);
problem_defn.SetZeroDisplacementNodes(fixed_nodes);
problem_defn.SetContractionModel(NONPHYSIOL1,0.01);
problem_defn.SetMechanicsSolveTimestep(0.01); //This is only set to make ElectroMechanicsProblemDefinition::Validate pass
//Cross fibre tension fractions to be tested
c_vector<double, 4> tension_fractions;
tension_fractions[0] = 0.0;
tension_fractions[1] = 0.1;
tension_fractions[2] = 0.5;
tension_fractions[3] = 1.0;
//Expected resulting deformed location of Node 4.
c_vector<double, 4> x;
c_vector<double, 4> y;
x[0] = 0.9732;
x[1] = 0.9759;
x[2] = 0.9865;
x[3] = 1.0; //Note, for cross_tension == 1.0 there should be no deformation of the tissue square (tensions balance)
y[0] = -0.0156;
y[1] = -0.0140;
y[2] = -0.0077;
y[3] = 0.0;
for(unsigned i=0; i < tension_fractions.size();i++)
{
problem_defn.SetApplyIsotropicCrossFibreTension(true,tension_fractions[i]);
TS_ASSERT_EQUALS(problem_defn.GetApplyCrossFibreTension(), true);
TS_ASSERT_DELTA(problem_defn.GetSheetTensionFraction(),tension_fractions[i], 1e-6);
TS_ASSERT_DELTA(problem_defn.GetSheetNormalTensionFraction(),tension_fractions[i], 1e-6);
// NONPHYSIOL1 => NonphysiologicalContractionModel 1
IncompressibleExplicitSolver2d solver(mesh,problem_defn,"TestExplicitCardiacMech");
// The following lines are not relevant to this test but need to be there
// as the solver is expecting an electrics node to be paired up with each mechanics node.
TetrahedralMesh<2,2>* p_fine_mesh = new TetrahedralMesh<2,2>();//electrics ignored in this test
p_fine_mesh->ConstructRegularSlabMesh(0.25, 1.0, 1.0);
FineCoarseMeshPair<2>* p_pair = new FineCoarseMeshPair<2>(*p_fine_mesh, mesh);
p_pair->SetUpBoxesOnFineMesh();
p_pair->ComputeFineElementsAndWeightsForCoarseQuadPoints(*(solver.GetQuadratureRule()), false);
p_pair->DeleteFineBoxCollection();
solver.SetFineCoarseMeshPair(p_pair);
///////////////////////////////////////////////////////////////////////////
solver.Initialise();
// coverage
QuadraturePointsGroup<2> quad_points(mesh, *(solver.GetQuadratureRule()));
std::vector<double> calcium_conc(solver.GetTotalNumQuadPoints(), 0.0);
std::vector<double> voltages(solver.GetTotalNumQuadPoints(), 0.0);
solver.SetCalciumAndVoltage(calcium_conc, voltages);
// solve UP TO t=0. So Ta(lam_n,t_{n+1})=5*sin(0)=0, ie no deformation
solver.Solve(-0.01,0.0,0.01);
TS_ASSERT_EQUALS(solver.GetNumNewtonIterations(),0u);
solver.Solve(0.24,0.25,0.01);
//// These fail due to changes from #2185 but no point fixing as these numbers will change later anyway (#2180)
TS_ASSERT_DELTA(solver.rGetDeformedPosition()[4](0), x[i], 1e-3);
TS_ASSERT_DELTA(solver.rGetDeformedPosition()[4](1), y[i], 1e-3);
//in need of deletion even if all these 3 have no influence at all on this test
delete p_fine_mesh;
delete p_pair;
}
}
