ComputeLayeredCosseratElasticityTensor::ComputeLayeredCosseratElasticityTensor(
const InputParameters & parameters)
: ComputeElasticityTensorBase(parameters),
_Eijkl(RankFourTensor()),
_Bijkl(RankFourTensor()),
_Cijkl(RankFourTensor()),
_elastic_flexural_rigidity_tensor(
declareProperty<RankFourTensor>("elastic_flexural_rigidity_tensor")),
_compliance(declareProperty<RankFourTensor>(_base_name + "compliance_tensor"))
{
// all tensors created by this class are always constant in time
issueGuarantee(_elasticity_tensor_name, Guarantee::CONSTANT_IN_TIME);
const Real E = getParam<Real>("young");
const Real nu = getParam<Real>("poisson");
const Real b = getParam<Real>("layer_thickness");
const Real kn = getParam<Real>("joint_normal_stiffness");
const Real ks = getParam<Real>("joint_shear_stiffness");
// shear modulus of solid
const Real G = 0.5 * E / (1.0 + nu);
// shear modulus of jointed material
const Real Gprime = G * b * ks / (b * ks + G);
const Real a0000 =
(b * kn > 0.0)
? E / (1.0 - nu * nu - Utility::pow<2>(nu * (1.0 + nu)) / (1.0 - nu * nu + E / b / kn))
: E / (1.0 - nu * nu);
const Real a0011 = nu * a0000 / (1.0 - nu);
const Real a2222 =
(b * kn > 0.0) ? 1.0 / ((1.0 + nu) * (1.0 - 2.0 * nu) / E / (1.0 - nu) + 1.0 / b / kn) : 0.0;
const Real a0022 = nu * a2222 / (1.0 - nu);
const Real a0101 = G;
const Real a66 = Gprime;
const Real a77 = 0.5 * (G + Gprime);
// Eijkl does not obey the usual symmetries, viz Eijkl != Ejikl, so must fill manually
_Eijkl(0, 0, 0, 0) = _Eijkl(1, 1, 1, 1) = a0000;
_Eijkl(0, 0, 1, 1) = _Eijkl(1, 1, 0, 0) = a0011;
_Eijkl(2, 2, 2, 2) = a2222;
_Eijkl(0, 0, 2, 2) = _Eijkl(1, 1, 2, 2) = _Eijkl(2, 2, 0, 0) = _Eijkl(2, 2, 1, 1) = a0022;
_Eijkl(0, 1, 0, 1) = _Eijkl(0, 1, 1, 0) = _Eijkl(1, 0, 0, 1) = _Eijkl(1, 0, 1, 0) = a0101;
_Eijkl(0, 2, 0, 2) = _Eijkl(0, 2, 2, 0) = _Eijkl(2, 0, 0, 2) = _Eijkl(1, 2, 1, 2) =
_Eijkl(1, 2, 2, 1) = _Eijkl(2, 1, 1, 2) = a66;
_Eijkl(2, 0, 2, 0) = _Eijkl(2, 1, 2, 1) = a77;
// most of Bijkl is zero since the only nonzero moment stresses are m01 and m10.
// It also does not have the usual symmetries.
const Real D0 = E * Utility::pow<3>(b) / 12.0 / (1.0 - nu * nu); // bending rigidity of a layer
const Real b0101 = D0 / b * G / (2.0 * b * ks + G);
const Real b0110 = -nu * b0101;
_Bijkl(0, 1, 0, 1) = _Bijkl(1, 0, 1, 0) = b0101;
_Bijkl(0, 1, 1, 0) = _Bijkl(1, 0, 0, 1) = b0110;
// The compliance tensor also does not obey the usual symmetries, and
// this is the main reason it is calculated here, since we can't use
// _Eijkl.invSymm()
const Real pre = (nu - 1.0) / (a0000 * (nu - 1.0) + 2.0 * a2222 * Utility::pow<2>(nu));
const Real cp0000 =
((a2222 - a0000) * nu * nu + 2.0 * a0000 * nu - a0000) / (2.0 * a0000 * nu - a0000);
const Real cp0011 = -((a0000 + a2222) * nu * nu - a0000 * nu) / (2.0 * a0000 * nu - a0000);
_Cijkl(0, 0, 0, 0) = _Cijkl(1, 1, 1, 1) = pre * cp0000;
_Cijkl(0, 0, 1, 1) = _Cijkl(1, 1, 0, 0) = pre * cp0011;
_Cijkl(2, 2, 2, 2) = pre * a0000 / a2222;
_Cijkl(0, 0, 2, 2) = _Cijkl(1, 1, 2, 2) = _Cijkl(2, 2, 0, 0) = _Cijkl(2, 2, 1, 1) = -nu * pre;
_Cijkl(0, 1, 0, 1) = _Cijkl(0, 1, 1, 0) = _Cijkl(1, 0, 0, 1) = _Cijkl(1, 0, 1, 0) = 0.25 / a0101;
const Real slip = 2.0 / (G - Gprime);
_Cijkl(0, 2, 2, 0) = _Cijkl(2, 0, 0, 2) = _Cijkl(1, 2, 2, 1) = _Cijkl(2, 1, 1, 2) = -slip;
_Cijkl(0, 2, 0, 2) = _Cijkl(1, 2, 1, 2) = (G + Gprime) * slip / 2.0 / Gprime;
_Cijkl(2, 0, 2, 0) = _Cijkl(2, 1, 2, 1) = slip;
}
ComputeLayeredCosseratElasticityTensor::ComputeLayeredCosseratElasticityTensor(const InputParameters & parameters) :
ComputeElasticityTensorBase(parameters),
_Eijkl(RankFourTensor()),
_Bijkl(RankFourTensor()),
_elastic_flexural_rigidity_tensor(declareProperty<RankFourTensor>("elastic_flexural_rigidity_tensor"))
{
const Real E = getParam<Real>("young");
const Real nu = getParam<Real>("poisson");
const Real b = getParam<Real>("layer_thickness");
const Real kn = getParam<Real>("joint_normal_stiffness");
const Real ks = getParam<Real>("joint_shear_stiffness");
// shear modulus of solid
const Real G = 0.5 * E / (1.0 + nu);
// shear modulus of jointed material
const Real Gprime = G * b * ks / (b * ks + G);
const Real a0000 = (b * kn > 0.0) ? E / (1.0 - nu * nu - std::pow(nu * (1.0 + nu), 2) / (1.0 - nu * nu + E / b / kn)) : E / (1.0 - nu * nu);
const Real a0011 = nu * a0000 / (1.0 - nu);
const Real a2222 = (b * kn > 0.0) ? 1.0 / ( (1.0 + nu) * (1.0 - 2.0 * nu) / E / (1.0 - nu) + 1.0 / b / kn) : 0.0;
const Real a0022 = nu * a2222 / (1.0 - nu);
const Real a0101 = G;
const Real a66 = Gprime;
const Real a77 = 0.5*(G + Gprime);
// Eijkl does not obey the usual symmetries, viz Eijkl != Ejikl, so must fill manually
_Eijkl(0, 0, 0, 0) = _Eijkl(1, 1, 1, 1) = a0000;
_Eijkl(0, 0, 1, 1) = _Eijkl(1, 1, 0, 0) = a0011;
_Eijkl(2, 2, 2, 2) = a2222;
_Eijkl(0, 0, 2, 2) = _Eijkl(1, 1, 2, 2) = _Eijkl(2, 2, 0, 0) = _Eijkl(2, 2, 1, 1) = a0022;
_Eijkl(0, 1, 0, 1) = _Eijkl(0, 1, 1, 0) = _Eijkl(1, 0, 0, 1) = _Eijkl(1, 0, 1, 0) = a0101;
_Eijkl(0, 2, 0, 2) = _Eijkl(0, 2, 2, 0) = _Eijkl(2, 0, 2, 0) = _Eijkl(1, 2, 1, 2) = _Eijkl(1, 2, 2, 1) = _Eijkl(2, 1, 2, 1) = a66;
_Eijkl(2, 0, 0, 2) = _Eijkl(2, 1, 1, 2) = a77;
// most of Bijkl is zero since the only nonzero moment stresses are m01 and m10.
// It also does not have the usual symmetries.
const Real D0 = E * std::pow(b, 3) / 12.0 / (1.0 - nu * nu); // bending rigidity of a layer
const Real b0101 = D0 / b * G / (2.0 * b * ks + G);
const Real b0110 = - nu * b0101;
_Bijkl(0, 1, 0, 1) = _Bijkl(1, 0, 1, 0) = b0101;
_Bijkl(0, 1, 1, 0) = _Bijkl(1, 0, 0, 1) = b0110;
}
