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gsVisitorNonLinearElasticity.h
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gsVisitorNonLinearElasticity.h
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/** @file gsVisitorNonLinearElasticity.h
@brief Element visitor for nonlinear elasticity for 2D plain strain and 3D continua.
This file is part of the G+Smo library.
This Source Code Form is subject to the terms of the Mozilla Public
License, v. 2.0. If a copy of the MPL was not distributed with this
file, You can obtain one at http://mozilla.org/MPL/2.0/.
Author(s):
O. Weeger (2012 - 2015, TU Kaiserslautern),
A.Shamanskiy (2016 - ...., TU Kaiserslautern)
*/
#pragma once
#include <gsElasticity/gsVisitorElUtils.h>
#include <gsElasticity/gsBasePde.h>
#include <gsAssembler/gsQuadrature.h>
#include <gsCore/gsFuncData.h>
namespace gismo
{
template <class T>
class gsVisitorNonLinearElasticity
{
public:
gsVisitorNonLinearElasticity(const gsPde<T> & pde_, const gsMultiPatch<T> & displacement_)
: pde_ptr(static_cast<const gsBasePde<T>*>(&pde_)),
displacement(displacement_) { }
void initialize(const gsBasisRefs<T> & basisRefs,
const index_t patchIndex,
const gsOptionList & options,
gsQuadRule<T> & rule)
{
// parametric dimension of the first displacement component
dim = basisRefs.front().dim();
// a quadrature rule is defined by the basis for the first displacement component.
rule = gsQuadrature::get(basisRefs.front(), options);
// saving necessary info
patch = patchIndex;
materialLaw = options.getInt("MaterialLaw");
T YM = options.getReal("YoungsModulus");
T PR = options.getReal("PoissonsRatio");
lambda = YM * PR / ( ( 1. + PR ) * ( 1. - 2. * PR ) );
mu = YM / ( 2. * ( 1. + PR ) );
forceScaling = options.getReal("ForceScaling");
localStiffening = options.getReal("LocalStiff");
// elasticity tensor
I = gsMatrix<T>::Identity(dim,dim);
if (materialLaw == 0)
{
matrixTraceTensor<T>(C,I,I);
C *= lambda;
symmetricIdentityTensor<T>(Ctemp,I);
C += mu*Ctemp;
}
// resize containers for global indices
globalIndices.resize(dim);
blockNumbers.resize(dim);
}
inline void evaluate(const gsBasisRefs<T> & basisRefs,
const gsGeometry<T> & geo,
const gsMatrix<T> & quNodes)
{
// store quadrature points of the element for geometry evaluation
md.points = quNodes;
// NEED_VALUE to get points in the physical domain for evaluation of the RHS
// NEED_MEASURE to get the Jacobian determinant values for integration
// NEED_GRAD_TRANSFORM to get the Jacobian matrix to transform gradient from the parametric to physical domain
md.flags = NEED_VALUE | NEED_MEASURE | NEED_GRAD_TRANSFORM;
// Compute image of the quadrature points plus gradient, jacobian and other necessary data
geo.computeMap(md);
// find local indices of the displacement basis functions active on the element
basisRefs.front().active_into(quNodes.col(0),localIndicesDisp);
N_D = localIndicesDisp.rows();
// Evaluate displacement basis functions and their derivatives on the element
basisRefs.front().evalAllDers_into(quNodes,1,basisValuesDisp);
// Evaluate right-hand side at the image of the quadrature points
pde_ptr->rhs()->eval_into(md.values[0],forceValues);
// store quadrature points of the element for displacement evaluation
mdDisplacement.points = quNodes;
// NEED_DERIV to compute deformation gradient
mdDisplacement.flags = NEED_DERIV;
// evaluate displacement gradient
displacement.patch(patch).computeMap(mdDisplacement);
}
inline void assemble(gsDomainIterator<T> & element,
const gsVector<T> & quWeights)
{
// initialize local matrix and rhs
localMat.setZero(dim*N_D,dim*N_D);
localRhs.setZero(dim*N_D,1);
// loop over quadrature nodes
for (index_t q = 0; q < quWeights.rows(); ++q)
{
const T weightForce = quWeights[q] * md.measure(q);
// Compute physical gradients of basis functions at q as a dim x numActiveFunction matrix
transformGradients(md,q,basisValuesDisp[1],physGrad);
// physical jacobian of displacemnt du/dx = du/dxi * dxi/dx
physDispJac = mdDisplacement.jacobian(q)*(md.jacobian(q).cramerInverse());
// deformation gradient F = I + du/dx
F = I + physDispJac;
// deformation jacobian J = det(F)
T J = F.determinant();
// Right Cauchy Green strain, C = F'*F
RCG = F.transpose() * F;
// Green-Lagrange strain, E = 0.5*(C-I), a.k.a. full geometric strain tensor
E = 0.5 * (RCG - I);
const T weightBody = quWeights[q] * pow(md.measure(q),-1.*localStiffening) * md.measure(q);
// Second Piola-Kirchhoff stress tensor
if (materialLaw == 0) // Saint Venant-Kirchhoff
S = lambda*E.trace()*I + 2*mu*E;
if (materialLaw == 1) // neo-Hooke ln(J)
{
GISMO_ENSURE(J>0,"Invalid configuration: J < 0");
RCGinv = RCG.cramerInverse();
S = (lambda*log(J)-mu)*RCGinv + mu*I;
// elasticity tensor
matrixTraceTensor<T>(C,RCGinv,RCGinv);
C *= lambda;
symmetricIdentityTensor<T>(Ctemp,RCGinv);
C += (mu-lambda*log(J))*Ctemp;
}
if (materialLaw == 2) // quad neo-Hooke
{
RCGinv = RCG.cramerInverse();
S = (lambda*(J*J-1)/2-mu)*RCGinv + mu*I;
// elasticity tensor
matrixTraceTensor<T>(C,RCGinv,RCGinv);
C *= lambda*J*J;
symmetricIdentityTensor<T>(Ctemp,RCGinv);
C += (mu-lambda*(J*J-1)/2)*Ctemp;
}
// loop over active basis functions (u_i)
for (index_t i = 0; i < N_D; i++)
{
// Material tangent K_tg_mat = B_i^T * C * B_j;
setB<T>(B_i,F,physGrad.col(i));
materialTangentTemp = B_i.transpose() * C;
// Geometric tangent K_tg_geo = gradB_i^T * S * gradB_j;
geometricTangentTemp = S * physGrad.col(i);
// loop over active basis functions (v_j)
for (index_t j = 0; j < N_D; j++)
{
setB<T>(B_j,F,physGrad.col(j));
materialTangent = materialTangentTemp * B_j;
T geometricTangent = geometricTangentTemp.transpose() * physGrad.col(j);
// K_tg = K_tg_mat + I*K_tg_geo;
for (short_t d = 0; d < dim; ++d)
materialTangent(d,d) += geometricTangent;
for (short_t di = 0; di < dim; ++di)
for (short_t dj = 0; dj < dim; ++dj)
localMat(di*N_D+i, dj*N_D+j) += weightBody * materialTangent(di,dj);
}
// Second Piola-Kirchhoff stress tensor as vector
voigtStress<T>(Svec,S);
// rhs = -r = force - B*Svec,
localResidual = B_i.transpose() * Svec;
for (short_t d = 0; d < dim; d++)
localRhs(d*N_D+i) -= weightBody * localResidual(d);
}
// contribution of volumetric load function to residual/rhs
for (short_t d = 0; d < dim; ++d)
localRhs.middleRows(d*N_D,N_D).noalias() += weightForce * forceScaling * forceValues(d,q) * basisValuesDisp[0].col(q);
}
}
inline void localToGlobal(const int patchIndex,
const std::vector<gsMatrix<T> > & eliminatedDofs,
gsSparseSystem<T> & system)
{
// computes global indices for displacement components
for (short_t d = 0; d < dim; ++d)
{
system.mapColIndices(localIndicesDisp, patchIndex, globalIndices[d], d);
blockNumbers.at(d) = d;
}
// push to global system
system.pushToRhs(localRhs,globalIndices,blockNumbers);
system.pushToMatrix(localMat,globalIndices,eliminatedDofs,blockNumbers,blockNumbers);
}
protected:
// problem info
short_t dim;
index_t patch; // current patch
const gsBasePde<T> * pde_ptr;
index_t materialLaw; // (0: St. Venant-Kirchhoff, 1: ln neo-Hooke, 2: quad neo-Hooke)
// Lame coefficients and force scaling factor
T lambda, mu, forceScaling;
// geometry mapping
gsMapData<T> md;
// local components of the global linear system
gsMatrix<T> localMat;
gsMatrix<T> localRhs;
// local indices (at the current patch) of the displacement basis functions active at the current element
gsMatrix<index_t> localIndicesDisp;
// number of displacement basis functions active at the current element
index_t N_D;
// values and derivatives of displacement basis functions at quadrature points at the current element
// values are stored as a N_D x numQuadPoints matrix; not sure about derivatives, must be smth like N_D*dim x numQuadPoints
std::vector<gsMatrix<T> > basisValuesDisp;
// RHS values at quadrature points at the current element; stored as a dim x numQuadPoints matrix
gsMatrix<T> forceValues;
// current displacement field
const gsMultiPatch<T> & displacement;
// evaluation data of the current displacement field
gsMapData<T> mdDisplacement;
// all temporary matrices defined here for efficiency
gsMatrix<T> C, Ctemp, physGrad, physDispJac, F, RCG, E, S, RCGinv, B_i, materialTangentTemp, B_j, materialTangent, I;
gsVector<T> geometricTangentTemp, Svec, localResidual;
T localStiffening;
// containers for global indices
std::vector< gsMatrix<index_t> > globalIndices;
gsVector<index_t> blockNumbers;
};
} // namespace gismo