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sv_struct.cpp
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sv_struct.cpp
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/* Copyright (c) Stanford University, The Regents of the University of California, and others.
*
* All Rights Reserved.
*
* See Copyright-SimVascular.txt for additional details.
*
* Permission is hereby granted, free of charge, to any person obtaining
* a copy of this software and associated documentation files (the
* "Software"), to deal in the Software without restriction, including
* without limitation the rights to use, copy, modify, merge, publish,
* distribute, sublicense, and/or sell copies of the Software, and to
* permit persons to whom the Software is furnished to do so, subject
* to the following conditions:
*
* The above copyright notice and this permission notice shall be included
* in all copies or substantial portions of the Software.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS
* IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
* TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A
* PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER
* OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
* EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
* PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
* PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
* LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
* NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
* SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*/
// Functions for solving nonlinear structural mechanics
// problems (pure displacement-based formulation).
//
// Replicates the Fortran functions in 'STRUCT.f'.
#include "sv_struct.h"
#include "all_fun.h"
#include "consts.h"
#include "lhsa.h"
#include "mat_fun.h"
#include "mat_fun_carray.h"
#include "mat_models.h"
#include "mat_models_carray.h"
#include "nn.h"
#include "utils.h"
namespace struct_ns {
void b_struct_2d(const ComMod& com_mod, const int eNoN, const double w, const Vector<double>& N,
const Array<double>& Nx, const Array<double>& dl, const Vector<double>& hl, const Vector<double>& nV,
Array<double>& lR, Array3<double>& lK)
{
int cEq = com_mod.cEq;
auto& eq = com_mod.eq[cEq];
double dt = com_mod.dt;
int dof = com_mod.dof;
double af = eq.af * eq.gam*dt;
double afm = af / eq.am;
int i = eq.s;
int j = i + 1;
Vector<double> nFi(2);
Array<double> NxFi(2,eNoN);
Array<double> F(2,2);
F(0,0) = 1.0;
F(1,1) = 1.0;
double h = 0.0;
for (int a = 0; a < eNoN; a++) {
h = h + N(a)*hl(a);
F(0,0) = F(0,0) + Nx(0,a)*dl(i,a);
F(0,1) = F(0,1) + Nx(1,a)*dl(i,a);
F(1,0) = F(1,0) + Nx(0,a)*dl(j,a);
F(1,1) = F(1,1) + Nx(1,a)*dl(j,a);
}
double Jac = F(0,0)*F(1,1) - F(0,1)*F(1,0);
auto Fi = mat_fun::mat_inv(F, 2);
for (int a = 0; a < eNoN; a++) {
NxFi(0,a) = Nx(0,a)*Fi(0,0) + Nx(1,a)*Fi(1,0);
NxFi(1,a) = Nx(0,a)*Fi(0,1) + Nx(1,a)*Fi(1,1);
}
nFi(0) = nV(0)*Fi(0,0) + nV(1)*Fi(1,0);
nFi(1) = nV(0)*Fi(0,1) + nV(1)*Fi(1,1);
double wl = w * Jac * h;
for (int a = 0; a < eNoN; a++) {
lR(0,a) = lR(0,a) - wl*N(a)*nFi(0);
lR(1,a) = lR(1,a) - wl*N(a)*nFi(1);
for (int b = 0; b < eNoN; b++) {
double Ku = wl*af*N(a)*(nFi(1)*NxFi(0,b) - nFi(0)*NxFi(1,b));
lK(1,a,b) = lK(1,a,b) + Ku;
lK(dof,a,b) = lK(dof,a,b) - Ku;
}
}
}
/// @brief Add follower pressure load contributions to the local residual and stiffness matrix.
/// @param com_mod
/// @param eNoN
/// @param w Gauss point weight times reference configuration area
/// @param N Shape function values at the Gauss point
/// @param Nx Shape function derivatives at the Gauss point
/// @param dl Displacement vector
/// @param hl Magnitude of pressure
/// @param nV Normal vector (in reference configuration)
/// @param lR Local residual
/// @param lK Local stiffness matrix
void b_struct_3d(const ComMod& com_mod, const int eNoN, const double w, const Vector<double>& N,
const Array<double>& Nx, const Array<double>& dl, const Vector<double>& hl, const Vector<double>& nV,
Array<double>& lR, Array3<double>& lK)
{
#define n_debug_b_struct_3d
#ifdef debug_b_struct_3d
DebugMsg dmsg(__func__, com_mod.cm.idcm());
dmsg.banner();
#endif
int cEq = com_mod.cEq;
auto& eq = com_mod.eq[cEq];
double dt = com_mod.dt;
int dof = com_mod.dof;
double af = eq.af * eq.beta*dt*dt;
int i = eq.s;
int j = i + 1;
int k = j + 1;
#ifdef debug_b_struct_3d
debug << "af: " << af;
debug << "i: " << i;
debug << "j: " << j;
debug << "k: " << k;
#endif
Vector<double> nFi(3);
Array<double> NxFi(3,eNoN);
Array<double> F(3,3);
F(0,0) = 1.0;
F(1,1) = 1.0;
F(2,2) = 1.0;
double h = 0.0;
// Compute deformation gradient tensor F
for (int a = 0; a < eNoN; a++) {
h = h + N(a)*hl(a);
F(0,0) = F(0,0) + Nx(0,a)*dl(i,a);
F(0,1) = F(0,1) + Nx(1,a)*dl(i,a);
F(0,2) = F(0,2) + Nx(2,a)*dl(i,a);
F(1,0) = F(1,0) + Nx(0,a)*dl(j,a);
F(1,1) = F(1,1) + Nx(1,a)*dl(j,a);
F(1,2) = F(1,2) + Nx(2,a)*dl(j,a);
F(2,0) = F(2,0) + Nx(0,a)*dl(k,a);
F(2,1) = F(2,1) + Nx(1,a)*dl(k,a);
F(2,2) = F(2,2) + Nx(2,a)*dl(k,a);
}
double Jac = mat_fun::mat_det(F, 3);
auto Fi = mat_fun::mat_inv(F, 3);
for (int a = 0; a < eNoN; a++) {
NxFi(0,a) = Nx(0,a)*Fi(0,0) + Nx(1,a)*Fi(1,0) + Nx(2,a)*Fi(2,0);
NxFi(1,a) = Nx(0,a)*Fi(0,1) + Nx(1,a)*Fi(1,1) + Nx(2,a)*Fi(2,1);
NxFi(2,a) = Nx(0,a)*Fi(0,2) + Nx(1,a)*Fi(1,2) + Nx(2,a)*Fi(2,2);
}
// Compute N.F^-1, used for Nanson' formula da.n = J*dA*N.F^-1
nFi(0) = nV(0)*Fi(0,0) + nV(1)*Fi(1,0) + nV(2)*Fi(2,0);
nFi(1) = nV(0)*Fi(0,1) + nV(1)*Fi(1,1) + nV(2)*Fi(2,1);
nFi(2) = nV(0)*Fi(0,2) + nV(1)*Fi(1,2) + nV(2)*Fi(2,2);
double wl = w * Jac * h;
#ifdef debug_b_struct_3d
debug;
debug << "Jac: " << Jac;
debug << "h: " << h;
debug << "wl: " << wl;
#endif
// Compute follower pressure load contributions to the local residual and stiffness matrix
for (int a = 0; a < eNoN; a++) {
lR(0,a) = lR(0,a) - wl*N(a)*nFi(0);
lR(1,a) = lR(1,a) - wl*N(a)*nFi(1);
lR(2,a) = lR(2,a) - wl*N(a)*nFi(2);
for (int b = 0; b < eNoN; b++) {
double Ku = wl * af * N(a) * (nFi(1)*NxFi(0,b) - nFi(0)*NxFi(1,b));
lK(1,a,b) = lK(1,a,b) + Ku;
lK(dof,a,b) = lK(dof,a,b) - Ku;
Ku = wl*af*N(a)*(nFi(2)*NxFi(0,b) - nFi(0)*NxFi(2,b));
lK(2,a,b) = lK(2,a,b) + Ku;
lK(2*dof,a,b) = lK(2*dof,a,b) - Ku;
Ku = wl*af*N(a)*(nFi(2)*NxFi(1,b) - nFi(1)*NxFi(2,b));
lK(dof+2,a,b) = lK(dof+2,a,b) + Ku;
lK(2*dof+1,a,b) = lK(2*dof+1,a,b) - Ku;
}
}
}
/// @brief Replicates the Fortan 'CONSTRUCT_dSOLID' subroutine.
//
void construct_dsolid(ComMod& com_mod, CepMod& cep_mod, const mshType& lM, const Array<double>& Ag, const Array<double>& Yg, const Array<double>& Dg)
{
using namespace consts;
#define n_debug_construct_dsolid
#ifdef debug_construct_dsolid
DebugMsg dmsg(__func__, com_mod.cm.idcm());
dmsg.banner();
#endif
auto& cem = cep_mod.cem;
const int nsd = com_mod.nsd;
const int tDof = com_mod.tDof;
const int dof = com_mod.dof;
const int cEq = com_mod.cEq;
const auto& eq = com_mod.eq[cEq];
auto cDmn = com_mod.cDmn;
const int nsymd = com_mod.nsymd;
auto& pS0 = com_mod.pS0;
auto& pSn = com_mod.pSn;
auto& pSa = com_mod.pSa;
bool pstEq = com_mod.pstEq;
int eNoN = lM.eNoN;
int nFn = lM.nFn;
if (nFn == 0) {
nFn = 1;
}
#ifdef debug_construct_dsolid
dmsg << "lM.nEl: " << lM.nEl;
dmsg << "eNoN: " << eNoN;
dmsg << "nsymd: " << nsymd;
dmsg << "nFn: " << nFn;
dmsg << "lM.nG: " << lM.nG;
#endif
// STRUCT: dof = nsd
Vector<int> ptr(eNoN);
Vector<double> pSl(nsymd), ya_l(eNoN), N(eNoN);
Array<double> xl(nsd,eNoN), al(tDof,eNoN), yl(tDof,eNoN), dl(tDof,eNoN),
bfl(nsd,eNoN), fN(nsd,nFn), pS0l(nsymd,eNoN), Nx(nsd,eNoN), lR(dof,eNoN);
Array3<double> lK(dof*dof,eNoN,eNoN);
// Loop over all elements of mesh
for (int e = 0; e < lM.nEl; e++) {
// Update domain and proceed if domain phys and eqn phys match
cDmn = all_fun::domain(com_mod, lM, cEq, e);
auto cPhys = eq.dmn[cDmn].phys;
if (cPhys != EquationType::phys_struct) {
continue;
}
// Update shape functions for NURBS
if (lM.eType == ElementType::NRB) {
//CALL NRBNNX(lM, e)
}
// Create local copies
fN = 0.0;
pS0l = 0.0;
ya_l = 0.0;
for (int a = 0; a < eNoN; a++) {
int Ac = lM.IEN(a,e);
ptr(a) = Ac;
for (int i = 0; i < nsd; i++) {
xl(i,a) = com_mod.x(i,Ac);
bfl(i,a) = com_mod.Bf(i,Ac);
}
for (int i = 0; i < tDof; i++) {
al(i,a) = Ag(i,Ac);
dl(i,a) = Dg(i,Ac);
yl(i,a) = Yg(i,Ac);
}
if (lM.fN.size() != 0) {
for (int iFn = 0; iFn < nFn; iFn++) {
for (int i = 0; i < nsd; i++) {
fN(i,iFn) = lM.fN(i+nsd*iFn,e);
}
}
}
if (pS0.size() != 0) {
pS0l.set_col(a, pS0.col(Ac));
}
if (cem.cpld) {
ya_l(a) = cem.Ya(Ac);
}
}
// Gauss integration
//
lR = 0.0;
lK = 0.0;
double Jac{0.0};
Array<double> ksix(nsd,nsd);
for (int g = 0; g < lM.nG; g++) {
if (g == 0 || !lM.lShpF) {
auto Nx_g = lM.Nx.slice(g);
nn::gnn(eNoN, nsd, nsd, Nx_g, xl, Nx, Jac, ksix);
if (utils::is_zero(Jac)) {
throw std::runtime_error("[construct_dsolid] Jacobian for element " + std::to_string(e) + " is < 0.");
}
}
double w = lM.w(g) * Jac;
N = lM.N.col(g);
pSl = 0.0;
if (nsd == 3) {
struct_3d_carray(com_mod, cep_mod, eNoN, nFn, w, N, Nx, al, yl, dl, bfl, fN, pS0l, pSl, ya_l, lR, lK);
//struct_3d(com_mod, cep_mod, eNoN, nFn, w, N, Nx, al, yl, dl, bfl, fN, pS0l, pSl, ya_l, lR, lK);
#if 0
if (e == 0 && g == 0) {
Array3<double>::write_enabled = true;
Array<double>::write_enabled = true;
lR.write("lR");
lK.write("lK");
exit(0);
}
#endif
} else if (nsd == 2) {
struct_2d(com_mod, cep_mod, eNoN, nFn, w, N, Nx, al, yl, dl, bfl, fN, pS0l, pSl, ya_l, lR, lK);
}
// Prestress
if (pstEq) {
for (int a = 0; a < eNoN; a++) {
int Ac = ptr(a);
pSa(Ac) = pSa(Ac) + w*N(a);
for (int i = 0; i < pSn.nrows(); i++) {
pSn(i,Ac) = pSn(i,Ac) + w*N(a)*pSl(i);
}
}
}
}
eq.linear_algebra->assemble(com_mod, eNoN, ptr, lK, lR);
}
}
/// @brief Reproduces Fortran 'STRUCT2D' subroutine.
//
void struct_2d(ComMod& com_mod, CepMod& cep_mod, const int eNoN, const int nFn, const double w,
const Vector<double>& N, const Array<double>& Nx, const Array<double>& al, const Array<double>& yl,
const Array<double>& dl, const Array<double>& bfl, const Array<double>& fN, const Array<double>& pS0l,
Vector<double>& pSl, const Vector<double>& ya_l, Array<double>& lR, Array3<double>& lK)
{
using namespace consts;
using namespace mat_fun;
#define n_debug_struct_2d
#ifdef debug_struct_2d
DebugMsg dmsg(__func__, com_mod.cm.idcm());
dmsg.banner();
#endif
const int dof = com_mod.dof;
int cEq = com_mod.cEq;
auto& eq = com_mod.eq[cEq];
int cDmn = com_mod.cDmn;
auto& dmn = eq.dmn[cDmn];
const double dt = com_mod.dt;
// Set parameters
//
double rho = dmn.prop.at(PhysicalProperyType::solid_density);
double mu = dmn.prop.at(PhysicalProperyType::solid_viscosity);
double dmp = dmn.prop.at(PhysicalProperyType::damping);
Vector<double> fb({dmn.prop.at(PhysicalProperyType::f_x), dmn.prop.at(PhysicalProperyType::f_y)});
double afu = eq.af * eq.beta*dt*dt;
double afv = eq.af * eq.gam*dt;
double amd = eq.am * rho + eq.af * eq.gam * dt * dmp;
double afl = eq.af * eq.beta * dt * dt;
int i = eq.s;
int j = i + 1;
#ifdef debug_struct_2d
debug << "i: " << i;
debug << "j: " << j;
debug << "amd: " << amd;
debug << "afl: " << afl;
debug << "w: " << w;
#endif
// Inertia, body force and deformation tensor (F)
//
Array<double> F(2,2), S0(2,2), vx(2,2);
Vector<double> ud(2);
ud = -rho*fb;
F = 0.0;
F(0,0) = 1.0;
F(1,1) = 1.0;
S0 = 0.0;
double ya_g = 0.0;
for (int a = 0; a < eNoN; a++) {
ud(0) = ud(0) + N(a)*(rho*(al(i,a)-bfl(0,a)) + dmp*yl(i,a));
ud(1) = ud(1) + N(a)*(rho*(al(j,a)-bfl(1,a)) + dmp*yl(j,a));
vx(0,0) = vx(0,0) + Nx(0,a)*yl(i,a);
vx(0,1) = vx(0,1) + Nx(1,a)*yl(i,a);
vx(1,0) = vx(1,0) + Nx(0,a)*yl(j,a);
vx(1,1) = vx(1,1) + Nx(1,a)*yl(j,a);
F(0,0) = F(0,0) + Nx(0,a)*dl(i,a);
F(0,1) = F(0,1) + Nx(1,a)*dl(i,a);
F(1,0) = F(1,0) + Nx(0,a)*dl(j,a);
F(1,1) = F(1,1) + Nx(1,a)*dl(j,a);
S0(0,0) = S0(0,0) + N(a)*pS0l(0,a);
S0(1,1) = S0(1,1) + N(a)*pS0l(1,a);
S0(0,1) = S0(0,1) + N(a)*pS0l(2,a);
ya_g = ya_g + N(a)*ya_l(a);
}
#ifdef debug_struct_2d
debug << "ud: " << ud(0) << " " << ud(1);
debug << "F: " << F(0,0);
debug << "ya_g: " << ya_g;
#endif
S0(1,0) = S0(0,1);
double Jac = mat_det(F, 2);
auto Fi = mat_inv(F, 2);
// Viscous contribution
// Velocity gradient in current configuration
auto VxFi = mat_mul(vx, Fi);
// Deviatoric strain tensor
auto ddev = mat_dev(mat_symm(VxFi,2), 2);
// 2nd Piola-Kirchhoff stress due to viscosity
auto Svis = mat_mul(ddev, transpose(Fi));
Svis = 2.0 * mu * Jac * mat_mul(Fi, Svis);
Array<double> S(2,2), Dm(3,3);
mat_models::get_pk2cc(com_mod, cep_mod, dmn, F, nFn, fN, ya_g, S, Dm);
// Elastic + Viscous stresses
S = S + Svis;
// Prestress
pSl(0) = S(0,0);
pSl(1) = S(1,1);
pSl(2) = S(0,1);
// Total 2nd Piola-Kirchhoff stress
S = S + S0;
// 1st Piola-Kirchhoff tensor (P)
//
Array<double> P(2,2), DBm(3,2);
Array3<double> Bm(3,2,eNoN);
P = mat_fun::mat_mul(F, S);
#ifdef debug_struct_2d
debug << "P: " << P(0,0) << " " << P(0,1);
debug << " " << P(1,0) << " " << P(1,1);
#endif
// Local residual
for (int a = 0; a < eNoN; a++) {
lR(0,a) = lR(0,a) + w*(N(a)*ud(0) + Nx(0,a)*P(0,0) + Nx(2,a)*P(0,1));
lR(1,a) = lR(1,a) + w*(N(a)*ud(1) + Nx(0,a)*P(1,0) + Nx(1,a)*P(1,1));
}
// Auxilary quantities for computing stiffness tensor
//
for (int a = 0; a < eNoN; a++) {
Bm(0,0,a) = Nx(0,a)*F(0,0);
Bm(0,1,a) = Nx(0,a)*F(1,0);
Bm(1,0,a) = Nx(1,a)*F(0,1);
Bm(1,1,a) = Nx(1,a)*F(1,1);
Bm(2,0,a) = (Nx(0,a)*F(0,1) + F(0,0)*Nx(1,a));
Bm(2,1,a) = (Nx(0,a)*F(1,1) + F(1,0)*Nx(1,a));
}
Array<double> NxFi(2,eNoN), DdNx(2,eNoN), VxNx(2,eNoN);
for (int a = 0; a < eNoN; a++) {
NxFi(0,a) = Nx(0,a)*Fi(0,0) + Nx(1,a)*Fi(1,0);
NxFi(1,a) = Nx(0,a)*Fi(0,1) + Nx(1,a)*Fi(1,1);
DdNx(0,a) = ddev(0,0)*NxFi(0,a) + ddev(0,1)*NxFi(1,a);
DdNx(1,a) = ddev(1,0)*NxFi(0,a) + ddev(1,1)*NxFi(1,a);
VxNx(0,a) = VxFi(0,0)*NxFi(0,a) + VxFi(1,0)*NxFi(1,a);
VxNx(1,a) = VxFi(0,1)*NxFi(0,a) + VxFi(1,1)*NxFi(1,a);
}
// Local stiffness tensor
//
double rmu = afu*mu*Jac;
double rmv = afv*mu*Jac;
double T1, Tv, NxNx, NxSNx, BmDBm;
for (int b = 0; b < eNoN; b++) {
for (int a = 0; a < eNoN; a++) {
// Geometric stiffness
NxSNx = Nx(0,a)*S(0,0)*Nx(0,b) + Nx(1,a)*S(1,0)*Nx(0,b) +
Nx(0,a)*S(0,1)*Nx(1,b) + Nx(1,a)*S(1,1)*Nx(1,b);
T1 = amd*N(a)*N(b) + afu*NxSNx;
// Material stiffness (Bt*D*B)
DBm(0,0) = Dm(0,0)*Bm(0,0,b) + Dm(0,1)*Bm(1,0,b) + Dm(0,2)*Bm(2,0,b);
DBm(0,1) = Dm(0,0)*Bm(0,1,b) + Dm(0,1)*Bm(1,1,b) + Dm(0,2)*Bm(2,1,b);
DBm(1,0) = Dm(1,0)*Bm(0,0,b) + Dm(1,1)*Bm(1,0,b) + Dm(1,2)*Bm(2,0,b);
DBm(1,1) = Dm(1,0)*Bm(0,1,b) + Dm(1,1)*Bm(1,1,b) + Dm(1,2)*Bm(2,1,b);
DBm(2,0) = Dm(2,0)*Bm(0,0,b) + Dm(2,1)*Bm(1,0,b) + Dm(2,2)*Bm(2,0,b);
DBm(2,1) = Dm(2,0)*Bm(0,1,b) + Dm(2,1)*Bm(1,1,b) + Dm(2,2)*Bm(2,1,b);
NxNx = NxFi(0,a)*NxFi(0,b) + NxFi(1,a)*NxFi(1,b);
// dM1/du1
// Material stiffness: Bt*D*B
BmDBm = Bm(0,0,a)*DBm(0,0) + Bm(1,0,a)*DBm(1,0) + Bm(2,0,a)*DBm(2,0);
// Viscous terms contribution
Tv = (2.0*(DdNx(0,a)*NxFi(0,b) - DdNx(0,b)*NxFi(0,a)) - (NxNx*VxFi(0,0) + NxFi(0,b)*VxNx(0,a) -
NxFi(0,a)*VxNx(0,b))) * rmu + (NxNx) * rmv;
lK(0,a,b) = lK(0,a,b) + w*(T1 + afu*BmDBm + Tv);
// dM1/du2
// Material stiffness: Bt*D*B
BmDBm = Bm(0,0,a)*DBm(0,1) + Bm(1,0,a)*DBm(1,1) + Bm(2,0,a)*DBm(2,1);
// Viscous terms contribution
Tv = (2.0*(DdNx(0,a)*NxFi(1,b) - DdNx(0,b)*NxFi(1,a)) -
(NxNx*VxFi(0,1) + NxFi(0,b)*VxNx(1,a) -
NxFi(0,a)*VxNx(1,b))) * rmu + (NxFi(1,a)*NxFi(0,b) -
NxFi(0,a)*NxFi(1,b)) * rmv;
lK(1,a,b) = lK(1,a,b) + w*(afu*BmDBm + Tv);
// dM2/du1
// Material stiffness: Bt*D*B
BmDBm = Bm(0,1,a)*DBm(0,0) + Bm(1,1,a)*DBm(1,0) + Bm(2,1,a)*DBm(2,0);
// Viscous terms contribution
Tv = (2.0*(DdNx(1,a)*NxFi(0,b) - DdNx(1,b)*NxFi(0,a)) -
(NxNx*VxFi(1,0) + NxFi(1,b)*VxNx(0,a) -
NxFi(1,a)*VxNx(0,b))) * rmu + (NxFi(0,a)*NxFi(1,b) -
NxFi(1,a)*NxFi(0,b)) * rmv;
lK(dof+0,a,b) = lK(dof+0,a,b) + w*(afu*BmDBm + Tv);
// dM2/du2
// Material stiffness: Bt*D*B
BmDBm = Bm(0,1,a)*DBm(0,1) + Bm(1,1,a)*DBm(1,1) + Bm(2,1,a)*DBm(2,1);
// Viscous terms contribution
Tv = (2.0*(DdNx(1,a)*NxFi(1,b) - DdNx(1,b)*NxFi(1,a)) - (NxNx*VxFi(1,1) + NxFi(1,b)*VxNx(1,a)
- NxFi(1,a)*VxNx(1,b))) * rmu + (NxNx) * rmv;
lK(dof+1,a,b) = lK(dof+1,a,b) + w*(T1 + afu*BmDBm + Tv);
}
}
}
/// @brief Reproduces Fortran 'STRUCT3D' subroutine using C++ arrays.
//
void struct_3d_carray(ComMod& com_mod, CepMod& cep_mod, const int eNoN, const int nFn, const double w,
const Vector<double>& N, const Array<double>& Nx, const Array<double>& al, const Array<double>& yl,
const Array<double>& dl, const Array<double>& bfl, const Array<double>& fN, const Array<double>& pS0l,
Vector<double>& pSl, const Vector<double>& ya_l, Array<double>& lR, Array3<double>& lK)
{
using namespace consts;
using namespace mat_fun;
#define n_debug_struct_3d
#ifdef debug_struct_3d
DebugMsg dmsg(__func__, com_mod.cm.idcm());
dmsg.banner();
dmsg << "eNoN: " << eNoN;
dmsg << "nFn: " << nFn;
#endif
const int dof = com_mod.dof;
int cEq = com_mod.cEq;
auto& eq = com_mod.eq[cEq];
int cDmn = com_mod.cDmn;
auto& dmn = eq.dmn[cDmn];
const double dt = com_mod.dt;
// Set parameters
//
double rho = dmn.prop.at(PhysicalProperyType::solid_density);
double mu = dmn.prop.at(PhysicalProperyType::solid_viscosity);
double dmp = dmn.prop.at(PhysicalProperyType::damping);
double fb[3]{dmn.prop.at(PhysicalProperyType::f_x),
dmn.prop.at(PhysicalProperyType::f_y),
dmn.prop.at(PhysicalProperyType::f_z)};
double afu = eq.af * eq.beta*dt*dt;
double afv = eq.af * eq.gam*dt;
double amd = eq.am * rho + eq.af * eq.gam * dt * dmp;
#ifdef debug_struct_3d
dmsg << "rho: " << rho;
dmsg << "mu: " << mu;
dmsg << "dmp: " << dmp;
dmsg << "afu: " << afu;
dmsg << "afv: " << afv;
dmsg << "amd: " << amd;
#endif
int i = eq.s;
int j = i + 1;
int k = j + 1;
// Inertia, body force and deformation tensor (F)
//
double F[3][3]={};
double S0[3][3]={};
double vx[3][3]={};
double ud[3] = {-rho*fb[0], -rho*fb[1], -rho*fb[2]};
F[0][0] = 1.0;
F[1][1] = 1.0;
F[2][2] = 1.0;
double ya_g = 0.0;
for (int a = 0; a < eNoN; a++) {
ud[0] += N(a)*(rho*(al(i,a)-bfl(0,a)) + dmp*yl(i,a));
ud[1] += N(a)*(rho*(al(j,a)-bfl(1,a)) + dmp*yl(j,a));
ud[2] += N(a)*(rho*(al(k,a)-bfl(2,a)) + dmp*yl(k,a));
vx[0][0] += Nx(0,a)*yl(i,a);
vx[0][1] += Nx(1,a)*yl(i,a);
vx[0][2] += Nx(2,a)*yl(i,a);
vx[1][0] += Nx(0,a)*yl(j,a);
vx[1][1] += Nx(1,a)*yl(j,a);
vx[1][2] += Nx(2,a)*yl(j,a);
vx[2][0] += Nx(0,a)*yl(k,a);
vx[2][1] += Nx(1,a)*yl(k,a);
vx[2][2] += Nx(2,a)*yl(k,a);
F[0][0] += Nx(0,a)*dl(i,a);
F[0][1] += Nx(1,a)*dl(i,a);
F[0][2] += Nx(2,a)*dl(i,a);
F[1][0] += Nx(0,a)*dl(j,a);
F[1][1] += Nx(1,a)*dl(j,a);
F[1][2] += Nx(2,a)*dl(j,a);
F[2][0] += Nx(0,a)*dl(k,a);
F[2][1] += Nx(1,a)*dl(k,a);
F[2][2] += Nx(2,a)*dl(k,a);
S0[0][0] += N(a)*pS0l(0,a);
S0[1][1] += N(a)*pS0l(1,a);
S0[2][2] += N(a)*pS0l(2,a);
S0[0][1] += N(a)*pS0l(3,a);
S0[1][2] += N(a)*pS0l(4,a);
S0[2][0] += N(a)*pS0l(5,a);
ya_g = ya_g + N(a)*ya_l(a);
}
S0[1][0] = S0[0][1];
S0[2][1] = S0[1][2];
S0[0][2] = S0[2][0];
double Jac = mat_fun_carray::mat_det<3>(F);
double Fi[3][3];
mat_fun_carray::mat_inv<3>(F, Fi);
// Viscous contribution
// Velocity gradient in current configuration
double VxFi[3][3];
mat_fun_carray::mat_mul(vx, Fi, VxFi);
// Deviatoric strain tensor
double VxFi_sym[3][3];
mat_fun_carray::mat_symm<3>(VxFi,VxFi_sym);
double ddev[3][3];
mat_fun_carray::mat_dev<3>(VxFi_sym, ddev);
// 2nd Piola-Kirchhoff stress due to viscosity
double Fi_transp[3][3];
mat_fun_carray::transpose<3>(Fi, Fi_transp);
double Svis[3][3];
mat_fun_carray::mat_mul<3>(ddev, Fi_transp, Svis);
double Fi_Svis_m[3][3];
mat_fun_carray::mat_mul<3>(Fi, Svis, Fi_Svis_m);
for (int i = 0; i < 3; i++) {
for (int j = 0; j < 3; j++) {
Svis[i][j] = 2.0 * mu * Jac * Fi_Svis_m[i][j];
}
}
// Initialize tensor indexing.
mat_fun_carray::ten_init(3);
// 2nd Piola-Kirchhoff tensor (S) and material stiffness tensor in
// Voigt notationa (Dm)
//
double S[3][3];
double Dm[6][6];
mat_models_carray::get_pk2cc<3>(com_mod, cep_mod, dmn, F, nFn, fN, ya_g, S, Dm);
// Elastic + Viscous stresses
for (int i = 0; i < 3; i++) {
for (int j = 0; j < 3; j++) {
S[i][j] += Svis[i][j];
}
}
#ifdef debug_struct_3d
dmsg << "Jac: " << Jac;
dmsg << "Fi: " << Fi;
dmsg << "VxFi: " << VxFi;
dmsg << "ddev: " << ddev;
dmsg << "S: " << S;
#endif
// Prestress
pSl(0) = S[0][0];
pSl(1) = S[1][1];
pSl(2) = S[2][2];
pSl(3) = S[0][1];
pSl(4) = S[1][2];
pSl(5) = S[2][0];
// Total 2nd Piola-Kirchhoff stress
for (int i = 0; i < 3; i++) {
for (int j = 0; j < 3; j++) {
S[i][j] += S0[i][j];
}
}
// 1st Piola-Kirchhoff tensor (P)
//
double P[3][3];
mat_fun_carray::mat_mul<3>(F, S, P);
// Local residual
for (int a = 0; a < eNoN; a++) {
lR(0,a) = lR(0,a) + w*(N(a)*ud[0] + Nx(0,a)*P[0][0] + Nx(1,a)*P[0][1] + Nx(2,a)*P[0][2]);
lR(1,a) = lR(1,a) + w*(N(a)*ud[1] + Nx(0,a)*P[1][0] + Nx(1,a)*P[1][1] + Nx(2,a)*P[1][2]);
lR(2,a) = lR(2,a) + w*(N(a)*ud[2] + Nx(0,a)*P[2][0] + Nx(1,a)*P[2][1] + Nx(2,a)*P[2][2]);
}
// Auxilary quantities for computing stiffness tensor
//
Array3<double> Bm(6,3,eNoN);
for (int a = 0; a < eNoN; a++) {
Bm(0,0,a) = Nx(0,a)*F[0][0];
Bm(0,1,a) = Nx(0,a)*F[1][0];
Bm(0,2,a) = Nx(0,a)*F[2][0];
Bm(1,0,a) = Nx(1,a)*F[0][1];
Bm(1,1,a) = Nx(1,a)*F[1][1];
Bm(1,2,a) = Nx(1,a)*F[2][1];
Bm(2,0,a) = Nx(2,a)*F[0][2];
Bm(2,1,a) = Nx(2,a)*F[1][2];
Bm(2,2,a) = Nx(2,a)*F[2][2];
Bm(3,0,a) = (Nx(0,a)*F[0][1] + F[0][0]*Nx(1,a));
Bm(3,1,a) = (Nx(0,a)*F[1][1] + F[1][0]*Nx(1,a));
Bm(3,2,a) = (Nx(0,a)*F[2][1] + F[2][0]*Nx(1,a));
Bm(4,0,a) = (Nx(1,a)*F[0][2] + F[0][1]*Nx(2,a));
Bm(4,1,a) = (Nx(1,a)*F[1][2] + F[1][1]*Nx(2,a));
Bm(4,2,a) = (Nx(1,a)*F[2][2] + F[2][1]*Nx(2,a));
Bm(5,0,a) = (Nx(2,a)*F[0][0] + F[0][2]*Nx(0,a));
Bm(5,1,a) = (Nx(2,a)*F[1][0] + F[1][2]*Nx(0,a));
Bm(5,2,a) = (Nx(2,a)*F[2][0] + F[2][2]*Nx(0,a));
}
// Below quantities are used for viscous stress contribution
// Shape function gradients in the current configuration
//
Array<double> NxFi(3,eNoN), DdNx(3,eNoN), VxNx(3,eNoN);
for (int a = 0; a < eNoN; a++) {
NxFi(0,a) = Nx(0,a)*Fi[0][0] + Nx(1,a)*Fi[1][0] + Nx(2,a)*Fi[2][0];
NxFi(1,a) = Nx(0,a)*Fi[0][1] + Nx(1,a)*Fi[1][1] + Nx(2,a)*Fi[2][1];
NxFi(2,a) = Nx(0,a)*Fi[0][2] + Nx(1,a)*Fi[1][2] + Nx(2,a)*Fi[2][2];
DdNx(0,a) = ddev[0][0]*NxFi(0,a) + ddev[0][1]*NxFi(1,a) + ddev[0][2]*NxFi(2,a);
DdNx(1,a) = ddev[1][0]*NxFi(0,a) + ddev[1][1]*NxFi(1,a) + ddev[1][2]*NxFi(2,a);
DdNx(2,a) = ddev[2][0]*NxFi(0,a) + ddev[2][1]*NxFi(1,a) + ddev[2][2]*NxFi(2,a);
VxNx(0,a) = VxFi[0][0]*NxFi(0,a) + VxFi[1][0]*NxFi(1,a) + VxFi[2][0]*NxFi(2,a);
VxNx(1,a) = VxFi[0][1]*NxFi(0,a) + VxFi[1][1]*NxFi(1,a) + VxFi[2][1]*NxFi(2,a);
VxNx(2,a) = VxFi[0][2]*NxFi(0,a) + VxFi[1][2]*NxFi(1,a) + VxFi[2][2]*NxFi(2,a);
}
// Local stiffness tensor
double r13 = 1.0 / 3.0;
double r23 = 2.0 / 3.0;
double rmu = afu * mu * Jac;
double rmv = afv * mu * Jac;
double NxSNx, T1, NxNx, BmDBm, Tv;
Array<double> DBm(6,3);
for (int b = 0; b < eNoN; b++) {
for (int a = 0; a < eNoN; a++) {
// Geometric stiffness
NxSNx = Nx(0,a)*S[0][0]*Nx(0,b) + Nx(1,a)*S[1][0]*Nx(0,b) +
Nx(2,a)*S[2][0]*Nx(0,b) + Nx(0,a)*S[0][1]*Nx(1,b) +
Nx(1,a)*S[1][1]*Nx(1,b) + Nx(2,a)*S[2][1]*Nx(1,b) +
Nx(0,a)*S[0][2]*Nx(2,b) + Nx(1,a)*S[1][2]*Nx(2,b) +
Nx(2,a)*S[2][2]*Nx(2,b);
T1 = amd*N(a)*N(b) + afu*NxSNx;
// Material Stiffness (Bt*D*B)
mat_fun_carray::mat_mul6x3<3>(Dm, Bm.rslice(b), DBm);
NxNx = NxFi(0,a)*NxFi(0,b) + NxFi(1,a)*NxFi(1,b) + NxFi(2,a)*NxFi(2,b);
// dM1/du1
// Material stiffness: Bt*D*B
BmDBm = Bm(0,0,a)*DBm(0,0) + Bm(1,0,a)*DBm(1,0) +
Bm(2,0,a)*DBm(2,0) + Bm(3,0,a)*DBm(3,0) +
Bm(4,0,a)*DBm(4,0) + Bm(5,0,a)*DBm(5,0);
// Viscous terms contribution
Tv = (2.0*(DdNx(0,a)*NxFi(0,b) - DdNx(0,b)*NxFi(0,a)) - (NxNx*VxFi[0][0] + NxFi(0,b)*VxNx(0,a) -
r23*NxFi(0,a)*VxNx(0,b))) * rmu + (r13*NxFi(0,a)*NxFi(0,b) + NxNx) * rmv;
lK(0,a,b) = lK(0,a,b) + w*(T1 + afu*BmDBm + Tv);
// dM1/du2
// Material stiffness: Bt*D*B
BmDBm = Bm(0,0,a)*DBm(0,1) + Bm(1,0,a)*DBm(1,1) +
Bm(2,0,a)*DBm(2,1) + Bm(3,0,a)*DBm(3,1) +
Bm(4,0,a)*DBm(4,1) + Bm(5,0,a)*DBm(5,1);
// Viscous terms contribution
Tv = (2.0*(DdNx(0,a)*NxFi(1,b) - DdNx(0,b)*NxFi(1,a))
- (NxNx*VxFi[0][1] + NxFi(0,b)*VxNx(1,a)
- r23*NxFi(0,a)*VxNx(1,b))) * rmu
+ (NxFi(1,a)*NxFi(0,b) - r23*NxFi(0,a)*NxFi(1,b)) * rmv;
lK(1,a,b) = lK(1,a,b) + w*(afu*BmDBm + Tv);
// dM1/du3
// Material stiffness: Bt*D*B
BmDBm = Bm(0,0,a)*DBm(0,2) + Bm(1,0,a)*DBm(1,2) +
Bm(2,0,a)*DBm(2,2) + Bm(3,0,a)*DBm(3,2) +
Bm(4,0,a)*DBm(4,2) + Bm(5,0,a)*DBm(5,2);
// Viscous terms contribution
Tv = (2.0*(DdNx(0,a)*NxFi(2,b) - DdNx(0,b)*NxFi(2,a)) -
(NxNx*VxFi[0][2] + NxFi(0,b)*VxNx(2,a) -
r23*NxFi(0,a)*VxNx(2,b))) * rmu +
(NxFi(2,a)*NxFi(0,b) - r23*NxFi(0,a)*NxFi(2,b)) * rmv;
lK(2,a,b) = lK(2,a,b) + w*(afu*BmDBm + Tv);
// dM2/du1
// Material stiffness: Bt*D*B
BmDBm = Bm(0,1,a)*DBm(0,0) + Bm(1,1,a)*DBm(1,0) +
Bm(2,1,a)*DBm(2,0) + Bm(3,1,a)*DBm(3,0) +
Bm(4,1,a)*DBm(4,0) + Bm(5,1,a)*DBm(5,0);
// Viscous terms contribution
Tv = (2.0*(DdNx(1,a)*NxFi(0,b) - DdNx(1,b)*NxFi(0,a)) -
(NxNx*VxFi[1][0] + NxFi(1,b)*VxNx(0,a) -
r23*NxFi(1,a)*VxNx(0,b))) * rmu +
(NxFi(0,a)*NxFi(1,b) - r23*NxFi(1,a)*NxFi(0,b)) * rmv;
lK(dof+0,a,b) = lK(dof+0,a,b) + w*(afu*BmDBm + Tv);
// dM2/du2
// Material stiffness: Bt*D*B
BmDBm = Bm(0,1,a)*DBm(0,1) + Bm(1,1,a)*DBm(1,1) +
Bm(2,1,a)*DBm(2,1) + Bm(3,1,a)*DBm(3,1) +
Bm(4,1,a)*DBm(4,1) + Bm(5,1,a)*DBm(5,1);
// Viscous terms contribution
Tv = (2.0*(DdNx(1,a)*NxFi(1,b) - DdNx(1,b)*NxFi(1,a)) -
(NxNx*VxFi[1][1] + NxFi(1,b)*VxNx(1,a) -
r23*NxFi(1,a)*VxNx(1,b))) * rmu +
(r13*NxFi(1,a)*NxFi(1,b) + NxNx) * rmv;
lK(dof+1,a,b) = lK(dof+1,a,b) + w*(T1 + afu*BmDBm + Tv);
// dM2/du3
// Material stiffness: Bt*D*B
BmDBm = Bm(0,1,a)*DBm(0,2) + Bm(1,1,a)*DBm(1,2) +
Bm(2,1,a)*DBm(2,2) + Bm(3,1,a)*DBm(3,2) +
Bm(4,1,a)*DBm(4,2) + Bm(5,1,a)*DBm(5,2);
// Viscous terms contribution
Tv = (2.0*(DdNx(1,a)*NxFi(2,b) - DdNx(1,b)*NxFi(2,a)) -
(NxNx*VxFi[1][2] + NxFi(1,b)*VxNx(2,a) -
r23*NxFi(1,a)*VxNx(2,b))) * rmu + (NxFi(2,a)*NxFi(1,b) -
r23*NxFi(1,a)*NxFi(2,b)) * rmv;
lK(dof+2,a,b) = lK(dof+2,a,b) + w*(afu*BmDBm + Tv);
// dM3/du1
// Material stiffness: Bt*D*B
BmDBm = Bm(0,2,a)*DBm(0,0) + Bm(1,2,a)*DBm(1,0) +
Bm(2,2,a)*DBm(2,0) + Bm(3,2,a)*DBm(3,0) +
Bm(4,2,a)*DBm(4,0) + Bm(5,2,a)*DBm(5,0);
// Viscous terms contribution
Tv = (2.0*(DdNx(2,a)*NxFi(0,b) - DdNx(2,b)*NxFi(0,a)) -
(NxNx*VxFi[2][0] + NxFi(2,b)*VxNx(0,a) -
r23*NxFi(2,a)*VxNx(0,b))) * rmu + (NxFi(0,a)*NxFi(2,b) -
r23*NxFi(2,a)*NxFi(0,b)) * rmv;
lK(2*dof+0,a,b) = lK(2*dof+0,a,b) + w*(afu*BmDBm + Tv);
// dM3/du2
// Material stiffness: Bt*D*B
BmDBm = Bm(0,2,a)*DBm(0,1) + Bm(1,2,a)*DBm(1,1) +
Bm(2,2,a)*DBm(2,1) + Bm(3,2,a)*DBm(3,1) +
Bm(4,2,a)*DBm(4,1) + Bm(5,2,a)*DBm(5,1);
// Viscous terms contribution
Tv = (2.0*(DdNx(2,a)*NxFi(1,b) - DdNx(2,b)*NxFi(1,a)) -
(NxNx*VxFi[2][1] + NxFi(2,b)*VxNx(1,a) -
r23*NxFi(2,a)*VxNx(1,b))) * rmu + (NxFi(1,a)*NxFi(2,b) -
r23*NxFi(2,a)*NxFi(1,b)) * rmv;
lK(2*dof+1,a,b) = lK(2*dof+1,a,b) + w*(afu*BmDBm + Tv);
// dM3/du3
// Material stiffness: Bt*D*B
BmDBm = Bm(0,2,a)*DBm(0,2) + Bm(1,2,a)*DBm(1,2) +
Bm(2,2,a)*DBm(2,2) + Bm(3,2,a)*DBm(3,2) +
Bm(4,2,a)*DBm(4,2) + Bm(5,2,a)*DBm(5,2);
// Viscous terms contribution
Tv = (2.0*(DdNx(2,a)*NxFi(2,b) - DdNx(2,b)*NxFi(2,a)) -
(NxNx*VxFi[2][2] + NxFi(2,b)*VxNx(2,a) -
r23*NxFi(2,a)*VxNx(2,b))) * rmu +
(r13*NxFi(2,a)*NxFi(2,b) + NxNx) * rmv;
lK(2*dof+2,a,b) = lK(2*dof+2,a,b) + w*(T1 + afu*BmDBm + Tv);
}
}
}
/// @brief Reproduces Fortran 'STRUCT3D' subroutine.
//
void struct_3d(ComMod& com_mod, CepMod& cep_mod, const int eNoN, const int nFn, const double w,
const Vector<double>& N, const Array<double>& Nx, const Array<double>& al, const Array<double>& yl,
const Array<double>& dl, const Array<double>& bfl, const Array<double>& fN, const Array<double>& pS0l,
Vector<double>& pSl, const Vector<double>& ya_l, Array<double>& lR, Array3<double>& lK)
{
using namespace consts;
using namespace mat_fun;
// std::cout << "\n==================== struct_3d ===============" << std::endl;
#define n_debug_struct_3d
#ifdef debug_struct_3d
DebugMsg dmsg(__func__, com_mod.cm.idcm());
dmsg.banner();
dmsg << "eNoN: " << eNoN;
dmsg << "nFn: " << nFn;
#endif