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-/*
- Written by Xuchen Han <xuchenhan2015@u.northwestern.edu>
-
- Bullet Continuous Collision Detection and Physics Library
- Copyright (c) 2019 Google Inc. http://bulletphysics.org
- This software is provided 'as-is', without any express or implied warranty.
- In no event will the authors be held liable for any damages arising from the use of this software.
- Permission is granted to anyone to use this software for any purpose,
- including commercial applications, and to alter it and redistribute it freely,
- subject to the following restrictions:
- 1. The origin of this software must not be misrepresented; you must not claim that you wrote the original software. If you use this software in a product, an acknowledgment in the product documentation would be appreciated but is not required.
- 2. Altered source versions must be plainly marked as such, and must not be misrepresented as being the original software.
- 3. This notice may not be removed or altered from any source distribution.
- */
-
-#ifndef BT_LINEAR_ELASTICITY_H
-#define BT_LINEAR_ELASTICITY_H
-
-#include "btDeformableLagrangianForce.h"
-#include "LinearMath/btQuickprof.h"
-#include "btSoftBodyInternals.h"
-#define TETRA_FLAT_THRESHOLD 0.01
-class btDeformableLinearElasticityForce : public btDeformableLagrangianForce
-{
-public:
- typedef btAlignedObjectArray<btVector3> TVStack;
- btScalar m_mu, m_lambda;
- btScalar m_E, m_nu; // Young's modulus and Poisson ratio
- btScalar m_damping_alpha, m_damping_beta;
- btDeformableLinearElasticityForce() : m_mu(1), m_lambda(1), m_damping_alpha(0.01), m_damping_beta(0.01)
- {
- updateYoungsModulusAndPoissonRatio();
- }
-
- btDeformableLinearElasticityForce(btScalar mu, btScalar lambda, btScalar damping_alpha = 0.01, btScalar damping_beta = 0.01) : m_mu(mu), m_lambda(lambda), m_damping_alpha(damping_alpha), m_damping_beta(damping_beta)
- {
- updateYoungsModulusAndPoissonRatio();
- }
-
- void updateYoungsModulusAndPoissonRatio()
- {
- // conversion from Lame Parameters to Young's modulus and Poisson ratio
- // https://en.wikipedia.org/wiki/Lam%C3%A9_parameters
- m_E = m_mu * (3 * m_lambda + 2 * m_mu) / (m_lambda + m_mu);
- m_nu = m_lambda * 0.5 / (m_mu + m_lambda);
- }
-
- void updateLameParameters()
- {
- // conversion from Young's modulus and Poisson ratio to Lame Parameters
- // https://en.wikipedia.org/wiki/Lam%C3%A9_parameters
- m_mu = m_E * 0.5 / (1 + m_nu);
- m_lambda = m_E * m_nu / ((1 + m_nu) * (1 - 2 * m_nu));
- }
-
- void setYoungsModulus(btScalar E)
- {
- m_E = E;
- updateLameParameters();
- }
-
- void setPoissonRatio(btScalar nu)
- {
- m_nu = nu;
- updateLameParameters();
- }
-
- void setDamping(btScalar damping_alpha, btScalar damping_beta)
- {
- m_damping_alpha = damping_alpha;
- m_damping_beta = damping_beta;
- }
-
- void setLameParameters(btScalar mu, btScalar lambda)
- {
- m_mu = mu;
- m_lambda = lambda;
- updateYoungsModulusAndPoissonRatio();
- }
-
- virtual void addScaledForces(btScalar scale, TVStack& force)
- {
- addScaledDampingForce(scale, force);
- addScaledElasticForce(scale, force);
- }
-
- virtual void addScaledExplicitForce(btScalar scale, TVStack& force)
- {
- addScaledElasticForce(scale, force);
- }
-
- // The damping matrix is calculated using the time n state as described in https://www.math.ucla.edu/~jteran/papers/GSSJT15.pdf to allow line search
- virtual void addScaledDampingForce(btScalar scale, TVStack& force)
- {
- if (m_damping_alpha == 0 && m_damping_beta == 0)
- return;
- btScalar mu_damp = m_damping_beta * m_mu;
- btScalar lambda_damp = m_damping_beta * m_lambda;
- int numNodes = getNumNodes();
- btAssert(numNodes <= force.size());
- btVector3 grad_N_hat_1st_col = btVector3(-1, -1, -1);
- for (int i = 0; i < m_softBodies.size(); ++i)
- {
- btSoftBody* psb = m_softBodies[i];
- if (!psb->isActive())
- {
- continue;
- }
- for (int j = 0; j < psb->m_tetras.size(); ++j)
- {
- bool close_to_flat = (psb->m_tetraScratches[j].m_J < TETRA_FLAT_THRESHOLD);
- btSoftBody::Tetra& tetra = psb->m_tetras[j];
- btSoftBody::Node* node0 = tetra.m_n[0];
- btSoftBody::Node* node1 = tetra.m_n[1];
- btSoftBody::Node* node2 = tetra.m_n[2];
- btSoftBody::Node* node3 = tetra.m_n[3];
- size_t id0 = node0->index;
- size_t id1 = node1->index;
- size_t id2 = node2->index;
- size_t id3 = node3->index;
- btMatrix3x3 dF = DsFromVelocity(node0, node1, node2, node3) * tetra.m_Dm_inverse;
- if (!close_to_flat)
- {
- dF = psb->m_tetraScratches[j].m_corotation.transpose() * dF;
- }
- btMatrix3x3 I;
- I.setIdentity();
- btMatrix3x3 dP = (dF + dF.transpose()) * mu_damp + I * ((dF[0][0] + dF[1][1] + dF[2][2]) * lambda_damp);
- btMatrix3x3 df_on_node123 = dP * tetra.m_Dm_inverse.transpose();
- if (!close_to_flat)
- {
- df_on_node123 = psb->m_tetraScratches[j].m_corotation * df_on_node123;
- }
- btVector3 df_on_node0 = df_on_node123 * grad_N_hat_1st_col;
- // damping force differential
- btScalar scale1 = scale * tetra.m_element_measure;
- force[id0] -= scale1 * df_on_node0;
- force[id1] -= scale1 * df_on_node123.getColumn(0);
- force[id2] -= scale1 * df_on_node123.getColumn(1);
- force[id3] -= scale1 * df_on_node123.getColumn(2);
- }
- for (int j = 0; j < psb->m_nodes.size(); ++j)
- {
- const btSoftBody::Node& node = psb->m_nodes[j];
- size_t id = node.index;
- if (node.m_im > 0)
- {
- force[id] -= scale * node.m_v / node.m_im * m_damping_alpha;
- }
- }
- }
- }
-
- virtual double totalElasticEnergy(btScalar dt)
- {
- double energy = 0;
- for (int i = 0; i < m_softBodies.size(); ++i)
- {
- btSoftBody* psb = m_softBodies[i];
- if (!psb->isActive())
- {
- continue;
- }
- for (int j = 0; j < psb->m_tetraScratches.size(); ++j)
- {
- btSoftBody::Tetra& tetra = psb->m_tetras[j];
- btSoftBody::TetraScratch& s = psb->m_tetraScratches[j];
- energy += tetra.m_element_measure * elasticEnergyDensity(s);
- }
- }
- return energy;
- }
-
- // The damping energy is formulated as in https://www.math.ucla.edu/~jteran/papers/GSSJT15.pdf to allow line search
- virtual double totalDampingEnergy(btScalar dt)
- {
- double energy = 0;
- int sz = 0;
- for (int i = 0; i < m_softBodies.size(); ++i)
- {
- btSoftBody* psb = m_softBodies[i];
- if (!psb->isActive())
- {
- continue;
- }
- for (int j = 0; j < psb->m_nodes.size(); ++j)
- {
- sz = btMax(sz, psb->m_nodes[j].index);
- }
- }
- TVStack dampingForce;
- dampingForce.resize(sz + 1);
- for (int i = 0; i < dampingForce.size(); ++i)
- dampingForce[i].setZero();
- addScaledDampingForce(0.5, dampingForce);
- for (int i = 0; i < m_softBodies.size(); ++i)
- {
- btSoftBody* psb = m_softBodies[i];
- for (int j = 0; j < psb->m_nodes.size(); ++j)
- {
- const btSoftBody::Node& node = psb->m_nodes[j];
- energy -= dampingForce[node.index].dot(node.m_v) / dt;
- }
- }
- return energy;
- }
-
- double elasticEnergyDensity(const btSoftBody::TetraScratch& s)
- {
- double density = 0;
- btMatrix3x3 epsilon = (s.m_F + s.m_F.transpose()) * 0.5 - btMatrix3x3::getIdentity();
- btScalar trace = epsilon[0][0] + epsilon[1][1] + epsilon[2][2];
- density += m_mu * (epsilon[0].length2() + epsilon[1].length2() + epsilon[2].length2());
- density += m_lambda * trace * trace * 0.5;
- return density;
- }
-
- virtual void addScaledElasticForce(btScalar scale, TVStack& force)
- {
- int numNodes = getNumNodes();
- btAssert(numNodes <= force.size());
- btVector3 grad_N_hat_1st_col = btVector3(-1, -1, -1);
- for (int i = 0; i < m_softBodies.size(); ++i)
- {
- btSoftBody* psb = m_softBodies[i];
- if (!psb->isActive())
- {
- continue;
- }
- btScalar max_p = psb->m_cfg.m_maxStress;
- for (int j = 0; j < psb->m_tetras.size(); ++j)
- {
- btSoftBody::Tetra& tetra = psb->m_tetras[j];
- btMatrix3x3 P;
- firstPiola(psb->m_tetraScratches[j], P);
-#if USE_SVD
- if (max_p > 0)
- {
- // since we want to clamp the principal stress to max_p, we only need to
- // calculate SVD when sigma_0^2 + sigma_1^2 + sigma_2^2 > max_p * max_p
- btScalar trPTP = (P[0].length2() + P[1].length2() + P[2].length2());
- if (trPTP > max_p * max_p)
- {
- btMatrix3x3 U, V;
- btVector3 sigma;
- singularValueDecomposition(P, U, sigma, V);
- sigma[0] = btMin(sigma[0], max_p);
- sigma[1] = btMin(sigma[1], max_p);
- sigma[2] = btMin(sigma[2], max_p);
- sigma[0] = btMax(sigma[0], -max_p);
- sigma[1] = btMax(sigma[1], -max_p);
- sigma[2] = btMax(sigma[2], -max_p);
- btMatrix3x3 Sigma;
- Sigma.setIdentity();
- Sigma[0][0] = sigma[0];
- Sigma[1][1] = sigma[1];
- Sigma[2][2] = sigma[2];
- P = U * Sigma * V.transpose();
- }
- }
-#endif
- // btVector3 force_on_node0 = P * (tetra.m_Dm_inverse.transpose()*grad_N_hat_1st_col);
- btMatrix3x3 force_on_node123 = psb->m_tetraScratches[j].m_corotation * P * tetra.m_Dm_inverse.transpose();
- btVector3 force_on_node0 = force_on_node123 * grad_N_hat_1st_col;
-
- btSoftBody::Node* node0 = tetra.m_n[0];
- btSoftBody::Node* node1 = tetra.m_n[1];
- btSoftBody::Node* node2 = tetra.m_n[2];
- btSoftBody::Node* node3 = tetra.m_n[3];
- size_t id0 = node0->index;
- size_t id1 = node1->index;
- size_t id2 = node2->index;
- size_t id3 = node3->index;
-
- // elastic force
- btScalar scale1 = scale * tetra.m_element_measure;
- force[id0] -= scale1 * force_on_node0;
- force[id1] -= scale1 * force_on_node123.getColumn(0);
- force[id2] -= scale1 * force_on_node123.getColumn(1);
- force[id3] -= scale1 * force_on_node123.getColumn(2);
- }
- }
- }
-
- virtual void buildDampingForceDifferentialDiagonal(btScalar scale, TVStack& diagA) {}
-
- // The damping matrix is calculated using the time n state as described in https://www.math.ucla.edu/~jteran/papers/GSSJT15.pdf to allow line search
- virtual void addScaledDampingForceDifferential(btScalar scale, const TVStack& dv, TVStack& df)
- {
- if (m_damping_alpha == 0 && m_damping_beta == 0)
- return;
- btScalar mu_damp = m_damping_beta * m_mu;
- btScalar lambda_damp = m_damping_beta * m_lambda;
- int numNodes = getNumNodes();
- btAssert(numNodes <= df.size());
- btVector3 grad_N_hat_1st_col = btVector3(-1, -1, -1);
- for (int i = 0; i < m_softBodies.size(); ++i)
- {
- btSoftBody* psb = m_softBodies[i];
- if (!psb->isActive())
- {
- continue;
- }
- for (int j = 0; j < psb->m_tetras.size(); ++j)
- {
- bool close_to_flat = (psb->m_tetraScratches[j].m_J < TETRA_FLAT_THRESHOLD);
- btSoftBody::Tetra& tetra = psb->m_tetras[j];
- btSoftBody::Node* node0 = tetra.m_n[0];
- btSoftBody::Node* node1 = tetra.m_n[1];
- btSoftBody::Node* node2 = tetra.m_n[2];
- btSoftBody::Node* node3 = tetra.m_n[3];
- size_t id0 = node0->index;
- size_t id1 = node1->index;
- size_t id2 = node2->index;
- size_t id3 = node3->index;
- btMatrix3x3 dF = Ds(id0, id1, id2, id3, dv) * tetra.m_Dm_inverse;
- if (!close_to_flat)
- {
- dF = psb->m_tetraScratches[j].m_corotation.transpose() * dF;
- }
- btMatrix3x3 I;
- I.setIdentity();
- btMatrix3x3 dP = (dF + dF.transpose()) * mu_damp + I * ((dF[0][0] + dF[1][1] + dF[2][2]) * lambda_damp);
- btMatrix3x3 df_on_node123 = dP * tetra.m_Dm_inverse.transpose();
- if (!close_to_flat)
- {
- df_on_node123 = psb->m_tetraScratches[j].m_corotation * df_on_node123;
- }
- btVector3 df_on_node0 = df_on_node123 * grad_N_hat_1st_col;
-
- // damping force differential
- btScalar scale1 = scale * tetra.m_element_measure;
- df[id0] -= scale1 * df_on_node0;
- df[id1] -= scale1 * df_on_node123.getColumn(0);
- df[id2] -= scale1 * df_on_node123.getColumn(1);
- df[id3] -= scale1 * df_on_node123.getColumn(2);
- }
- for (int j = 0; j < psb->m_nodes.size(); ++j)
- {
- const btSoftBody::Node& node = psb->m_nodes[j];
- size_t id = node.index;
- if (node.m_im > 0)
- {
- df[id] -= scale * dv[id] / node.m_im * m_damping_alpha;
- }
- }
- }
- }
-
- virtual void addScaledElasticForceDifferential(btScalar scale, const TVStack& dx, TVStack& df)
- {
- int numNodes = getNumNodes();
- btAssert(numNodes <= df.size());
- btVector3 grad_N_hat_1st_col = btVector3(-1, -1, -1);
- for (int i = 0; i < m_softBodies.size(); ++i)
- {
- btSoftBody* psb = m_softBodies[i];
- if (!psb->isActive())
- {
- continue;
- }
- for (int j = 0; j < psb->m_tetras.size(); ++j)
- {
- btSoftBody::Tetra& tetra = psb->m_tetras[j];
- btSoftBody::Node* node0 = tetra.m_n[0];
- btSoftBody::Node* node1 = tetra.m_n[1];
- btSoftBody::Node* node2 = tetra.m_n[2];
- btSoftBody::Node* node3 = tetra.m_n[3];
- size_t id0 = node0->index;
- size_t id1 = node1->index;
- size_t id2 = node2->index;
- size_t id3 = node3->index;
- btMatrix3x3 dF = psb->m_tetraScratches[j].m_corotation.transpose() * Ds(id0, id1, id2, id3, dx) * tetra.m_Dm_inverse;
- btMatrix3x3 dP;
- firstPiolaDifferential(psb->m_tetraScratches[j], dF, dP);
- // btVector3 df_on_node0 = dP * (tetra.m_Dm_inverse.transpose()*grad_N_hat_1st_col);
- btMatrix3x3 df_on_node123 = psb->m_tetraScratches[j].m_corotation * dP * tetra.m_Dm_inverse.transpose();
- btVector3 df_on_node0 = df_on_node123 * grad_N_hat_1st_col;
-
- // elastic force differential
- btScalar scale1 = scale * tetra.m_element_measure;
- df[id0] -= scale1 * df_on_node0;
- df[id1] -= scale1 * df_on_node123.getColumn(0);
- df[id2] -= scale1 * df_on_node123.getColumn(1);
- df[id3] -= scale1 * df_on_node123.getColumn(2);
- }
- }
- }
-
- void firstPiola(const btSoftBody::TetraScratch& s, btMatrix3x3& P)
- {
- btMatrix3x3 corotated_F = s.m_corotation.transpose() * s.m_F;
-
- btMatrix3x3 epsilon = (corotated_F + corotated_F.transpose()) * 0.5 - btMatrix3x3::getIdentity();
- btScalar trace = epsilon[0][0] + epsilon[1][1] + epsilon[2][2];
- P = epsilon * btScalar(2) * m_mu + btMatrix3x3::getIdentity() * m_lambda * trace;
- }
-
- // Let P be the first piola stress.
- // This function calculates the dP = dP/dF * dF
- void firstPiolaDifferential(const btSoftBody::TetraScratch& s, const btMatrix3x3& dF, btMatrix3x3& dP)
- {
- btScalar trace = (dF[0][0] + dF[1][1] + dF[2][2]);
- dP = (dF + dF.transpose()) * m_mu + btMatrix3x3::getIdentity() * m_lambda * trace;
- }
-
- // Let Q be the damping stress.
- // This function calculates the dP = dQ/dF * dF
- void firstPiolaDampingDifferential(const btSoftBody::TetraScratch& s, const btMatrix3x3& dF, btMatrix3x3& dP)
- {
- btScalar mu_damp = m_damping_beta * m_mu;
- btScalar lambda_damp = m_damping_beta * m_lambda;
- btScalar trace = (dF[0][0] + dF[1][1] + dF[2][2]);
- dP = (dF + dF.transpose()) * mu_damp + btMatrix3x3::getIdentity() * lambda_damp * trace;
- }
-
- virtual void addScaledHessian(btScalar scale)
- {
- btVector3 grad_N_hat_1st_col = btVector3(-1, -1, -1);
- for (int i = 0; i < m_softBodies.size(); ++i)
- {
- btSoftBody* psb = m_softBodies[i];
- if (!psb->isActive())
- {
- continue;
- }
- for (int j = 0; j < psb->m_tetras.size(); ++j)
- {
- btSoftBody::Tetra& tetra = psb->m_tetras[j];
- btMatrix3x3 P;
- firstPiola(psb->m_tetraScratches[j], P); // make sure scratch is evaluated at x_n + dt * vn
- btMatrix3x3 force_on_node123 = psb->m_tetraScratches[j].m_corotation * P * tetra.m_Dm_inverse.transpose();
- btVector3 force_on_node0 = force_on_node123 * grad_N_hat_1st_col;
- btSoftBody::Node* node0 = tetra.m_n[0];
- btSoftBody::Node* node1 = tetra.m_n[1];
- btSoftBody::Node* node2 = tetra.m_n[2];
- btSoftBody::Node* node3 = tetra.m_n[3];
- btScalar scale1 = scale * (scale + m_damping_beta) * tetra.m_element_measure; // stiff and stiffness-damping terms;
- node0->m_effectiveMass += OuterProduct(force_on_node0, force_on_node0) * scale1;
- node1->m_effectiveMass += OuterProduct(force_on_node123.getColumn(0), force_on_node123.getColumn(0)) * scale1;
- node2->m_effectiveMass += OuterProduct(force_on_node123.getColumn(1), force_on_node123.getColumn(1)) * scale1;
- node3->m_effectiveMass += OuterProduct(force_on_node123.getColumn(2), force_on_node123.getColumn(2)) * scale1;
- }
- for (int j = 0; j < psb->m_nodes.size(); ++j)
- {
- btSoftBody::Node& node = psb->m_nodes[j];
- if (node.m_im > 0)
- {
- btMatrix3x3 I;
- I.setIdentity();
- node.m_effectiveMass += I * (scale * (1.0 / node.m_im) * m_damping_alpha);
- }
- }
- }
- }
-
- virtual btDeformableLagrangianForceType getForceType()
- {
- return BT_LINEAR_ELASTICITY_FORCE;
- }
-};
-#endif /* BT_LINEAR_ELASTICITY_H */
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