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Diffstat (limited to 'extern/bullet2/src/BulletSoftBody/btDeformableLinearElasticityForce.h')
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diff --git a/extern/bullet2/src/BulletSoftBody/btDeformableLinearElasticityForce.h b/extern/bullet2/src/BulletSoftBody/btDeformableLinearElasticityForce.h new file mode 100644 index 00000000000..971192050b4 --- /dev/null +++ b/extern/bullet2/src/BulletSoftBody/btDeformableLinearElasticityForce.h @@ -0,0 +1,462 @@ +/* + 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 */ |