.. _program_listing_file_SPlisHSPlasH_Elasticity_Elasticity_Becker2009.cpp:

Program Listing for File Elasticity_Becker2009.cpp
==================================================

|exhale_lsh| :ref:`Return to documentation for file <file_SPlisHSPlasH_Elasticity_Elasticity_Becker2009.cpp>` (``SPlisHSPlasH/Elasticity/Elasticity_Becker2009.cpp``)

.. |exhale_lsh| unicode:: U+021B0 .. UPWARDS ARROW WITH TIP LEFTWARDS

.. code-block:: cpp

   #include "Elasticity_Becker2009.h"
   #include "SPlisHSPlasH/Simulation.h"
   #include "SPlisHSPlasH/Utilities/MathFunctions.h"
   
   using namespace SPH;
   using namespace GenParam;
   
   std::string Elasticity_Becker2009::METHOD_NAME = "Becker et al. 2009";
   int Elasticity_Becker2009::YOUNGS_MODULUS = -1;
   int Elasticity_Becker2009::POISSON_RATIO = -1;
   int Elasticity_Becker2009::FIXED_BOX_MIN = -1;
   int Elasticity_Becker2009::FIXED_BOX_MAX = -1;
   int Elasticity_Becker2009::ALPHA = -1;
   
   
   Elasticity_Becker2009::Elasticity_Becker2009(FluidModel *model) :
       NonPressureForceBase(model)
   {
       const unsigned int numParticles = model->numActiveParticles();
       m_restVolumes.resize(numParticles);
       m_current_to_initial_index.resize(numParticles);
       m_initial_to_current_index.resize(numParticles);
       m_initialNeighbors.resize(numParticles);
       m_rotations.resize(numParticles, Matrix3r::Identity());
       m_stress.resize(numParticles);
       m_F.resize(numParticles);
   
       m_youngsModulus = static_cast<Real>(100000.0);
       m_poissonRatio = static_cast<Real>(0.3);
       m_alpha = 0.0;
       m_fixedBoxMin.setZero();
       m_fixedBoxMax.setZero();
   
       model->addField({ "rest volume", METHOD_NAME, FieldType::Scalar, [&](const unsigned int i) -> Real* { return &m_restVolumes[i]; }, true });
       model->addField({ "rotation", METHOD_NAME, FieldType::Matrix3, [&](const unsigned int i) -> Real* { return &m_rotations[i](0,0); } });
       model->addField({ "stress", METHOD_NAME, FieldType::Vector6, [&](const unsigned int i) -> Real* { return &m_stress[i][0]; } });
       model->addField({ "deformation gradient", METHOD_NAME, FieldType::Matrix3, [&](const unsigned int i) -> Real* { return &m_F[i](0,0); } });
   }
   
   Elasticity_Becker2009::~Elasticity_Becker2009(void)
   {
       m_model->removeFieldByName("rest volume");
       m_model->removeFieldByName("rotation");
       m_model->removeFieldByName("stress");
       m_model->removeFieldByName("deformation gradient");
   }
   
   void Elasticity_Becker2009::deferredInit()
   {
       initValues();
   }
   
   void Elasticity_Becker2009::initParameters()
   {
       NonPressureForceBase::initParameters();
   
       YOUNGS_MODULUS = createNumericParameter("youngsModulus", "Young`s modulus", &m_youngsModulus);
       setGroup(YOUNGS_MODULUS, "Fluid Model|Elasticity");
       setDescription(YOUNGS_MODULUS, "Stiffness of the elastic material");
       RealParameter* rparam = static_cast<RealParameter*>(getParameter(YOUNGS_MODULUS));
       rparam->setMinValue(0.0);
   
       POISSON_RATIO = createNumericParameter("poissonsRatio", "Poisson`s ratio", &m_poissonRatio);
       setGroup(POISSON_RATIO, "Fluid Model|Elasticity");
       setDescription(POISSON_RATIO, "Ratio of transversal expansion and axial compression");
       rparam = static_cast<RealParameter*>(getParameter(POISSON_RATIO));
       rparam->setMinValue(static_cast<Real>(-1.0 + 1e-4));
       rparam->setMaxValue(static_cast<Real>(0.5 - 1e-4));
   
       ParameterBase::GetVecFunc<Real> getFct = [&]()-> Real* { return m_fixedBoxMin.data(); };
       ParameterBase::SetVecFunc<Real> setFct = [&](Real* val)
       {
           m_fixedBoxMin = Vector3r(val[0], val[1], val[2]);
           determineFixedParticles();
       };
       FIXED_BOX_MIN = createVectorParameter("fixedBoxMin", "Fixed box min", 3u, getFct, setFct);
       setGroup(FIXED_BOX_MIN, "Fluid Model|Elasticity");
       setDescription(FIXED_BOX_MIN, "Minimum point of box of which contains the fixed particles.");
       getParameter(FIXED_BOX_MIN)->setReadOnly(true);
   
   
       ParameterBase::GetVecFunc<Real> getFct2 = [&]()-> Real* { return m_fixedBoxMax.data(); };
       ParameterBase::SetVecFunc<Real> setFct2 = [&](Real* val)
       {
           m_fixedBoxMax = Vector3r(val[0], val[1], val[2]);
           determineFixedParticles();
       };
       FIXED_BOX_MAX = createVectorParameter("fixedBoxMax", "Fixed box max", 3u, getFct2, setFct2);
       setGroup(FIXED_BOX_MAX, "Fluid Model|Elasticity");
       setDescription(FIXED_BOX_MAX, "Maximum point of box of which contains the fixed particles.");
       getParameter(FIXED_BOX_MAX)->setReadOnly(true);
   
       ALPHA = createNumericParameter("alpha", "Zero-energy modes suppression", &m_alpha);
       setGroup(ALPHA, "Fluid Model|Elasticity");
       setDescription(ALPHA, "Coefficent for zero-energy modes suppression method");
       rparam = static_cast<RealParameter*>(getParameter(ALPHA));
       rparam->setMinValue(0.0);
   }
   
   void Elasticity_Becker2009::determineFixedParticles()
   {
       const unsigned int numParticles = m_model->numActiveParticles();
   
       if (!m_fixedBoxMin.isZero() || !m_fixedBoxMax.isZero())
       {
           for (int i = 0; i < (int)numParticles; i++)
           {
               const Vector3r& x = m_model->getPosition0(i);
               if ((x[0] > m_fixedBoxMin[0]) && (x[1] > m_fixedBoxMin[1]) && (x[2] > m_fixedBoxMin[2]) &&
                   (x[0] < m_fixedBoxMax[0]) && (x[1] < m_fixedBoxMax[1]) && (x[2] < m_fixedBoxMax[2]))
               {
                   m_model->setParticleState(i, ParticleState::Fixed);
               }
           }
       }
   }
   
   void Elasticity_Becker2009::initValues()
   {
       Simulation *sim = Simulation::getCurrent();
       sim->getNeighborhoodSearch()->find_neighbors();
   
       FluidModel *model = m_model;
       const unsigned int numParticles = model->numActiveParticles();
       const unsigned int fluidModelIndex = model->getPointSetIndex();
   
       // Store the neighbors in the reference configurations and
       // compute the volume of each particle in rest state
       #pragma omp parallel default(shared)
       {
           #pragma omp for schedule(static) 
           for (int i = 0; i < (int)numParticles; i++)
           {
               m_current_to_initial_index[i] = i;
               m_initial_to_current_index[i] = i;
   
               // reset particle state
               if (model->getParticleState(i) == ParticleState::Fixed)
                   model->setParticleState(i, ParticleState::Active);
   
               // only neighbors in same phase will influence elasticity
               const unsigned int numNeighbors = sim->numberOfNeighbors(fluidModelIndex, fluidModelIndex, i);
               m_initialNeighbors[i].resize(numNeighbors);
               for (unsigned int j = 0; j < numNeighbors; j++)
                   m_initialNeighbors[i][j] = sim->getNeighbor(fluidModelIndex, fluidModelIndex, i, j);
   
               // compute volume
               Real density = model->getMass(i) * sim->W_zero();
               const Vector3r &xi = model->getPosition(i);
               for (size_t j = 0; j < m_initialNeighbors[i].size(); j++)
               {
                   const unsigned int neighborIndex = m_initialNeighbors[i][j];
                   const Vector3r& xj = model->getPosition(neighborIndex);
                   density += model->getMass(neighborIndex) * sim->W(xi - xj);
               }
               m_restVolumes[i] = model->getMass(i) / density;
               m_rotations[i].setIdentity();
           }
       }
   
       // mark all particles in the bounding box as fixed
       determineFixedParticles();
   }
   
   void Elasticity_Becker2009::step()
   {
       computeRotations();
       computeStress();
       computeForces();
   }
   
   
   void Elasticity_Becker2009::reset()
   {
       initValues();
   }
   
   void Elasticity_Becker2009::performNeighborhoodSearchSort()
   {
       const unsigned int numPart = m_model->numActiveParticles();
       if (numPart == 0)
           return;
   
       Simulation *sim = Simulation::getCurrent();
       auto const& d = sim->getNeighborhoodSearch()->point_set(m_model->getPointSetIndex());
       d.sort_field(&m_restVolumes[0]);
       d.sort_field(&m_current_to_initial_index[0]);
   
       for (unsigned int i = 0; i < numPart; i++)
           m_initial_to_current_index[m_current_to_initial_index[i]] = i;
   }
   
   void Elasticity_Becker2009::computeRotations()
   {
       Simulation *sim = Simulation::getCurrent();
       const unsigned int numParticles = m_model->numActiveParticles();
       const unsigned int fluidModelIndex = m_model->getPointSetIndex();
       FluidModel *model = m_model;
   
       #pragma omp parallel default(shared)
       {
           #pragma omp for schedule(static)  
           for (int i = 0; i < (int)numParticles; i++)
           {
               const unsigned int i0 = m_current_to_initial_index[i];
               const Vector3r &xi = m_model->getPosition(i);
               const Vector3r &xi0 = m_model->getPosition0(i0);
               Matrix3r Apq;
               Apq.setZero();
   
               const size_t numNeighbors = m_initialNeighbors[i0].size();
   
               // Fluid
               for (unsigned int j = 0; j < numNeighbors; j++)
               {
                   const unsigned int neighborIndex = m_initial_to_current_index[m_initialNeighbors[i0][j]];
                   // get initial neighbor index considering the current particle order 
                   const unsigned int neighborIndex0 = m_initialNeighbors[i0][j];
   
                   const Vector3r &xj = model->getPosition(neighborIndex);
                   const Vector3r &xj0 = m_model->getPosition0(neighborIndex0);
                   const Vector3r xj_xi = xj - xi;
                   const Vector3r xj_xi_0 = xj0 - xi0;
                   Apq += m_model->getMass(neighborIndex) * sim->W(xj_xi_0) * (xj_xi * xj_xi_0.transpose());
               }
   
   //          Vector3r sigma;
   //          Matrix3r U, VT;
   //          MathFunctions::svdWithInversionHandling(Apq, sigma, U, VT);
   //          m_rotations[i] = U * VT;
               Quaternionr q(m_rotations[i]);
               MathFunctions::extractRotation(Apq, q, 10);
               m_rotations[i] = q.matrix();
           }
       }
   }
   
   void Elasticity_Becker2009::computeStress()
   {
       Simulation *sim = Simulation::getCurrent();
       const unsigned int numParticles = m_model->numActiveParticles();
       const unsigned int fluidModelIndex = m_model->getPointSetIndex();
       FluidModel *model = m_model;
   
       Real mu = m_youngsModulus / (static_cast<Real>(2.0) * (static_cast<Real>(1.0) + m_poissonRatio));
       Real lambda = m_youngsModulus * m_poissonRatio / ((static_cast<Real>(1.0) + m_poissonRatio) * (static_cast<Real>(1.0) - static_cast<Real>(2.0) * m_poissonRatio));
   
       #pragma omp parallel default(shared)
       {
           #pragma omp for schedule(static)  
           for (int i = 0; i < (int)numParticles; i++)
           {
               const unsigned int i0 = m_current_to_initial_index[i];
               const Vector3r& xi = m_model->getPosition(i);
               const Vector3r& xi0 = m_model->getPosition0(i0);
   
               Matrix3r nablaU;
               nablaU.setZero();
               const size_t numNeighbors = m_initialNeighbors[i0].size();
   
               // Fluid
               for (unsigned int j = 0; j < numNeighbors; j++)
               {
                   const unsigned int neighborIndex = m_initial_to_current_index[m_initialNeighbors[i0][j]];
                   // get initial neighbor index considering the current particle order 
                   const unsigned int neighborIndex0 = m_initialNeighbors[i0][j];
   
                   const Vector3r& xj = model->getPosition(neighborIndex);
                   const Vector3r& xj0 = m_model->getPosition0(neighborIndex0);
   
                   const Vector3r xj_xi = xj - xi;
                   const Vector3r xj_xi_0 = xj0 - xi0;
   
                   const Vector3r uji = m_rotations[i].transpose() * xj_xi - xj_xi_0;
                   // subtract because kernel gradient is taken in direction of xji0 instead of xij0
                   nablaU -= (m_restVolumes[neighborIndex] * uji) * sim->gradW(xj_xi_0).transpose();
               }
               m_F[i] = nablaU + Matrix3r::Identity();
   
               // compute Cauchy strain: epsilon = 0.5 (nabla u + nabla u^T)
               Vector6r strain;
               strain[0] = nablaU(0, 0);                       // \epsilon_{00}
               strain[1] = nablaU(1, 1);                       // \epsilon_{11}
               strain[2] = nablaU(2, 2);                       // \epsilon_{22}
               strain[3] = static_cast<Real>(0.5) * (nablaU(0, 1) + nablaU(1, 0)); // \epsilon_{01}
               strain[4] = static_cast<Real>(0.5) * (nablaU(0, 2) + nablaU(2, 0)); // \epsilon_{02}
               strain[5] = static_cast<Real>(0.5) * (nablaU(1, 2) + nablaU(2, 1)); // \epsilon_{12}
   
               // First Piola Kirchhoff stress = 2 mu epsilon + lambda trace(epsilon) I
               const Real trace = strain[0] + strain[1] + strain[2];
               const Real ltrace = lambda * trace;
               Vector6r& stress = m_stress[i];
               stress[0] = static_cast<Real>(2.0) * mu * strain[0] + ltrace;
               stress[1] = static_cast<Real>(2.0) * mu * strain[1] + ltrace;
               stress[2] = static_cast<Real>(2.0) * mu * strain[2] + ltrace;
               stress[3] = static_cast<Real>(2.0) * mu * strain[3];
               stress[4] = static_cast<Real>(2.0) * mu * strain[4];
               stress[5] = static_cast<Real>(2.0) * mu * strain[5];
           }
       }
   }
   
   void Elasticity_Becker2009::computeForces()
   {
       Simulation *sim = Simulation::getCurrent();
       const unsigned int numParticles = m_model->numActiveParticles();
       const unsigned int fluidModelIndex = m_model->getPointSetIndex();
       FluidModel *model = m_model;
   
       #pragma omp parallel default(shared)
       {
           #pragma omp for schedule(static)  
           for (int i = 0; i < (int)numParticles; i++)
           {
               if (model->getParticleState(i) == ParticleState::Active)
               {
                   const unsigned int i0 = m_current_to_initial_index[i];
                   const Vector3r& xi0 = m_model->getPosition0(i0);
   
                   const size_t numNeighbors = m_initialNeighbors[i0].size();
                   Vector3r fi;
                   fi.setZero();
   
                   // Fluid
                   for (unsigned int j = 0; j < numNeighbors; j++)
                   {
                       const unsigned int neighborIndex = m_initial_to_current_index[m_initialNeighbors[i0][j]];
                       // get initial neighbor index considering the current particle order 
                       const unsigned int neighborIndex0 = m_initialNeighbors[i0][j];
   
                       const Vector3r& xj0 = m_model->getPosition0(neighborIndex0);
   
                       const Vector3r xj_xi_0 = xj0 - xi0;
                       const Vector3r gradW0 = sim->gradW(xj_xi_0);
   
                       const Vector3r dji = m_restVolumes[i] * gradW0;
                       const Vector3r dij = -m_restVolumes[neighborIndex] * gradW0;
   
                       Vector3r sdji, sdij;
                       symMatTimesVec(m_stress[neighborIndex], dji, sdji);
                       symMatTimesVec(m_stress[i], dij, sdij);
   
                       const Vector3r fij = -m_restVolumes[neighborIndex] * sdji;
                       const Vector3r fji = -m_restVolumes[i] * sdij;
   
                       fi += m_rotations[neighborIndex] * fij - m_rotations[i] * fji;
                   }
                   fi = 0.5*fi;
   
                   if (m_alpha != 0.0)
                   {
                       // Ganzenmüller, G.C. 2015. An hourglass control algorithm for Lagrangian
                       // Smooth Particle Hydrodynamics. Computer Methods in Applied Mechanics and 
                       // Engineering 286, 87.106.
                       Vector3r fi_hg;
                       fi_hg.setZero();
                       const Vector3r& xi = m_model->getPosition(i);
                       for (unsigned int j = 0; j < numNeighbors; j++)
                       {
                           const unsigned int neighborIndex = m_initial_to_current_index[m_initialNeighbors[i0][j]];
                           // get initial neighbor index considering the current particle order 
                           const unsigned int neighborIndex0 = m_initialNeighbors[i0][j];
   
                           const Vector3r& xj = model->getPosition(neighborIndex);
                           const Vector3r& xj0 = m_model->getPosition0(neighborIndex0);
   
                           // Note: Ganzenm�ller defines xij = xj-xi
                           const Vector3r xi_xj = -(xi - xj);
                           const Real xixj_l = xi_xj.norm();
                           if (xixj_l > 1.0e-6)
                           {
                               // Note: Ganzenm�ller defines xij = xj-xi
                               const Vector3r xi_xj_0 = -(xi0 - xj0);
                               const Real xixj0_l2 = xi_xj_0.squaredNorm();
                               const Real W0 = sim->W(xi_xj_0);
   
                               const Vector3r xij_i = m_F[i] * m_rotations[i] * xi_xj_0;
                               const Vector3r xji_j = -m_F[neighborIndex] * m_rotations[neighborIndex] * xi_xj_0;
                               const Vector3r epsilon_ij_i = xij_i - xi_xj;
                               const Vector3r epsilon_ji_j = xji_j + xi_xj;
   
                               const Real delta_ij_i = epsilon_ij_i.dot(xi_xj) / xixj_l;
                               const Real delta_ji_j = -epsilon_ji_j.dot(xi_xj) / xixj_l;
   
                               fi_hg -= m_restVolumes[neighborIndex] * W0 / xixj0_l2 * (delta_ij_i + delta_ji_j) * xi_xj / xixj_l;
                           }
                       }
                       fi_hg *= m_alpha * m_youngsModulus * m_restVolumes[i];
                       model->getAcceleration(i) += fi_hg / model->getMass(i);
                   }
   
                   // elastic acceleration
                   Vector3r& ai = model->getAcceleration(i);
                   ai += fi / model->getMass(i);
               }
           }
       }
   }
   
   void SPH::Elasticity_Becker2009::saveState(BinaryFileWriter &binWriter)
   {
       binWriter.writeBuffer((char*)m_current_to_initial_index.data(), m_current_to_initial_index.size() * sizeof(unsigned int));
       binWriter.writeBuffer((char*)m_initial_to_current_index.data(), m_initial_to_current_index.size() * sizeof(unsigned int));
   }
   
   void SPH::Elasticity_Becker2009::loadState(BinaryFileReader &binReader)
   {
       binReader.readBuffer((char*)m_current_to_initial_index.data(), m_current_to_initial_index.size() * sizeof(unsigned int));
       binReader.readBuffer((char*)m_initial_to_current_index.data(), m_initial_to_current_index.size() * sizeof(unsigned int));
   }