Abstract
MPS (Moving Particle Semi-implicit) method has been developed for solid and shell dynamics. Since the particle methods are expected to apply to large deformation and fracture, geometrical non-linearity is studied for the MPS methods. Quaternion is employed as the nonlinear rotation angle system. Finite rigid-body rotation can be removed from the deformation gradient tensor using the quaternion. Strain is defined using the right stretch tensor involving the first-order sensitivity. When the quaternion of each particle is implicitly calculated, Hamiltonian can be derived and energy conservation is achieved by employing symplectic schemes.
