A finite micro-rotation material point method for micropolar solid and fluid dynamics with three-dimensional evolving contacts and free surfaces

Abstract

This paper introduces an explicit material point method designed specifically for simulating the micropolar continuum dynamics in the finite deformation and finite microrotation regime. The material point method enables us to simulate large deformation problems while circumventing the potential mesh distortion without remeshing. To eliminate rotational motion damping and loss of angular momentum during the projection, we introduce the mapping for microinertia and angular momentum between particles and grids through the affine particle-in-cell approach. The microrotation and the curvature at each particle are updated through zero-order forward integration of the microgyration and its spatial gradient. We show that the microinertia and the angular momentum are conserved during the projections between particles and grids in our formulation. We verify the formulation and implementation by comparing with the analytical dispersion relation of micropolar waves under the small strain and small microrotation, as well as the analytical soliton solution for solids undergoing large deformation and large microrotation. Additionally we also demonstrate the capacity of the proposed computational framework to handle a wide spectrum of simulations that exhibit size effects in the geometrical nonlinear regime through three representative numerical examples, i.e., a cantilever beam torsion problem, a fragment-impact penetration problem, and a micropolar fluid discharging problem.