A novel implicit FEM-MPM coupling framework using convex cone programming for elastoplastic problems

Xi‐Wen Zhou

doi:10.1016/j.cma.2024.117153

2024-09-01

PRE

DOI：10.1016/j.cma.2024.117153

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摘要

En 中文

Most existing Finite Element Method and the Material Point Method (FEM-MPM) coupling is designed for explicit solvers. By contrast, implicit schemes offer the advantage of substantially larger time steps while maintaining enhanced stability, particularly beneficial for tackling stiff nonlinear problems. Despite this, the development of implicit FEM-MPM coupling has not been extensively explored, leaving a notable gap in the context of contact and elastoplastic deformation challenges. Thus, this paper proposes a novel unified FEM-MPM coupling approach within implicit time integration under the framework of multivariable variational principle and convex cone programming, termed CP-FEMP. The CP-FEMP is the first successful attempt to impose the contact constraints via Lagrange multiplier and barrier method under convex cone programming, which can tackle not only the tie constraints but also the frictional contact between MPM and FEM domains with ensuring convergence and feasibility regardless of the time step size or the mesh resolutions. The contact locking issue in tie contact is circumvented using a well-defined interpolation space. The governing equations, associated frictional contact model, and associated elastoplastic constitutive law are formulated into a global convex optimisation problem, which is efficiently solved using primal-dual interior-point method. Through a succession of standard contact and elastoplastic benchmarks, the CP-FEMP demonstrates its proficiency in the precise transference of contact forces across MPM and FEM domains while showcasing commendable energy conservation attributes. Finally, the CP-FEMP is applied to a slope-retaining wall interaction problem. All results demonstrate CP-FEMP provides a comprehensive solution for FEM-MPM coupling, allowing for large incremental step under nonlinear contact , elastoplastic large deformation and guaranteeing strict, hard non -penetration conditions without convergence issues.

Keyword:

Implicit time integration

FEM-MPM coupling

Elastoplastic deformation

Tie contact

Frictional contact

Convex cone programming