Addressing Numerical Challenges in Frictional Contact Simulation for Finite-Deformation Solid Mechanics

Abstract: The numerical simulation of contact phenomena in implicit, finite-deformation solid mechanics codes presents significant challenges due to the introduction of nonlinear and non-smooth operators. These complexities necessitate specialized linear and nonlinear solvers to be performant at scale. In this context, our finite element package, Ratel, distinguishes itself by employing high-order matrix-free methods, contrasting with the prevailing industry standard of low-order solvers applied to sparse assembled Jacobian matrices. Ratel capitalizes on the robust solver infrastructure provided by the Portable Extensible Toolkit for Scientific Computing (PETSc) and integrates the flexible matrix-free library libCEED, enabling highly scalable performance across both CPU and GPU architectures. Ratel supports level-set based frictional contact, which can be enforced by either Nitsche’s method or a penalty method. This talk will elucidate approaches to several numerical challenges associated with these contact formulations, particularly for high-order and matrix-free methods. These challenges include the computation of material stresses on contact surfaces, the solution of the asymmetric, indefinite, and/or poorly conditioned Jacobian matrices, and the numerical instability and slow nonlinear solver convergence behavior due to non-smooth friction models.