Mixed Finite Element Formulation for Solid Mechanics Problems

This seminar from the FEM@LLNL Series features Łukasz Kaczmarczyk of the University of Glasgow presenting "Mixed Finite Element Formulation for Solid Mechanics Problems." Explore the implementation of mixed finite element methods for small-strain elasticity and their extension to large-strain nearly incompressible problems. The presentation details a formulation with four independently approximated fields: stresses, logarithmic stretches, rotation vectors, and displacements, with stresses approximated in the H-div space and the remaining fields in the L2 space. Learn how this approach creates a sparse system of equations that can be efficiently solved in parallel using hybridization with a block solver, enabling highly scalable and robust solutions. The speaker demonstrates how this methodology naturally accommodates crack simulation without changing mesh topology, efficiently calculates face crack release energy, and creates an extremely sparse matrix structure suitable for multigrid solvers and parallel GPU implementations. Part of the MFEM project's seminar series focusing on finite element research and applications.