Unilateral Contact simulations with a stable LaTIn solver for non-conforming "Cut" finite elements

We have recently developed an unfitted finite element solver for sets of solids that are interacting through unilateral contact. The analysis mesh is regular and the geometry of the solids is allowed to cut through the elements. The two pictures below illustrate the capabilities of our solver

The solver itself combines the best of two world. On the one hand, we use elements of the CutFEM technology pioneered by P. Hansbo, E. Burman, MG Larson in order to allow interfaces to cut through the mesh without altering the convergence rate associated with finite element solvers. On the other hand, different phases of the composite are coupled using the LaTIn solver, first proposed by P. Ladevèze, and whose versatility has been proven over the years. We modified the discrete mixed formulation associated with LaTIn in order to stabilise the interface solution, ensuring that the condition number of  successive linear systems of equations is controlled an that the convergence with mesh refinement is optimum.  More detailed about our general strategy can be found in the wide audience paper that we have written for NAFEMS magazine Benchmark, available in draft form here.

Some more pictures of the geometry of the 3D woven composite material. The fibres are easily described by using a set of appropriate level set functions. The matrix bloc can be meshed "by hand" as it is not requires to conform to the complex geometry of the interfaces between phases of the composite.

The simulations were performed using the CutFEM FEniCS library.

Susanne Claus, Pierre Kerfriden, A stable and optimally convergent LaTIn-Cut Finite Element Method for multiple unilateral contact problems, IJNME, 2016