Fiber Monte Carlo-Enabled Contact Topology Optimization: Addressing Finite Deformation and Non-smooth Contact Interfaces

Abstract

Contact topology optimization under large deformation remains challenging due to geometric, material, and contact nonlinearities associated with evolving contact interfaces. Based on our previous work on contact modeling using the Fiber Monte Carlo (FMC) method, we propose a new approach for contact topology optimization, in which the underlying contact formulation can handle non-smooth boundaries (e.g., sharp corners), does not require predefined contact interfaces, is independent of mesh conformity, and avoids explicit complementarity constraints. In this method, a staggered strategy is developed to separate the contact analysis from the topology optimization procedure, thereby avoiding the non-smooth sensitivity issues typically encountered in complementarity-based contact formulations. Based on this framework, a contact topology optimization formulation is developed for multiple cases with distinct objective functions under a volume fraction constraint. Several numerical examples of increasing complexity have been solved, ranging from single rigid-elastic indentation in two dimensions to problems involving multiple rigid bodies, followed by multi-design-domain contact between elastic bodies, and finally to three-dimensional contact topology optimization. The results demonstrate the capability of the proposed approach in handling contact topology optimization problems involving non-smooth contact interfaces.