A Non-Smooth Dual-Primal Meshless Approach for Deformable Multibody Dynamics

This work introduces a novel implicit time integration scheme for simulating deformable materials in multibody systems, leveraging a meshless formulation grounded in bond-based peridynamics. The proposed approach enables robust modeling of large deformations, plasticity, and fracture while circumventing key computational bottlenecks inherent in conventional methods. By reformulating bond forces as compliant constraints within a Differential-Algebraic Equation (DAE) framework, the method eliminates the need for explicit tangent stiffness matrices in implicit integration. Instead, the system is efficiently solved via saddle-point optimization, where dual variables naturally represent bond forces through straightforward constraint Jacobians.Furthermore, the framework extends naturally to non-smooth dynamics through Measure Differential Inclusions (MDIs), where bond constraints are recast as complementarity conditions in case of fractured materials. This advancement significantly improves the treatment of contact between particles compared to traditional peridynamic methods, which often rely on ad hoc repulsive force fields. The resulting dual-primal formulation offers enhanced numerical robustness and efficiency, particularly for problems involving complex fractures and contact interactions, while preserving the meshless flexibility of the underlying method.