A non-smooth dual-primal meshless approach for deformable multibody dynamics

Abstract 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 introducing dual variables that represent bond forces and their corresponding constraint Jacobians. The framework is further generalized to accommodate non-smooth dynamics via Measure Differential Inclusions (MDIs), wherein fractured bonds are modeled through complementarity conditions. 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 peridynamics.