A convex optimization method for contact dynamics between flexible bodies with surface parameterization and residual compliance

A convex optimization approach is proposed for nonsmooth frictional contact dynamics between deformable bodies by combining surface parameterization with a new cone complementarity formulation. Surface regions with potential contacts are first mapped from discrete meshes to regular parameter domains by conformal mappings. In the parameter domain, the contact geometry and key field quantities, including modal fields and residual compliance, are fitted offline and stored in compressed form. Flexible deformation is described by a free-interface component mode synthesis, in which the global dynamic response is represented in a modal-reduced form, whereas the local high-frequency deformation induced by interface forces is represented by residual compliance and recovered through quasi-static correction under the current interface forces. The smooth surface representation in the parameter domain enables on-demand identification and discretization of contact regions, which avoids preassigning a large number of interface displacement degrees of freedom over the entire potential contact region and reduces the dependence of contact discretization on the original mesh. Hence, a cone complementarity contact formulation is constructed to enforce deformation, impenetrability, and Coulomb friction constraints consistently. Numerical results show good agreement with the reference solutions and provide quantitative evidence of accuracy, numerical robustness, and online computational efficiency within the tested cases.