A Total‐Lagrangian Generalized Particle Domain Method for Explicit Solid Dynamics

ABSTRACT This paper introduces a total‐Lagrangian generalized particle domain method (TLGPDM) for explicit solid dynamics. In contrast to the updated Lagrangian generalized particle domain method (ULGPDM), TLGPDM consistently references the initial configuration throughout the computation. As a result, the basis functions and their derivatives are computed only once prior to the simulation loop, thereby substantially reducing the computational cost. In addition, a comprehensive contact algorithm is developed within the TLGPDM framework. Building upon the pinball contact algorithm, it incorporates a global search, a local search, and a refined contact force computation, thus enhancing the robustness and accuracy of contact treatment under the total‐Lagrangian formulation. Four benchmark examples are presented to validate the proposed method and to assess its performance. The numerical results demonstrate that TLGPDM achieves superior computational efficiency compared with ULGPDM. Moreover, the proposed contact algorithm outperforms the conventional pinball contact algorithm in both accuracy and efficiency when applied within the TLGPDM framework.