Robust explicit computational strategies based on penalty method for large-deformation impact problems

To improve the accuracy and robustness of the explicit finite element algorithm based on penalty method for simulating large deformation impact-contact problem, a new large-deformation non-penetration contact algorithm based on forward incremental displacement central difference (FIDCD) is developed. On the one hand, according to FIDCD, the solving step of the dynamic equation is decomposed into an estimated step without considering contact and a correction step considering contact constraint. At the current moment, a contact force is applied through the penalty method to make the deformation of entities satisfy the non-penetration condition. The contact force is calculated by a soft constraint penalty stiffness, which helps to maintain stability of contact localization. It refines the numerical accuracy of the explicit contact computation. On the other hand, to accurately calculate the large-deformation internal force of the next moment while only obtaining the displacement, the internal force term of the dynamic equation is mapped to a known configuration for solution based on the arbitrary reference configurations (ARC) theory. It avoids using the values of variables at intermediate configuration to approximate them, thereby improving the numerical accuracy of the large deformation computation. More rigorous contact algorithms and geometric nonlinear solution strategy can effectively suppress mesh distortion and non-physical penetration between entities during large-deformation impact simulation. This thus improves the robustness of the new explicit algorithm. Finally, the computational program written according to the new developed algorithm is applied to simulate several impact and penetration examples with different impact velocities. By comparing the simulation results with those obtained from commercial software, the correctness of the developed algorithm and computational program is verified. At the same time, it can also be proven that the algorithm proposed is more robust in simulating high-speed and large-deformation impact problems than the classical explicit impact-contact algorithm based on the frog jump center difference scheme combining with penalty method.