The Basic Formulas Derivation and Degradation Verification of the 3-D Dynamic Elastoplastic TD-BEM

In the field of dynamics research, in-depth exploration of three-dimensional (3-D) elastoplastic dynamics is crucial for understanding material behavior under complex dynamic loads. The findings hold significant guiding implications for design optimization in practical engineering domains such as aerospace and mechanical engineering. Current methodologies for solving 3-D dynamic elastoplastic problems face challenges: While traditional finite element methods (FEMs) excel in handling material nonlinearity, they encounter limitations in 3-D dynamic analysis, especially difficulties in simulating infinite domains. Although classical time-domain boundary element methods (TD-BEMs) effectively reduce computational dimensionality through dimension reduction and time-domain fundamental solutions, they remain underdeveloped for 3-D elastoplastic analysis. This study mainly includes the following contributions: First, we derived the 3-D dynamic elastoplastic boundary integral equations using the initial strain method for the first time, which aligns with the physical essence of strain decomposition in elastoplastic theory. Second, kernel functions for displacement, traction, and strain influence coefficients are analytically obtained by integrating time-domain fundamental solutions with physical and geometric equations. To validate the formulation, a 3-D-to-2-D transformation is implemented through an integral degradation method, converting the problem into a verified dynamic plane strain elastoplastic system.