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

Weidong Lei, Bingzhen Wu and Hongjun Li ()
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Weidong Lei: School of Civil and Environmental Engineering, Harbin Institute of Technology Shenzhen, Shenzhen 518055, China
Bingzhen Wu: School of Civil and Environmental Engineering, Harbin Institute of Technology Shenzhen, Shenzhen 518055, China
Hongjun Li: Hebei Key Laboratory of Structural Safety and Low-Carbon Construction for Rural Buildings, Hebei Agricultural University, Baoding 071001, China

Mathematics, 2025, vol. 13, issue 7, 1-13

Abstract: 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.

Keywords: Three-dimensional elastoplastic dynamics; initial strain method; time-domain boundary integral equation; integral degradation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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