Time-domain boundary element method with von Mises model for solving 2-D elastoplastic dynamic problems

The analytical-based time-domain boundary element method (TD-BEM) can make maximal use of its advantages with negligible computational errors and has been verified for elastodynamic problems. However, the application of the method is limited because structures subjected to the severe loading tend to exhibit inelastic behavior that is beyond the method’s cope. Thus, an analytical-based TD-BEM that can deal with elastoplastic dynamic problems is necessary. This study first introduced time-dependent fundamental solutions for displacement and traction, as well as stress. The Mises model was selected as the constitutive model, and two different types of the model were considered. Second, the discretization of the constitutive equation was given in order to incorporate it into the TD-BEM. The analytical integration method, the Hadamard principle integral, was adopted for dealing with the singularities that exist in solving integral equations; we also give analytical solutions of singularities. Finally, two illustrative examples—that is, a cantilever plate and an infinite circular cavity—were selected to verify the analytical TD-BEM proposed in the study. The results showed that the numerical solutions agree well with the analytical solutions for the cantilever plate example and coincided with the numerical solutions calculated by the finite element method (FEM) for the infinite circular cavity example. Thus, the analytical TD-BEM can be applied for solving elastoplastic dynamic problems with high accuracy and efficiency.