Parallel Algorithms for Coupled Bem-Fem with Elastoplastic Deformations in the Fe-Domain

The classical linear elastoplastic model with the von Mises yield criterion and an associative flow rule, postulating $${\varepsilon ^e} = \varepsilon - {\varepsilon ^p}$$ yields $$\psi (\varepsilon - {\varepsilon ^p}) = {1 \over 2}(\varepsilon - {\varepsilon ^p}):{C^e}:(\varepsilon - {\varepsilon ^p})$$ with the total (geometrical) strain e and the plastic strain e p , see e.g. Lubliner, 1990. The stresses follow as $$\sigma = {\partial _\varepsilon }\psi (\varepsilon - {\varepsilon ^p}) = {C^e}:(\varepsilon - {\varepsilon ^p})$$ The associated flow rule with isotropic hardening is described by $${\dot \varepsilon ^p} = \lambda {\partial _\sigma }\Phi (\sigma ,\alpha )with\Phi (\sigma ,\alpha ) = \left\| {dev\sigma } \right\| - {2 \over 3}({y_0} + H\alpha )$$ where H, y 0 are material constants, and α is an internal variable. The loading-unloading conditions can be expressed in the Kuhn-Tucker form as $$\lambda \ge 0,\Phi (\sigma ,\alpha ) \le 0,\lambda \Phi (\sigma ,\alpha ) = 0$$ The solution of the coupled elastoplastic problem is obtained by a standard return mapping algorithm (Simo and Taylor, 1986).