Boundary Integral Formulation for Inelastic Problems

Although applications of integral equations in elasticity were already known in the 1960s, it was only during the last decade that the first papers on nonlinear material problems appeared. The first publication on this subject was due to Swedlow and Cruse [1] in 1971. The article was concerned with the generalization of the strain hardening elastoplastic constitutive equations, previously presented by the first author, to compressible and anisotropic plastic flow, and presented an extended form of Somigliana’s identity including plastic strain rates. In addition, the starting boundary integral equation for the direct boundary element formulation was first introduced, for three-dimensional problems, but examples were not shown nor was the integral expression for internal stresses given. The authors, however, pointed out the existence of a domain integral which accounts for the plastic strains contribution to the formulation.