ACCELERATION-WAVES IN ELASTOPLASTICITY

A spectral analysis of the acceleration wave problem in general elasto-plastic materials is carried out, whereby explicit expressions for the eigenvalues and eigenvectors are obtained. In case of nonassociated plasticity, all eigenvectors become nonorthogonal and one eigenvalue always remains unchanged and equal to the shear modulus. For a very broad class of nonassociated plasticity models, it is shown that the eigenvalues are always real, implying that so-called "divergence" instability can occur, while "flutter" instability can never occur. It is found that a certain value of the hardening modulus exists for which specific propagation directions will always imply that all wave speeds are identical and equal to the elastic distortion wave speed. Moreover, in this situation the eigenvectors are arbitrary, corresponding to a state of diffuse wave modes. The criteria of von Mises and Rankine are used to illustrate some of the findings.