Instability analysis of non-homogeneous materials under biaxial loading

In this paper, we formulate the instability problem of non-homogeneous materials under biaxial loading, in the sense that the mechanical parameters, and more specifically the strain hardening or softening and the strain-rate sensitivity, are spatially dependent functions. We first study the time behavior of the process and present the evolution of strain non-uniformities before the critical time, to show that it depends on the interplay between the spatial distribution of mechanical parameters and the initial non-uniformities. We next study the instability modes of a material exhibiting inhomogeneities along one direction by an effective instability analysis [Dudzinski, D., Molinari, A., 1991. Perturbation analysis of thermoviscoplastic instabilities in biaxial loading. International Journal of Solids and Structures 27 (5), 601–628] adapted to the non-homogeneous case. This method is based on a suitable non-uniform reference solution and allows to select the localization modes activated at different deformation levels for different “deformation paths” of the material zones.