Stability and Localization of Deformation in Finitely Strained Solids and Structures : Static and High Strain Rate Dynamic Aspects.

Summary Localization of deformation in finitely strained ductile solids is the instability mechanism leading to their failure by rupture. This phenomenon occurs under static and dynamic loading conditions. It can appear in the bulk of solids, in which case it is referred to as a material instability phenomenon or in a structure, in which case one talks about a structural instability problem. The thesis at hand studies localization in the material and structural context, both under static and dynamic conditions, using a common tool: the evolution of a geometrically localized perturbation.An introduction to the localization of deformation problem in solid mechanics is presented in Chapter 1. The material instability aspect of localization of deformation in microstructured solids under quasistatic loading and its connection to macroscopic ellipticity – the continuum criterion for the presence of a discontinuous strain field – are addressed in Chapter 2. In this part we show the connection of the homogenized post-bifurcation response to the presence or absence of a localized deformation field in an infinite, fiber-reinforced composite under plane strain compression. The material instability aspect of localization of deformation under dynamic loading, i.e. where inertia becomes important, is addressed in Chapter 3. In this part we study the influence cones for the wave propagation emerging from a point perturbation in an infinite, biaxially strained plate whose constitutive response loses ellipticity at finite level of strain. The structural instability aspect of localization of deformation is investigated under dynamic loading conditions in Chapter 4 by studying the dynamic compression on an electromagnetically loaded metallic ring. In contrast to the quasistatic case, where a global failure mode is observed, the failure pattern for the rapidly compressed ring shows highly localized deformation areas.