WEN Guangyang

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.

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The localization of deformation in a deformed ductile medium is the instability mechanism that causes the final failure. This phenomenon occurs under static as well as dynamic load. It can be found within the materials, in which case it is called material instability, or on the whole structure, in which case it is called geometrical instability. This thesis studies the phenomenon of deformation localization in material or geometrical contexts and with static or dynamic loading conditions. In all cases, a unified tool is used: the evolution of the perturbation with localized support.The first chapter serves as an introduction to the problem of deformation localization in solid mechanics. The second chapter is devoted to the material instability aspect of strain localization in microstructured media under quasi-static compression, as well as its connection to macroscopic ellipticity (the continuum criterion of the presence of a discontinuous deformation field). In this chapter we demonstrate the connection between the homogenized post-bifurcation solution and the presence or absence of a localized deformation field in an infinitely large domain of fiber reinforced composites under compression. The third chapter is devoted to the material instability aspect of the deformation localization under dynamic loading, where the inertia effect becomes non-negligible. In this chapter we study a singular perturbation on an infinitely wide plate under biaxial tension and its influence cones, with a behavior law that loses ellipticity. The fourth chapter is devoted to the geometric instability aspect of deformation localization under dynamic loading, in which we study the dynamic compression of a metal ring under electromagnetic loading. Unlike the quasi-static case, localized deformation domains are observed in the failure mode of the ring.

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No summary available.