Bifurcation and stability in dissipative media (plasticity, friction, fracture)
Résumé
This paper addresses stability and bifurcation analysis for common systems of solids in the framework of plasticity, of friction and of fracture mechanics. Although physically different, usual time-independent laws adopted in these fields lead to a certain mathematical similarity concerning the quasi-static behaviour of materials and structures. These mechanical systems can be described practically in the same mathematical manner concerning their quasi-static evolution and the stability of their response. Our objective is to present within this framework a review of principal results of the recent literature on these subjects in relation with some energy-related considerations and with an unified description based upon the energy and dissipation analysis.