Plasticity Over 150 Years (1864–2014)

Abstract

Plasticity theory in continuum mechanics has evolved from Coulomb’s and Tresca’s experiments to the exploitation of powerful thermo-mechanical concepts (e.g., second law of thermodynamics) and sophisticated mathematical tools (e.g., convex analysis). The present contribution peruses this development over more than a hundred and fifty years with special attention paid to original but forgotten works of Duhem, the introduction of various yield criteria, the formulation of incremental and normality laws, the influence of thermodynamic concepts (in particular the dissipation inequality) and the resulting variational formulations and inequalities, the fortunate complementarity between, and confluence of, “mathematical” and “physical” plasticity theories, some doomed attempts such as hypoelasticity, the birth of a rational approach to plasticity in finite deformations, and further progress in anisotropic studies, numerical plasticity, homogenization, visco-plasticity, coupling with other physical properties, and the recent gradient plasticity. This is achieved in a historical comprehensive vision with a minimum of technicalities, but always paying tribute to the most influential and well articulated contributors. Both primary and secondary sources are exploited.