Mechanics of isotropic elastic-plastic flow in pressure-sensitive damaging bodies under finite strains - revisited

The general theoretical framework for modeling the plastic flow at finite strain is reconsidered. The Eckard-Mandel concept of multiplicative decomposition of the total deformation tensor is used together with the logarithmic elastic strain measure as external state variable. The rate constitutive relations formulated in the mobile Lagrangian description are transformed to the form appropriate for application of updated Lagrangian numerical techniques. This exhibits the structure of plastic increment of total strain (defined in Hill-Rice Lagrangian first order plasticity theory) following from application of multiplicative decomposition of the deformation tensor. The rate equations are reduced to the fairly simple form by making plausible physical assumptions concerning deformation behavior of real plastically deformed non-rubber like materials. Since most of such materials exhibits small distortional elastic strains, and possibly large dilatational deformation under sufficiently high pressure, the postulated mathematical form of elastic shear strain energy function is the same as in usual infinitesimal theories. The general method for incorporation of the pressure sensitivity (including hydrodynamic behaviour of metals at high pressure) and possible damage into the framework of the usual theory of plasticity is discussed. The material (the derived non-associated flow law) and the mechanical descriptions are combined through the relevant bridging equation and the simple choice of the orientation of material element in the conceptual unloaded configuration (vanishing spin of permanent strains). The general rate boundary value problem is formulated and estimation method of the primary bifurcation state is revived. (C) 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim