An elastoplastic framework for granular materials becoming cohesive through mechanical densification. Part II – the formulation of elastoplastic coupling at large strain

Abstract

The two key phenomena occurring in the process of ceramic powder compaction are the progressive gain in cohesion and the increase of elastic stiffness, both related to the development of plastic deformation. The latter effect is an example of 'elastoplastic coupling', in which the plastic flow affects the elastic properties of the material, and has been so far considered only within the framework of small strain assumption (mainly to describe elastic degradation in rock-like materials), so that it remains completely unexplored for large strain. Therefore, a new finite strain generalization of elastoplastic coupling theory is given to describe the mechanical behaviour of materials evolving from a granular to a dense state.The correct account of elastoplastic coupling and of the specific characteristics of materials evolving from a loose to a dense state (for instance, nonlinear -or linear-dependence of the elastic part of the deformation on the forming pressure in the granular -or dense-state) makes the use of existing large strain formulations awkward, if even possible. Therfore, first, we have resorted to a very general setting allowing general transformations between work-conjugate stress and strain measures; second, we have introduced the multiplicative decomposition of the deformation gradient and, third, employing isotropy and hyperelasticity of elastic response, we have obtained a relation between the Biot stress and its 'total' and 'plastic' work-conjugate strain measure. This is a key result, since it allows an 1 immediate achievement of the rate elastoplastic constitutive equations. Knowing the general form of these equations, all the specific laws governing the behaviour of ceramic powders are finally introduced as generalizations of the small strain counterparts given in Part I of this paper.

Factorial Numerical Analysis of Flexible Pavement Foundations with Emphasis on Groundwater Table Effect

“…The soil nonlinear response expressed by Equations (1) and (2) above was proved efficient in representing the elastic behavior of dense granular materials (Piccolroaz et al 2006). On the other hand, the AC surface layer was treated as a linear and impervious material (one phase medium) for simplicity (Erlingsson et al 2009).…”

Strong discontinuities in partially saturated poroplastic solids

“…If compared with results based on the partial stress concept, the storage modulus C ab in (29) considers the elastic porosity n e as an approximation of the total porosity n. This assumption avoids a coupling between the elastic and plastic parts that would require significant modifications to ensure thermodynamic consistency of the continuum model [37,45]. In standard multiphase problems, the saturation degree derivative s a;p c typically exhibits a wide range of variation.…”

Finite-strain formulation and FE implementation of a constitutive model for powder compaction

“…In this work, incremental (finite-step) constitutive equations are developed and implemented for the finite-deformation version of the PBG model. In order to improve the computational efficiency, the original model [11] is slightly modified, but its essential features, including the elastoplastic coupling, are preserved. Note that a consistent finiteelement implementation of the elastoplastic coupling at finite strain has not been reported in the literature so far.…”