A general framework for continuum damage models. I. Infinitesimal plastic damage models in stress space

We identify in this paper a general framework for the development of contin uum damage models in their fully coupled plastic damage form. The focus of this paper is directed to the general formulation of infinitesimal models d efined by yield and damage surfaces in stress space. The main feature of th e proposed formulation is the direct and independent consideration of the d amage mechanisms (isotropic damage, cracking, etc.) degrading the stiffness of the material, thus allowing for a complete physical characterization of these effects. This modular structure is accomplished by a kinematic decom position of the strains in an elastic, plastic and multiple damage parts, a s belonging to each activated damage mechanism. An additive decomposition i n the infinitesimal range of interest is considered. Based on this decompos ition, the constitutive characterization alluded to above for each damage m echanism is carried out in a complete thermodynamically consistent framewor k. One of the virtues of the considered framework is the fact that it inclu des many of the diverse damage models existing in the literature as particu lar cases. In this way, the developments presented herein furnish a unified framework for the formulation of continuum damage models, including isotro pic damage, compliance based formulations, effective stress anisotropic mod els, smeared crack models and the related formulations of cracking and dama ge based on strong discontinuities. Besides the clear physical significance added to these existing formulations, the proposed framework also defines a very convenient context for the efficient numerical integration of the re sulting models. This aspect is explored in Part II of this work, as it is t he application of the framework proposed herein to the numerical simulation of porous metals. (C) 2000 Elsevier Science Ltd. All rights reserved.