On the coupling of anisotropic damage and plasticity models for ductile materials

An Extended Endochronic Theory Formulation of Plastically Deformed Damaged Indian Bamboo under Uniaxial Compression

“…The constitutive equations for the damaged material are written according to the principle of strain equivalence between the virgin Indian bamboo material and the damaged material. In this approach the damaged Indian bamboo is modeled using the constitutive laws of the effective undamaged material, the nominal stresses being replaced by the effective stresses [13].…”

“…The accumulation of micro-damages has a tendency to form macroscopically localized damage, which is precursor to failure. This progressive physical process of degradation of the material mechanical properties will lead to damage and consequently leading the material to complete failure [13]. A material that is exposed to loading will at a certain total strain level starts to deteriorate and small cracks, voids and cavities of various forms will appear.…”

“…This principle states that the elastic strain energy of the damaged material is the same in form as that of an undamaged material except that the stress and the strain are replaced by the effective stress and the effective strain [12,13,16]. The stored elastic energy W, in the damaged Indian bamboo material is given as:…”

“…Many models estimating the microdamage accumulation in materials have been published. Some of these models are based on damage micro-mechanics (known as micromechanical damage models) while others, based on the continuum damage theory, are known as phenomenological damage models [13]. Phenomenological models, which are applied in this article to explain the damage mechanics of Indian bamboo, are based on the initial concept of Kachanov (1958) who was the first to introduce the one dimensional damage variable for the isotropic case.…”

Numerical Predictions of the Occurrence of Necking in Deep Drawing Processes

“…It was initiated by Gurson [17], modified by Tvergaard and Needleman [18], and subsequently improved by a number of contributors (see, e.g., [19][20][21][22]). The second theory, known as continuum damage mechanics (see, e.g., [23,24]), is based on the introduction of a damage variable, which represents the surface density of defects, and can be modeled as isotropic scalar variable (see, e.g., [23,25]), or tensor variable for anisotropic damage (see, e.g., [26][27][28]). …”