Coupled damage-plasticity constitutive model and direct stress interpolation

Abstract

International audienceIn this paper we develop the governing equations of the coupled damage-plasticity model, which is capable of representing the main mechanisms of inelastic behavior including irreversible plastic deformation, change of elastic response and the localized failure. We show in particular how such model should be implemented within the stress-based variational formulation, providing an important advantage for local computation of the internal variables, which thus remains very robust and even non-iterative for the case of linear hardening model. Several simple examples are presented in order to illustrate the kind of response the model can represent

A thermodynamically consistent plastic-damage framework for localized failure in quasi-brittle solids: Material model and strain localization analysis

“…Coupled plastic-damage models have been widely adopted to describe stiffness degradation and plastic strains of materials; see Armero and Oller (2000); Ibrahimbegovic et al (2008);Ju (1989);Ortiz (1985); Voyiadjis and Kattan (1992); Zhu et al (2010) among many others and the large volume of references in the texts (Ibrahimbegovic, 2009;Krajcinovic, 2003). In this section a unified elastoplastic damage framework (Meschke et al, 1998;Wu and Xu, 2011) is presented based on the irreversible thermodynamics with internal variables (Horstemeyer and Bammann, 2010).…”

“…Accordingly, the overall nonlinear behavior of the weakened solid can be described by tensorial constitutive relations in terms of stress versus strain equipped with internal variables. Plasticity (Chaboche, 2008;Chen, 1994) and damage mechanics (Krajcinovic, 2003;Lemaitre, 1996) or their combination (Armero and Oller, 2000;Ibrahimbegovic, 2009;Ju, 1989;Ortiz, 1985;Voyiadjis and Dorgan, 2007;Voyiadjis and Kattan, 1992;Wu et al, 2006;Zhu et al, 2010) are frequently employed to develop appropriate inelastic constitutive laws; see Abu Al-Rub and Darabi (2012); Ibrahimbegovic et al (2008) and the references therein. To guarantee objectivity of the energy dissipation during the failure process, the softening regime is in general regularized by introducing the fracture energy and an appropriately identified length scale (Bažant and Oh, 1983).…”

Performance Based Earthquake-Resistant Design: Migrating Towards Nonlinear Models and Probabilistic Framework

“…21.4). All these concepts, initially developed for quasi-statics applications, have been recently brought to bear upon dynamics providing very robust computational methods, both implicit and explicit (Ibrahimbegovic et al 2008;Delaplace and Ibrahimbegovic 2006). The list of mechanisms that must be represented when trying to model dynamic response for three different phases of earthquake is rather long: (i) plasticity for residual deformation, (ii) damage for modification of elastic response, (iii) viscosity for rate sensitivity, (iv) different hardening phenomena and (v) softening phenomena for final failure mode.…”

“…However, it is only since recent times that we have acquired the modelling capabilities; e.g. see (Benkemoun et al 2010;Dominguez et al 2005;Ibrahimbegovic and Brancherie 2003;Ibrahimbegovic and Delaplace 2003;Ibrahimbegovic and Markovic 2003;Ibrahimbegovic and Melnyk 2007;Ibrahimbegovic 2009;Ibrahimbegovic et al 2008Ibrahimbegovic et al , 2010Jehel et al 2010;Markovic and Ibrahimbegovic 2004) to provide a more refined interpretation of the local failure mechanisms rather than the global, push-over-type models. We have also very well advanced in the long process, from early works (Ibrahimbegovic andWilson 1990, 1992) to more recent works (Ibrahimbegovic and Markovic 2003) or (Ibrahimbegovic et al 2008) in development of the robust computational procedure that is able to isolate the most severely damaged zone and deliver the corresponding scenario on the interplay of different local mechanisms in building the global failure mechanisms for structures and systems of any complexity.…”

Stable splitting scheme for general form of associated plasticity including different scales of space and time

“…[9,17,35,37,38,43,48,40,45]) have turned to the implicit integration schemes, patterned after the work of Hughes and Taylor [18]. The central problem of computational plasticity has nowadays been significantly extended in order to provide more reliable interpretations of inelastic behavior mechanisms and the corresponding plastic deformation; we can handle the localized inelastic strain in the case of strain softening [20], several computing mechanisms activated simultaneously [5,8,24,20] or multi-scale representation of plastic strain field [25] requires the corresponding solution of boundary value problem at the fine scale, or yet different time scales variation of internal variables [21]. This work is concerned with important stability issues [44] in the implementation of implicit integration schemes in the case of a general form of the rate-independent elastoplastic constitutive equations, where neither the yield condition has a simple (quadratic) form, nor the elastic modulus is constant.…”