On coupled gradient-dependent plasticity and damage theories with a view to localization analysis

Borst, René de; Pamin, Jerzy; Geers, Mgd Marc

doi:10.1016/s0997-7538(99)00114-x

Cited by 160 publications

(101 citation statements)

References 24 publications

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“…They are, as we show, largely understandable in terms of the existing theoretical background, and signal that no continuum solution actually exists for the adopted model. Some localization limiting procedure [Bazant et al, 1984;de Borst, 1988;Needleman, 1988;de Borst et al, 1999] would need to be added to the constitutive description in order for a solution to exist (for more details, see de Borst and van der Giessen [1998] and Bazant and Jirasek [2002]). That is an important goal for continuing work, although even without such a procedure we can gain some important perspectives.…”

Section: Plastic Strain Localizationmentioning

confidence: 99%

Off‐fault plasticity and earthquake rupture dynamics: 1. Dry materials or neglect of fluid pressure changes

2008

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[1] We analyze inelastic off-fault response during earthquakes. Spontaneous crack-like rupture, with slip weakening, is modeled in 2-D plane strain using an explicit dynamic finite element procedure. A Mohr-Coulomb type elastic-plastic description describes the material bordering the fault. We identify the factors which control the extent and distribution of off-fault plasticity during dynamic rupture. Those include the angle with the fault of the maximum compressive prestress, the seismic S ratio, and the closeness of the initial stress state to Mohr-Coulomb failure. Plastic response can significantly alter the rupture propagation velocity, delaying or even preventing a transition to supershear rupture in some cases. Plastic straining also alters the residual stress field left near the fault. In part 1, we consider ''dry'' materials bordering the fault, or at least neglect pore pressure changes within them. Part 2 addresses the effects of fluid saturation, showing that analysis procedures of this part can describe undrained fluid-saturated response. Elastic-plastic laws of the type used are prone to shear localization, resulting in an inherent grid dependence in some numerical solutions. Nevertheless, we show that in the problems addressed, the overall sizes of plastic regions and the dynamics of rupture propagation seem little different from what are obtained when we increase the assumed plastic hardening modulus or dilatancy parameter above the theoretical threshold for localization, obtaining a locally smooth numerical solution at the grid scale. Evidence for scaling of some localization features with a real (nongrid) length scale in the model is also presented.Citation: Templeton, E. L., and J. R. Rice (2008), Off-fault plasticity and earthquake rupture dynamics: 1. Dry materials or neglect of fluid pressure changes,

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Section: Plastic Strain Localizationmentioning

confidence: 99%

Off‐fault plasticity and earthquake rupture dynamics: 1. Dry materials or neglect of fluid pressure changes

2008

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“…Since the local action (ii) and the material simplicity (iv) (see Section 2.1) are not necessarily satisfied and their relevance is therefore questionable [27], the nonlocal continuum theory can be used to integrate the weighted averages [28] and higher-order gradients of state variables, such as the observable variables (strain, temperature) or internal variables (characteristic of the dissipative processes under consideration) [12,29]. Gradient theories are therefore widely used to model the localization of the strain and damage in a large class of solid materials [30][31][32][33][34][35][36][37][38][39].…”

Section: Nonlocal Approach: Gradient Modelling With the Temperature Amentioning

confidence: 99%

On a New Kinetic Modelling Approach of the Irreversible Quasi-Surface Metallurgical Phase Transformations

Antoni

2014

Journal of Solid State Physics

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Irreversible quasi-surface metallurgical phase transformations are the specific response of some metallic materials-such as metals and alloys-subjected to high thermomechanical loads applied very near their surface during the manufacturing processes or after being put into operation. These solid/solid phase transformations can be observed, for example, on the tread of many rails in railroad networks frequented by freight trains. The severe thermal and mechanical loads imposed on the surface of the rails and in the immediate vicinity of the surface by the wheel/rail contact often result in highly localized irreversible metallurgical transformations. A new kinetic model based on a previous study is presented here, which accounts more realistically for the nucleation and growth of these irreversible solid/solid phase transformations resulting from high thermomechanical loads. This metallurgical behavioral model was developed in the framework of continuum thermodynamics with gradients of temperature and internal variables.

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“…Indeed, models that exploit the non-local interactions in the fracture process zone can be physically as well motivated and numerically more effective. Among these models, the gradient-enhanced models have shown to be computationally the most efficient, either in a plasticity-based format [47][48][49], a damage-based format [50,51], or a combination of both [52]. Especially the gradient-enhanced damage model of Peerlings et al [50,51] has proven to be robust and effective, not only for damage evolution under monotonic loading conditions, but also for fatigue loading [53].…”

Section: Higher-order Continuum Theoriesmentioning

confidence: 99%

Cohesive‐zone models, higher‐order continuum theories and reliability methods for computational failure analysis

Borst

Gutiérrez

Wells

et al. 2004

Numerical Meth Engineering

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SUMMARYA concise overview is given of various numerical methods that can be used to analyse localization and failure in engineering materials. The importance of the cohesive-zone approach is emphasized and various ways to incorporate the cohesive-zone methodology in discretization methods are discussed. Numerical representations of cohesive-zone models suffer from a certain mesh bias. For discrete representations this is caused by the initial mesh design, while for smeared representations it is rooted in the ill-posedness of the rate boundary value problem that arises upon the introduction of decohesion. A proper representation of the discrete character of cohesive-zone formulations which avoids any mesh bias can be obtained elegantly when exploiting the partition-of-unity property of finite element shape functions. The effectiveness of the approach is demonstrated for some examples at different scales. Moreover, examples are shown how this concept can be used to obtain a proper transition from a plastifying or damaging continuum to a shear band with gross sliding or to a fully open crack (true discontinuum). When adhering to a continuum description of failure, higher-order continuum models must be used. Meshless methods are ideally suited to assess the importance of the higher-order gradient terms, as will be shown. Finally, regularized strain-softening models are used in finite element reliability analyses to quantify the probability of the emergence of various possible failure modes.

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On coupled gradient-dependent plasticity and damage theories with a view to localization analysis

Cited by 160 publications

References 24 publications

Off‐fault plasticity and earthquake rupture dynamics: 1. Dry materials or neglect of fluid pressure changes

Off‐fault plasticity and earthquake rupture dynamics: 1. Dry materials or neglect of fluid pressure changes

On a New Kinetic Modelling Approach of the Irreversible Quasi-Surface Metallurgical Phase Transformations

Cohesive‐zone models, higher‐order continuum theories and reliability methods for computational failure analysis

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