Reconsideration on the elastic damage/degradation theory for the modeling of microcrack closure-reopening (MCR) effects

Wu, Jian‐Ying; Xu, Sheng

doi:10.1016/j.ijsolstr.2012.11.012

Cited by 38 publications

(20 citation statements)

References 27 publications

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“…The cases D 0 and D 1 correspond to the classical plasticity model (Chen, 1994) and the elastic damage (degradation) model (Carol et al, 1994;Wu and Xu, 2013), respectively. For the intermediate parameter 2 .0; 1/, both the material compliance C (or the damage one C d ) and the plastic strain p are internal variables, resulting in a combined plastic-damage model.…”

Section: Evolution Laws and Rate Constitutive Relationsmentioning

confidence: 99%

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

Cervera

2016

International Journal of Solids and Structures

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Aiming for the modeling of localized failure in quasi-brittle solids, this paper addresses a thermodynamically consistent plastic-damage framework and the corresponding strain localization analysis. A unified elastoplastic damage model is first presented based on two alternative kinematic decompositions assuming infinitesimal deformations, with the evolution laws of involved internal variables characterized by a dissipative flow tensor. For the strong (or regularized) discontinuity to form in such inelastic quasi-brittle solids and to evolve eventually into a fully softened one, a novel strain localization analysis is then suggested. A kinematic constraint more demanding than the classical discontinuous bifurcation condition is derived by accounting for the traction continuity and the loading/unloading states consistent with the kinematics of a strong (or regularized) discontinuity. More specifically, the strain jumps characterized by Maxwell's kinematic condition have to be completely inelastic (energy dissipative). Reproduction of this kinematics implies vanishing of the aforesaid dissipative flow tensorial components in the directions orthogonal to the discontinuity orientation. This property allows naturally developing a localized plastic-damage model for the discontinuity (band), with its orientation and the traction-based failure criterion consistently determined a posteriori from the given stress-based counterpart. The general results are then particularized to the 2D conditions of plane stress and plane strain. It is found that in the case of plane stress, strain localization into a strong (or regularized) discontinuity can occur at the onset of strain softening. Contrariwise, owing to an extra kinematic constraint, in the condition of plane strain some continuous inelastic deformations and substantial re-orientation of principal strain directions in general have to take place in the softening regime prior to strain localization. The classical Rankine, Mohr-Coulomb, von Mises (J 2 ) and Drucker-Prager criteria are analyzed as illustrative examples. In particular, both the closed-form solutions for the discontinuity angles validated by numerical simulations and the corresponding traction-based failure criteria are obtained.

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Section: Evolution Laws and Rate Constitutive Relationsmentioning

confidence: 99%

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

Cervera

2016

International Journal of Solids and Structures

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“…Stiffness recovery due to crack closure (sometimes referred to as the ‘unilateral effect’) has been considered in a number of continuum damage and plastic‐damage constitutive models . A particular procedure involving the recovery of stiffness in models that decompose the stress and strain tensors into positive and negative parts was shown (under certain circumstances) to lead to thermodynamically inconsistent results , but these issues appear to have been resolved in a recent formulation by Wu and Xu .…”

Section: Introductionmentioning

confidence: 99%

The simulation of crack opening-closing and aggregate interlock behaviour in finite element concrete models

Jefferson

Mihai

2015

Int. J. Numer. Meth. Engng

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The ability to model crack-closure behaviour and aggregate interlock in finite element concrete models is extremely important. Both of these phenomena arise from the same contact mechanisms, and the advantages of modelling them in a unified manner are highlighted. An example illustrating the numerical difficulties that arise when abrupt crack closure is modelled is presented, and the benefits of smoothing this behaviour are discussed. We present a new crack-plane model that uses an effective contact surface derived directly from experimental data and which is described by a signed-distance function in relative-displacement space. The introduction of a crack-closure transition function into the formulation improves its accuracy and enhances its robustness. The characteristic behaviour of the new smoothed crack-plane model is illustrated for a series of relative-displacement paths. We describe a method for incorporating the model into continuum elements using a crack-band approach and address a previously overlooked issue associated with scaling the inelastic shear response of a crack band. A consistent algorithmic tangent and associated stress recovery procedure are derived. Finally, a series of examples are presented, demonstrating that the new model is able to represent a range of cracked concrete behaviour with good accuracy and robustness. Figure 10. Uniaxial opening and closing response.Figure 11. Cracks opened in uniaxial tension and subsequently loaded in shear. EMBEDDED CRACK PLANES IN A THREE-DIMENSIONAL CONSTITUTIVE MODEL Embedded smeared cracksWhen the crack-plane model is applied to continuum elements, cracks are effectively smeared over elements and are represented by directional damage. The term h is no longer employed directly to define the local strains; instead, the crack-band approach of Bazant and Oh [3] is used. This involves scaling the governing fracture softening stress-strain curve, using the fracture energy parameter .G f /, such that the energy consumed in fully opening a mode 1 crack is the same irrespective of the element size. A key assumption in this method is that (numerically) strains localise into a band of elements, one element wide, early enough in the fracture process for the fracture energy consumed outside this band to be negligible. If this assumption is valid, the inelastic fracture strain vector (i.e. the reduced form of the strain tensor) can be related to the inelastic relative-displacement vector . M u/ as follows:The characteristic length is equal to the length of the longest straight line that could be drawn within a finite element normal to the crack plane. This gives a length in between that is computed by 'Oliver's first and second methods', which are described in References [52] and [64].The element local strain vector .Q ©/ is then defined as the sum of the inelastic and elastic strain components:in which ı denotes a third-order-matrix vector contraction. The incremental fracture strains are then given by Equation (35):

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“…      I P P P (74) Remark 6.1: Wu and Xu (2013) demonstrate that the derivative expressed by Eq. (71) also serves as the thermodynamically consistent projection operator such that : .…”

Section: Accepted Manuscriptmentioning

confidence: 99%

3D elastoplastic damage model for concrete based on novel decomposition of stress

Zhang

2016

International Journal of Solids and Structures

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Confining effectUnilateral effect Damage Plasticity Concrete A B S T R A C T This study aims to develop a versatile constitutive framework for concrete that can be used in various stress states and under reversed cyclic loading. A multi-axial compression stress state is decomposed into a hydrostatic confining part and a biaxial net part to distinguish concrete behavior in triaxial and biaxial compression while preserving their similarity. This novel decomposition is combined with the positivenegative decomposition of stress, and on its basis is developed a 3D elastoplastic damage model. The suppression on damage of the net part of stress from the presence of the confining part is introduced through an increase in microscopic fracture strains, and confining effects in ductility and lateral deformation are introduced, respectively, by hardening slowdown and dilation reduction. In the meantime, independent damage/plasticity evolution in tension and compression is incorporated in the proposed 3D model with two damage variables and two hardening variables. An elastic-plasticdamage operator split integration algorithm with the backward Euler return mapping is derived, and a series of numerical simulations are carried out in comparison with tests under uniaxial, biaxial, pseudo-triaxial, and true triaxial loading with satisfactory agreement.

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Reconsideration on the elastic damage/degradation theory for the modeling of microcrack closure-reopening (MCR) effects

Cited by 38 publications

References 27 publications

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

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

The simulation of crack opening-closing and aggregate interlock behaviour in finite element concrete models

3D elastoplastic damage model for concrete based on novel decomposition of stress

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