A thermodynamically motivated implicit gradient damage framework and its application to brick masonry cracking

Peerlings, Rhj Ron; Massart, TJ Thierry; Geers, Mgd Marc

doi:10.1016/j.cma.2003.10.021

Cited by 95 publications

(66 citation statements)

References 32 publications

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“…It was noted in [21] that the regularized hardening law (2.24) differs from the function R(χ ) which is obtained by substituting the variable p by the micromorphic/regularized variable χ in the hardening function, as initially proposed in [59]. This inconsistency leads to difficulties in combining hardening and softening material behaviour, as recognized in [20,60,61], difficulties that are settled by adopting the previous thermodynamic framework.…”

Section: (B) Scalar Microstrainmentioning

confidence: 99%

“…= {u, χ ∼ }. The theory is presented here in the case of a symmetric microstrain tensor χ ∼ following [20,41,53] which is less general than Eringen's original nonsymmetric microdeformation. The microstrain components χ ij are generally distinct from those of the classical small strain tensor ε ij = (u i,j + u j,i )/2.…”

Section: (A) Microstrain Tensor Modelmentioning

confidence: 99%

“…simple tension or shear) and with all variables depending on x only, the plastic microstrain variable is solution of the following differential equation derived from equation (3.7) for a power-law potential: 20) where the prime indicates derivation with respect to the single spatial coordinate. The enhanced hardening rule becomes…”

Section: (B) Logarithmic Potentialmentioning

confidence: 99%

“…This is for instance the case of the regularization strategy proposed for softening plasticity and damage in [9,[16][17][18][19] where the additional field equations and their coupling to the physical equations are postulated as PDEs independent of the specific form of the mechanical constitutive equations. By contrast, thermodynamically based formulations have been proposed where regularization differential operators are derived from new balance equations of generalized forces [20][21][22][23]. The form of the regularization operator then follows from the choice of constitutive equations linking generalized stresses and generalized strains and is not given a priori.…”

Section: Introductionmentioning

confidence: 99%

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Nonlinear regularization operators as derived from the micromorphic approach to gradient elasticity, viscoplasticity and damage

Forest¹

2016

Proc. R. Soc. A.

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International audienceThe construction of regularization operators presented in this work is based on the introduction of strain or damage micromorphic degrees of freedom in addition to the displacement vector and of their gradients into the Helmholtz free energy function of the constitutive material model. The combination of a new balance equation for generalized stresses and of the micromorphic constitutive equations generates the regularization operator. Within the small strain framework, the choice of a quadratic potential w.r.t. the gradient term provides the widely used Helmholtz operator whose regularization properties are well known: smoothing of discontinuities at interfaces and boundary layers in hardening materials, and finite width localization bands in softening materials. The objective is to review and propose nonlinear extensions of micromorphic and strain/damage gradient models along two lines: the first one introducing nonlinear relations between generalized stresses and strains; the second one envisaging several classes of finite deformation model formulations. The generic approach is applicable to a large class of elastoviscoplastic and damage models including anisothermal and multiphysics coupling. Two standard procedures of extension of classical constitutive laws to large strains are combined with the micromorphic approach: additive split of some Lagrangian strain measure or choice of a local objective rotating frame. Three distinct operators are finally derived using the multiplicative decomposition of the deformation gradient. A new feature is that a free energy function depending solely on variables defined in the intermediate isoclinic configuration leads to the existence of additional kinematic hardening induced by the gradient of a scalar micromorphic variable

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Section: (B) Scalar Microstrainmentioning

confidence: 99%

Section: (A) Microstrain Tensor Modelmentioning

confidence: 99%

Section: (B) Logarithmic Potentialmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Nonlinear regularization operators as derived from the micromorphic approach to gradient elasticity, viscoplasticity and damage

Forest¹

2016

Proc. R. Soc. A.

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“…This equation expresses "that no direct energy exchange can exist with the surroundings of the body and ensures that the net dissipation in the body vanishes for constant damage" [55] However, as it will be shown in the next section, this boundary condition will be accounted for when establishing the finite-element formulation, and will not have to be enforced explicitly during the computation.…”

Section: Governing Equationsmentioning

confidence: 99%

A multiscale mean-field homogenization method for fiber-reinforced composites with gradient-enhanced damage models

Noels

Adam³

et al. 2012

Computer Methods in Applied Mechanics and Engineering

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In this work, a gradient-enhanced homogenization procedure is proposed for fiber reinforced materials. In this approach, the fiber is assumed to remain linear elastic while the matrix material is modeled as elasto-plastic coupled with a damage law described by a non-local constitutive model. Toward this end, the mean-field homogenization is based on the knowledge of the macroscopic deformation tensors, internal variables and their gradients, which are applied to a micro-structural representative volume element (RVE). The macro-stress is then obtained from a homogenization procedure. The methodology holds for 2-phase composites with moderate fiber volume ratios, and for which, at the RVE size, the matrix can be considered as homogeneous isotropic and the ellipsoidal fibers can be considered as homogeneous transversely isotropic. Under these assumptions, the method is successfully applied to simulate the damage process occurring in unidirectional carbon-fiber reinforced epoxy composites submitted to different loading conditions.

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High‐performance parallel simulation of structure degradation using non‐local damage models

Germain

Besson

Feyel

et al. 2006

Numerical Meth Engineering

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International audienceSimulating damage and failure of metallic or composite structures often fails when using standard finite element discretizations and a Newton-Raphson solving procedure. The difficulties arise from an uncontrolled mesh dependency caused by damage localization, to structural instabilities and to an increase of computational costs. The first problem can be overcome by using non-local damage constitutive equations together with a specific finite element model. The second problem can then be solved with an arc-length method which manages instabilities and snap-backs. They are caused by the loss of strength-carrying capacity of the damaged material. Finally, the whole computational scheme is parallelized. The main contribution of this paper consists in bringing together the three numerical techniques: non-local material model; piloting and parallel computations. The resulting numerical scheme allows to go beyond the overly simplistic cases often encountered in the literature. It allows robust industrial simulations with a high number of degrees of freedom, both in two and three dimensions, and deepened studies involving a large number of simulations

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A thermodynamically motivated implicit gradient damage framework and its application to brick masonry cracking

Cited by 95 publications

References 32 publications

Nonlinear regularization operators as derived from the micromorphic approach to gradient elasticity, viscoplasticity and damage

Nonlinear regularization operators as derived from the micromorphic approach to gradient elasticity, viscoplasticity and damage

A multiscale mean-field homogenization method for fiber-reinforced composites with gradient-enhanced damage models

High‐performance parallel simulation of structure degradation using non‐local damage models

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