A micromorphic approach for gradient-enhanced anisotropic ductile damage

Langenfeld, Kai; Mosler, Jörn

doi:10.1016/j.cma.2019.112717

Cited by 23 publications

(20 citation statements)

References 40 publications

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“…In the absence of friction ( = 0 or = 0) this reduces to the simple failure condition | | = considered in section 2.1. The scenario whereby tensile failure is active ( < 0) is not considered in this paper but is easily incorporated into the model using the standard approach for opening cracks [21][22][23][24][25].…”

Section: Mohr-coulomb Failure Modelmentioning

confidence: 99%

“…Mathematical modelling of the growth of opening cracks in tension has been widely studied , whereas the growth of non-opening, frictional sliding cracks in compression has received less attention. A range of methods and models have been proposed for modelling brittle and ductile crack opening problems: continuum-based models such as the finite element method (FEM) [2], the extended finite element method (XFEM) [2,4], the phase field method [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20], damage models [21][22][23][24][25], the numerical manifold method [26] and the material point erosion method [27]. Closed crack problems for modelling brittle materials in compression range from the finite-discrete element method (FDEM) [28] to damage models [29][30][31][32][33], phase field models [34][35][36][37][38] as well as particle-based models [39][40][41][42] and plasticity models [37].…”

Section: Introductionmentioning

confidence: 99%

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A damage model for the frictional shear failure of brittle materials in compression

Gill¹

2021

Preprint

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Damage models have been successfully employed for many decades in the modelling of tensile failure, where the crack surfaces separate as a crack grows. The advantage of this approach is that crack trajectories can be computed simply and efficiently on a fixed finite element mesh without explicit tracking. The development of damage models for shear failure in compression, where the crack faces slide over each other subject to friction, is a non-trivial extension of this approach. A major difference is that part of the material stiffness in the damaged region must be retained to avoid interpenetration of the crack faces. This problem is resolved here by employing an anisotropic modification to the elastic stiffness tensor in the damaged region. This has the benefit of driving frictional cracks into the correct orientation, according to the Mohr-Coulomb failure criteria, but three issues remain. The first is that the shear discontinuity introduces some spurious stress perturbations around crack regions that are narrow (less than 3-4 elements wide). This is ameliorated by Helmholtz smoothing to allow efficient simulation on a coarse mesh. The second is that the complementarity of shear stress means that the shear stiffness is removed normal to the crack interface as well as parallel to it, and the third is that there are two potentially active failure planes at each point. Both these latter two issues are resolved by the introduction of a novel failure plane selection variable, which regulates either single plane or dual plane failure, and prevents the growth of erroneous cracks normal to the crack face. Both local and non-local models are investigated for linear and exponential strain softening responses. Unlike the non-local model, the local model demonstrates some mesh-size dependence, but it still retains some properties of interest, in that it supports narrower cracks and more rapidly forms a preference for the growth of a single crack when there are a number of competing cracks. The model is implemented in commercial finite element package COMSOL Multiphysics v5.5 and validated against two benchmark simulations: biaxial compression and the failure of a 45 o slope. The correct crack angles, stipulated by the Mohr-Coulomb friction angle, are correctly reproduced, as is the postfailure residual frictional force in biaxial compression. The effect of the shear fracture energy on the force-displacement response is investigated, demonstrating the successful simulation of the range of material behaviour expected in geological samples, from broad ranged gradual collapse to sharp, almost instantaneous failure.PREPRINT: A damage model for the frictional shear failure of brittle materials in compression PREPRINT: A damage model for the frictional shear failure of brittle materials in compression they "…are computationally efficient and thus suitable for large-scale engineering simulations, phase field methods are quite demanding and therefore currently limited to small-scale problems." [47]. As such, it is an objective of ...

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Section: Mohr-coulomb Failure Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A damage model for the frictional shear failure of brittle materials in compression

Gill¹

2021

Preprint

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“…It is worth nothing that, from a mathematical view point, the implicit gradient regularization resembles phase-field fracture models as a particular case of averaging equation [12,13]. Non-local damage mechanics via the implicit gradient approach has been mainly implemented in FE by means of a monolithic scheme of the overall problem as pursued in many relevant works that studied the application of such a regularization technique on different types of damage models [14,15]. However, the elevated computational cost of the FE implementation limits the geometrical complexity and the discretization level of the numerical simulations that, in most cases, are restricted to two-dimensional problems [16,17,18].…”

Section: Introductionmentioning

confidence: 99%

An FFT framework for simulating non-local ductile failure in heterogeneous materials

Magri,

Lucarini,

Lemoine

et al. 2021

Preprint

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The simulation of fracture using continuum ductile damage models attains a pathological discretization dependence caused by strain localization, after loss of ellipticity of the problem, in regions whose size is connected to the spatial discretization. Implicit gradient techniques suppress this problem introducing some inelastic non-local fields and solving an enriched formulation where the classical balance of linear momentum is fully coupled with a Helmholtz-type equation for each of the non-local variable. Such Helmholtz-type equations determine the distribution of the non-local fields in bands whose width is controlled by a characteristic length, independently on the spatial discretization. The numerical resolution of this coupled problem using the Finite Element method is computationally very expensive and its use to simulate the damage process in 3D multi-phase microstructures becomes prohibitive.In this work, we propose a novel FFT-based iterative algorithm for simulating gradient ductile damage in computational homogenization problems. In particular, the Helmholtz-type equation of the implicit gradient approach is properly generalized to model the regularization of damage in multi-phase media, where multiple damage variables and different characteristic lengths may come into play. In the proposed iterative algorithm, two distinct problems are solved in a staggered fashion: (i) a conventional mechanical problem via a FFT-Galerkin solver with mixed macroscopic loading control and (ii) the generalized Helmholtz-type equation using a Krylov-based algorithm combined with an efficient pre-conditioner. The numerical implementation is firstly validated on simple two-dimensional microstructures, showing identical responses for different spatial discretizations and reproducing a ductility change dependent on the characteristic length. Finally, the robustness and efficiency of the algorithm is demonstrated in the simulation of failure of complex 3D particle reinforced composites characterized by millions of degrees of freedom.

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“…These changes may be captured by an approach which, by means of related mappings, introduces a fictitious undamaged configuration and which defines a tensorial damage variable, see [17,[41][42][43] amongst others. Research on anisotropic damage formulations is a continuously active area of research, see, e.g., [29,64], to name but a few.…”

Section: Introductionmentioning

confidence: 99%

“…the damage state itself. Another focus lies on the regularisation of anisotropic damage formulations, see, e.g., [1,29].…”

Section: Introductionmentioning

confidence: 99%

A large strain gradient-enhanced ductile damage model: finite element formulation, experiment and parameter identification

Sprave

Menzel

2020

Acta Mech

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A gradient-enhanced ductile damage model at finite strains is presented, and its parameters are identified so as to match the behaviour of DP800. Within the micromorphic framework, a multi-surface model coupling isotropic Lemaitre-type damage to von Mises plasticity with nonlinear isotropic hardening is developed. In analogy to the effective stress entering the yield criterion, an effective damage driving force—increasing with increasing plastic strains—entering the damage dissipation potential is proposed. After an outline of the basic model properties, the setup of the (micro)tensile experiment is discussed and the importance of including unloading for a parameter identification with a material model including damage is emphasised. Optimal parameters, based on an objective function including measured forces and the displacement field obtained from digital image correlation, are identified. The response of the proposed model is compared to a tensile experiment of a specimen with a different geometry as a first approach to validate the identified parameters.

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A micromorphic approach for gradient-enhanced anisotropic ductile damage

Cited by 23 publications

References 40 publications

A damage model for the frictional shear failure of brittle materials in compression

A damage model for the frictional shear failure of brittle materials in compression

An FFT framework for simulating non-local ductile failure in heterogeneous materials

A large strain gradient-enhanced ductile damage model: finite element formulation, experiment and parameter identification

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