Efficient algorithmic incorporation of tension compression asymmetry into an anisotropic damage model

Fassin, Marek; Eggersmann, Robert; Wulfinghoff, Stephan; Reese, Stefanie

doi:10.1016/j.cma.2019.03.051

Cited by 27 publications

(23 citation statements)

References 45 publications

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“…The presented anisotropic damage model, recently developed by the authors (see [1] and [2]), utilizes two internal variables ν = {D, α}, where D represents a symmetric second order damage tensor and α a scalar damage hardening variable. Using the micromorphic approach according to [3], in addition to the displacement field u, the scalar variable α χ (micromorphic counterpart to α) is introduced as global degree of freedom, based on which the gradient extension of the model is accomplished.…”

Section: Theorymentioning

confidence: 99%

“…Using the micromorphic approach according to [3], in addition to the displacement field u, the scalar variable α χ (micromorphic counterpart to α) is introduced as global degree of freedom, based on which the gradient extension of the model is accomplished. A global incremental potential approach is pursued which allows for large time/load steps (see [4] for a comparison with a standard implementation). Starting point is the time-discrete form of the global incremental potential given by…”

Section: Theorymentioning

confidence: 99%

“…[2]) The first part accounts for the gradient of the additionally introduced micromorphic field variable α χ , with l representing the internal length.…”

Section: Theorymentioning

confidence: 99%

“…Three different values for h tc are studied, see Fig. For the effect of stiffness recovery on structural level, see [2]. Considering no TCA (h tc = 1.0) delivers the lowest peak load, based on which all curves are normalized.…”

Section: Cantilever Beammentioning

confidence: 99%

“…

The work presents a gradient-extended ansisotropic damage model for brittle materials utilizing a second order damage tensor. A global incremental potential approach is pursued which allows for large time/load steps (see [4] for a comparison with a standard implementation). The formulation is based on a global incremental potential allowing for large time/load steps.

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An anisotropic brittle damage model with a damage tensor of second order using a micromorphic approach

Fassin

Eggersmann

Wulfinghoff

et al. 2019

Proc Appl Math and Mech

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The work presents a gradient-extended ansisotropic damage model for brittle materials utilizing a second order damage tensor. In order to take into account tension compression asymmetry (TCA), the strain tensor is split into a tension and a compression related part by means of a spectral decomposition. The formulation is based on a global incremental potential allowing for large time/load steps. The gradient extension is accomplished using the micromorphic approach. Although using a damage tensor of second order, only one scalar additional degree of freedom (micromorphic variable) is introduced. First, the effects of TCA are illustrated with a simple uniaxial loading case at integration point level. Afterwards, the effect of the additionally introduced artificial viscosity, used in order to circumvent snapback situations, is shown for a structural example (without TCA). Finally, a structural example considering TCA is presented for which spurious failure in compression can be avoided.The presented anisotropic damage model, recently developed by the authors (see [1] and [2]), utilizes two internal variables ν = {D, α}, where D represents a symmetric second order damage tensor and α a scalar damage hardening variable. Using the micromorphic approach according to [3], in addition to the displacement field u, the scalar variable α χ (micromorphic counterpart to α) is introduced as global degree of freedom, based on which the gradient extension of the model is accomplished. A global incremental potential approach is pursued which allows for large time/load steps (see [4] for a comparison with a standard implementation). Starting point is the time-discrete form of the global incremental potential given byHere, the time-discrete form of the local incremental potential π is given by (for details, see [5, 6]):where the specific expression for the dissipation potential φ can be found in [1]. Following the work of [3], the Helmholtz free energy has a standard local contribution and a micromorphic contribution (in order to accomplish the gradient extension):The micromorphic energy is given by ψ micr = 1 2 µl 2 ∇α χ 2 + 1 2 H χ (α χ − α) 2 . The first part accounts for the gradient of the additionally introduced micromorphic field variable α χ , with l representing the internal length. The second term acts as penalty term and penalizes the difference between the 'local' α and its micromorphic counterpart α χ by means of the penalty parameter H χ . The local part includes the elastic strain energy and damage hardening. Based on the spectral decomposition of the strain tensor the following form for ψ e is used in order account for tension compression asymmetry (cf.The parameters λ and µ represent the Lamé-constants, ϑ controls the damage anisotropy of the µ-term and h tc is the TCA parameter (h tc = 1: no TCA, h tc = 0: full TCA). The function g(D) damages the λ-term in an isotropic manner, for possible expressions see [1]. Furthermore, the following definitions are used: tr + (ε) = tr(ε) , tr − (ε) = − −tr(ε) , and

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Section: Theorymentioning

confidence: 99%

Section: Theorymentioning

confidence: 99%

“…[2]) The first part accounts for the gradient of the additionally introduced micromorphic field variable α χ , with l representing the internal length.…”

Section: Theorymentioning

confidence: 99%

Section: Cantilever Beammentioning

confidence: 99%

“…

…”

mentioning

confidence: 99%

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An anisotropic brittle damage model with a damage tensor of second order using a micromorphic approach

Fassin

Eggersmann

Wulfinghoff

et al. 2019

Proc Appl Math and Mech

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A comparative study of micromorphic gradient‐extensions for anisotropic damage at finite strains

van der Velden,

Brepols,

Reese

et al. 2024

Numerical Meth Engineering

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Modern inelastic material model formulations rely on the use of tensor‐valued internal variables. When inelastic phenomena include softening, simulations of the former are prone to localization. Thus, an accurate regularization of the tensor‐valued internal variables is essential to obtain physically correct results. Here, we focus on the regularization of anisotropic damage at finite strains. Thus, a flexible anisotropic damage model with isotropic, kinematic, and distortional hardening is equipped with three gradient‐extensions using a full and two reduced regularizations of the damage tensor. Theoretical and numerical comparisons of the three gradient‐extensions yield excellent agreement between the full and the reduced regularization based on a volumetric‐deviatoric regularization using only two nonlocal degrees of freedom.

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A thermodynamically consistent anisotropic damage model for metallic glasses

Shi

Markert

2023

Proc Appl Math and Mech

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The recent success in manufacturing large‐size, also called bulk metallic glasses (BMGs) using 3D‐printing based on laser powder bed fusion (LPBF) opens an avenue for the broad application of this material class. To explore the great potential of both as‐cast and 3D‐printed BMGs, a comprehensive understanding and an accurate prediction of the plastic deformation and damage behaviour of this material class are indispensable. In this study, we develop a thermodynamically consistent anisotropic damage model incorporating tension‐compression asymmetry (TCA) to describe the unique inelastic deformation and damage behaviours of metallic glasses. The widely observed normal stress sensitivity and plastic dilatancy in metallic glasses are considered by using an extended Mohr‐Coulomb criterion in the constitutive description. Furthermore, a second‐order damage tensor is adopted for describing the anisotropic damage behaviour. By augmenting the Helmholtz free energy function to be dependent on the gradient of the free volume concentration and the gradient of the nonlocal damage parameter, the governing equations for the corresponding internal variables are derived within the framework of finite deformation. The damage localisation and mesh dependency are correspondingly alleviated. The simulation result shows that the shear band patterns are in good agreement with the experimental observations from literature.

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Efficient algorithmic incorporation of tension compression asymmetry into an anisotropic damage model

Cited by 27 publications

References 45 publications

An anisotropic brittle damage model with a damage tensor of second order using a micromorphic approach

An anisotropic brittle damage model with a damage tensor of second order using a micromorphic approach

A comparative study of micromorphic gradient‐extensions for anisotropic damage at finite strains

A thermodynamically consistent anisotropic damage model for metallic glasses

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