A Fast and Robust Numerical Treatment of a Gradient-Enhanced Model for Brittle Damage

Proc Appl Math and Mech

2019

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The prediction of failure mechanism in structures are always an important topic in the field of computational mechanics. Finite element computations of an inelastic material involving softening behavior (e.g. softening plasticity or damage) can suffer from strongly mesh-dependent results. Therefore, such continuum models should be equipped with a regularization (localization limiter) strategy to overcome the above-mentioned problem.In this study, we present a framework for gradient-enhancement for coupled damage-plasticity material model derived by means of Hamilton's principle for non-conservative continua. This model is applied for the numerical investigation of wear processes as they occur, e.g. in the case of mechanized tunneling. These investigations require a fine resolution of the involved constituents (cut sheet and abrasive particles in the soil). Consequently, a numerical strategy for the damage-plasticity model is demanded that allows for time-efficient simulations.In this paper, we present a first step to the mentioned ultimate goal. To this end, a numerical framework for gradientenhanced damage-plasticity coupling is proposed that is based on a combination of the finite element method with strategies from meshless methods. We demonstrate that this framework keeps the computational effort limited and for each load step close to the purely elastic problems. Several numerical examples prove the elimination of the pathological mesh dependency of the results. Furthermore, first results to the simulation of wear in tunneling machines are presented. Material ModelTo derive a model for a material undergoing isotropic brittle damage coupled with plasticity, we chose an energy-based, variational approach. To this end, we need to specify the Helmholtz free energy, the internal variables and the dissipation function. In the current material model, we investigate the linear isotropic hardening with the plastic potential w(α p ) = 1 2 K H α 2 p , and a twice differentiable damage function f (d) = exp(−d) with d ∈ [0, ∞). Utilization of the damage function f (d) leads to a softening behavior and causes the ill-posedness and numerically instability problems. Therefore, the regularization of the model is achieved by the gradient enhancement of the damage function f , specifically by adding a potential that is convex in the highest gradients to the mechanical contribution of the Helmholtz free energy. The total Helmholtz free energy thus readswhere β stands for the gradient parameter and used as a switch between local and enhanced model: setting β = 0 obtains a local coupled damage-plasticity model. In this study for brittle damage and classical rate-independent plasticity, we chose the dissipation function as D = D d + D p = r d |ḋ| + r p |ε p |, which is a homogeneous function of order one in both rates. Application of Hamilton's principle yields the evolution equations for the plastic strains, the hardening variable, and the damage function. Details are given in [1]. Thus, the evolution equation and yield function ...

Section: Materials Modelmentioning

confidence: 99%

Section: Materials Modelmentioning

confidence: 99%

See 1 more Smart Citation

Numerical investigation of wear processes by a gradient‐enhanced damage‐plasticity model

Hoormazdi

Hackl

Proc Appl Math and Mech

2019

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“…For that reason, regularization strategies, which somehow take into account the non-local behavior, have to be applied in order to prevent ill-posedness and to achieve mesh-independence. Hereto, most commonly gradient-enhanced formulations [1,2] are considered, but also integral-type [3,4] and viscous [5,6] regularization are well-known.Gradient-enhanced damage models such as [1,2], to what group our new model [7] basically belongs, come along with a field function acting on the non-local level. Two variational equations are resulting and, however, usually the number of nodal unknowns is increased and consequently the numerical effort is increased as well.In contrast, we present an improved algorithm for brittle damage [7] combining finite element and meshless methods resulting in a quick update of the field function.…”

mentioning

confidence: 99%

“…Gradient-enhanced damage models such as [1,2], to what group our new model [7] basically belongs, come along with a field function acting on the non-local level. Two variational equations are resulting and, however, usually the number of nodal unknowns is increased and consequently the numerical effort is increased as well.…”

mentioning

confidence: 99%

An Efficient Treatment of the Laplacian in a Gradient‐Enhanced Damage Model

Schwarz

Hackl

Proc Appl Math and Mech

2019

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As is well-known, softening effects that are characteristic for damage models are accompanied by ill-posed boundary value problems. This arises from non-convex and non-coercive energies and results in mesh-dependent finite element results. For that reason, regularization strategies, which somehow take into account the non-local behavior, have to be applied in order to prevent ill-posedness and to achieve mesh-independence. Hereto, most commonly gradient-enhanced formulations [1, 2] are considered, but also integral-type [3,4] and viscous [5,6] regularization are well-known.Gradient-enhanced damage models such as [1,2], to what group our new model [7] basically belongs, come along with a field function acting on the non-local level. Two variational equations are resulting and, however, usually the number of nodal unknowns is increased and consequently the numerical effort is increased as well.In contrast, we present an improved algorithm for brittle damage [7] combining finite element and meshless methods resulting in a quick update of the field function. Thereby, an efficient evaluation of the Laplace operator is applied as introduced in [8]. In the end, the numerical effort of the novel approach is almost comparable with an elastic problem while maintaining well-posedness and therefore mesh-independent results.

Adaptive and highly accurate numerical treatment for a gradient‐enhanced brittle damage model

Vogel

Numerical Meth Engineering

2020

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We present an adaptive numerical treatment for a recently published model for brittle damage with gradient enhancement. We employ adaptive strategies both in time and space, yielding detailed investigations of the convergence behavior: the damage distribution can be resolved with very high accuracy, turning the damage behavior into cracks known from fracture mechanics. Although the localization is extreme, mesh-independent results are obtained thanks to the spatial adaptivity and allow for a detailed investigation of the influence of the regularization parameter. K E Y W O R D Sadaptive finite element method, brittle damage, gradient-enhanced regularization, Laplace operator, snapback 1 This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.