A gradient-enhanced damage model coupled to plasticity—multi-surface formulation and algorithmic concepts

Kiefer, Björn; Waffenschmidt, Tobias; Sprave, Leon; Menzel, Andreas

doi:10.1177/1056789516676306

Cited by 55 publications

(57 citation statements)

References 120 publications

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“…The numerical solution is then mesh dependent and the actual results are not reliable. Often, size effects and localization mechanisms can be captured with non-local models (Dimitrijevic and Hackl, 2008;Waffenschmidt et al, 2014;He et al, 2015;Kiefer et al, 2017), which use gradients of the variables and introduce a characteristic length. In the current work the proposed damage model is formulated and implemented in the framework of CDM with the assumption of diffuse damage prior to damage localization.…”

Section: Remarks and Discussionmentioning

confidence: 99%

Hybrid micromechanical-phenomenological modelling of anisotropic damage and anelasticity induced by micro-cracks in unidirectional composites

Praud

Chatzigeorgiou

Chemisky

et al. 2017

Composite Structures

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Section: Remarks and Discussionmentioning

confidence: 99%

Hybrid micromechanical-phenomenological modelling of anisotropic damage and anelasticity induced by micro-cracks in unidirectional composites

Praud

Chatzigeorgiou

Chemisky

et al. 2017

Composite Structures

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“…However, the response for a higher hardening modulus drops earlier and more rapidly -explained by the dependence on only the elastic strains of the damage driving force q. A more detailed analysis of the influence of material parameters for a very similar model can be found in [4]. The regularisation behaviour is analysed in Figure 1b.…”

Section: Simulation Resultsmentioning

confidence: 94%

“…The main advantage of this approach is to keep the KKT conditions at material point level, allowing the incorporation of many established isotropic damage models. The governing equations for this model follow from a variational approach with homogeneous Neumann boundary conditions for the nonlocal damage field, see [3][4][5]].…”

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confidence: 99%

A multisurface model for gradient‐enhanced damage coupled to finite plasticity

Sprave

Menzel

2017

Proc Appl Math and Mech

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A gradient-enhanced damage formulation is coupled to isotropic plasticity in the framework of finite strains. Within the finite element method, an additional field variable representing nonlocal damage is introduced and linked to its local counterpart in order to allow a standard local formulation at the material point level. The onset of damage and plasticity is governed by damage and yield criteria respectively. This multisurface approach requires the determination of the two Lagrange multipliers. By using logarithmic strains, a formulation in principal axes in combination with a von Mises yield criterion is implemented. The damage functions are defined by means of exponential functions in order to avoid further constraints on the local damage variable. The model is able to capture a wide range of material responses, ranging from brittle to ductile damage and plasticitiy dominated behaviour. The mesh independence of the model is shown by means of representative finite element examples. Nonlocal damage variableClassical gradient-enhanced damage models require, in the context of finite elements, a global handling of the underlying Karush-Kuhn-Tucker (KKT) conditions, e.g. an active set method to determine on which nodes damage evolves. In this work, however, following approaches in [1,2], an additional scalar field variable φ representing nonlocal damage is introduced. Local and nonlocal damage is weakly linked via a penalty approach. The gradient-enhancement of the model can then be achieved by incorporating the gradient of the nonlocal damage variable. Hence, the free Helmholtz energy is additively combined of a local and nonlocal contribution

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“…The approach chosen here follows the small strain formulation [1,2] and, in particular, the finite deformation gradient-enhanced framework established in [3,4]. Modelling details of a related small strain model are discussed in [5]. In the framework an additional scalar field variable φ, representing non-local damage, is introduced and linked to the local damage variable d in penalty form.…”

Section: Model Descriptionmentioning

confidence: 99%

Gradient‐enhanced ductile damage — a finite deformation framework with application to DP800

Sprave

Menzel

2018

Proc Appl Math and Mech

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Gradient-enhanced ductile damage is implemented in the finite element method by means of an additional field variable, representing non-local damage which is linked to the local damage variable. At material point level the isotropic damage formulation uses exponential damage functions to circumvent further constraints on the value set of the local damage variable. The ductility of the model is achieved by a coupling of damage to finite strain plasticity. In a multisurface approach the onset of damage and plasticity is each governed by damage and yield criteria respectively. Linear and exponential isotropic hardening is implemented. With the help of the F-bar method the results of the finite element simulation exhibit mesh independent behaviour. In order to model the behaviour of DP800 with the material model discussed here, elastic and plastic parameters are identified. Model descriptionThere are various possibilities to enhance a material model with gradients. The approach chosen here follows the small strain formulation [1, 2] and, in particular, the finite deformation gradient-enhanced framework established in [3,4]. Modelling details of a related small strain model are discussed in [5]. In the framework an additional scalar field variable φ, representing non-local damage, is introduced and linked to the local damage variable d in penalty form. Furthermore, only the gradient of the field variable, ∇ X φ, and not the gradient of the local damage, ∇ X d, enters the energy functional. Thereby, in the context of finite elements, a local formulation of the material model at quadrature point level is possible despite the gradient-enhancement. The local part of the free Helmholtz energy is formulated in terms of logarithmic elastic strains, ε e = ln(b e ) with b e = F e · F e t , assuming a multiplicative split of the deformation gradient into elastic and plastic parts, i.e. F = F e · F p . The energy functional then takes the formwhere the volumetric and isochoric contributions are each weighted by a so-called damage function f vol and f iso . The regularisation parameter c d has to be chosen sufficiently large and controls the width of the damage zone. The damage function f maps the positive but otherwise unbounded local damage variable d to the interval ]0, 1], i.e.Additional constraints on the link between φ and d can thus be avoided. Damage driving force q, isotropic hardening stress β and Mandel stresses m are derived within the framework of generalised standard dissipative materials. Following the postulate of strain equivalence, the effective Mandel stress tensor m eff is defined asIn this multisurface formulation the evolution of plasticity and damage is each governed by its own potential. For the plastic evolution a von Mises yield criterion Φ p based on the effective Mandel stresses including non-linear isotropic hardening is used. The damage potential Φ d simply compares the damage driving force q with a variable threshold in the form ofIn terms of the algorithmic implementation, d and α are integrated by...

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A gradient-enhanced damage model coupled to plasticity—multi-surface formulation and algorithmic concepts

Cited by 55 publications

References 120 publications

Hybrid micromechanical-phenomenological modelling of anisotropic damage and anelasticity induced by micro-cracks in unidirectional composites

Hybrid micromechanical-phenomenological modelling of anisotropic damage and anelasticity induced by micro-cracks in unidirectional composites

A multisurface model for gradient‐enhanced damage coupled to finite plasticity

Gradient‐enhanced ductile damage — a finite deformation framework with application to DP800

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