Using structural tensors for inelastic material modeling in the finite strain regime – A novel approach to anisotropic damage

Reese, Stefanie; Brepols, Tim; Fassin, Marek; Poggenpohl, Lukas; Wulfinghoff, Stephan

doi:10.1016/j.jmps.2020.104174

Cited by 40 publications

(24 citation statements)

References 63 publications

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“…Consequently, the direction-dependent response is characterized by the secondorder structural tensor M := a ⊗ a. (10) The introduction of additional preferred directions can be easily incorporated in future work, following, e.g., [78]. The solid B is loaded by prescribed deformations and external tractions on the boundary, defined by time-dependent Dirichlet conditions and Neumann conditions…”

Section: Basic Continuum Mechanicsmentioning

confidence: 99%

Bayesian inversion for unified ductile phase-field fracture

et al. 2021

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The prediction of crack initiation and propagation in ductile failure processes are challenging tasks for the design and fabrication of metallic materials and structures on a large scale. Numerical aspects of ductile failure dictate a sub-optimal calibration of plasticity- and fracture-related parameters for a large number of material properties. These parameters enter the system of partial differential equations as a forward model. Thus, an accurate estimation of the material parameters enables the precise determination of the material response in different stages, particularly for the post-yielding regime, where crack initiation and propagation take place. In this work, we develop a Bayesian inversion framework for ductile fracture to provide accurate knowledge regarding the effective mechanical parameters. To this end, synthetic and experimental observations are used to estimate the posterior density of the unknowns. To model the ductile failure behavior of solid materials, we rely on the phase-field approach to fracture, for which we present a unified formulation that allows recovering different models on a variational basis. In the variational framework, incremental minimization principles for a class of gradient-type dissipative materials are used to derive the governing equations. The overall formulation is revisited and extended to the case of anisotropic ductile fracture. Three different models are subsequently recovered by certain choices of parameters and constitutive functions, which are later assessed through Bayesian inversion techniques. A step-wise Bayesian inversion method is proposed to determine the posterior density of the material unknowns for a ductile phase-field fracture process. To estimate the posterior density function of ductile material parameters, three common Markov chain Monte Carlo (MCMC) techniques are employed: (i) the Metropolis–Hastings algorithm, (ii) delayed-rejection adaptive Metropolis, and (iii) ensemble Kalman filter combined with MCMC. To examine the computational efficiency of the MCMC methods, we employ the $$\hat{R}{-}convergence$$ R ^ - c o n v e r g e n c e tool. The resulting framework is algorithmically described in detail and substantiated with numerical examples.

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Section: Basic Continuum Mechanicsmentioning

confidence: 99%

Bayesian inversion for unified ductile phase-field fracture

et al. 2021

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“…However, for metallic materials, and in most of industrial applications, the adoption of an isotropic scalar variable can give satisfactory results. For sake of completeness, the reader is referred to [47,48] for examples of tensorial damage variables. Usually, the process discussed in the 'ductile fracture' bullet point of the previous section can be described by the addition of one, or more, internal variables in elastoplastic constitutive theories.…”

Section: Damage Preliminaries and Characterization Of The Stress Statementioning

confidence: 99%

“…A first strategy consists in describing the damage by means of set of vectors associated with predefined directions [116,117]. Alternatively, the damage can be described by second-order tensors [48,118,119] even though a second-order damage tensor itself can not properly describe the damage induced anisotropy in the fourth order elastic tensor. Lastly, the damage can be described by a fourth-order tensor which is derived consistently from the effective stress concept, and it has been widely adopted in the literature [97,[120][121][122].…”

Section: Models Comparison and Computational Aspectsmentioning

confidence: 99%

Ductile fracture modeling of metallic materials: a short review

Fincato

Tsutsumi

2021

Frattura Ed Integrità Strutturale

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Since the end of the last century a lot of research on ductile damaging and fracture process has been carried out. The interest and the attention on the topic are due to several aspects. The margin to reduce the costs of production or maintenance can be still improved by a better knowledge of the ductile failure, leading to the necessity to overcome traditional approaches. New materials or technologies introduced in the industrial market require new strategies and approaches to model the metal behavior. In particular, the increase of the computational power together with the use of finite elements (FE), extended finite elements (X-FE), discrete elements (DE) methods need the formulation of constitutive models capable of describing accurately the physical phenomenon of the damaging process. Therefore, the recent development of novel constitutive models and damage criteria. This work offers an overview on the current state of the art in non-linear deformation and damaging process reviewing the main constitutive models and their numerical applications.

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“…Second-order damage-tensors are always orthotropic w. r. t. their eigenbasis, limiting their degree of generality. More often than not, such a limitation is interpreted as a feature, and specific orthotropic damage models are developed, for instance for brittle materials (Kim et al., 2016), in elastoplastic and finite-strain damage coupling (Ganjiani, 2018; Reese et al., 2021), or for ceramic-matrix composites (Alabdullah and Ghoniem, 2020).…”

Section: Introductionmentioning

confidence: 99%

A convex anisotropic damage model based on the compliance tensor

Görthofer

Schneider

Hrymak

et al. 2021

International Journal of Damage Mechanics

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This work is devoted to anisotropic continuum-damage mechanics in the quasi-static, isothermal, small-strain setting. We propose a framework for anisotropic damage evolution based on the compliance tensor as primary damage variable, in the context of generalized standard models for dissipative solids. Based on the observation that the Hookean strain energy density of linear elasticity is jointly convex in the strain and the compliance tensor, we design thermodynamically consistent anisotropic damage models that satisfy Wulfinghoff’s damage-growth criterion and feature a convex free energy. The latter property permits obtaining mesh-independent results on component scale without the necessity of introducing gradients of the damage field. We introduce the concepts of stress-extraction tensors and damage-hardening functions, implicitly describing a rigorous damage-analogue of yield surfaces in elastoplasticity. These damage surfaces may be combined in a modular fashion and give rise to complex damage-degradation behavior. We discuss how to efficiently integrate Biot’s equation implicitly, and show how to design specific stress-extraction tensors and damage-hardening functions based on Puck’s anisotropic failure criteria. Last but not least we demonstrate the versatility of our proposed model and the efficiency of the integration procedure for a variety of examples of interest.

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Using structural tensors for inelastic material modeling in the finite strain regime – A novel approach to anisotropic damage

Cited by 40 publications

References 63 publications

Bayesian inversion for unified ductile phase-field fracture

Bayesian inversion for unified ductile phase-field fracture

Ductile fracture modeling of metallic materials: a short review

A convex anisotropic damage model based on the compliance tensor

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