An anisotropic cohesive fracture model: Advantages and limitations of length-scale insensitive phase-field damage models

Rezaei, Shahed; Harandi, Ali; Brepols, Tim; Reese, Stefanie

doi:10.1016/j.engfracmech.2021.108177

Cited by 27 publications

(15 citation statements)

References 73 publications

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“…4. Solving the system of equations without using the arc-length method, leads to a sudden drop in the force-displacement curve; see [5] for more details. Models are sharing the same path until the softening regime.…”

Section: A Numerical Example: An Asymmetrically Notched Specimenmentioning

confidence: 99%

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A comparative study between phase‐field and micromorphic gradient‐extended damage models for brittle fracture

Harandi

Tabib

Alatassi

et al. 2023

Proc Appl Math and Mech

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To circumvent a mesh dependency of damage models, non-local approaches such as phase-field and gradient-extended damage models have shown a good capability and attracted a lot of attention for modeling fracture. These models can predict crack nucleation, kinking, and branching. The gradient-extended formulation proposed by [1,2], which includes a micromorphic degree of freedom for damage, is connected to a phase-field damage model presented in [3]; by connecting fracture parameters in brittle fracture. The latter is followed by comparing the thermodynamic consistency of these models. Despite having similarities in the formulation, gradient-extended models differ from the standard phase-field ones by having a damage threshold. Besides that, the local iteration exists in the gradient-extended damage models. By employing the cohesive phase-field model or the Angiotensin type 1 (AT1), a damage threshold appears in the formulation; by having a linear term for damage in the crack density function, see [4,5,12]. A comparison between these models is made, by taking several numerical examples and comparing their responses in a quasi-static case. Moreover, the feasibility of different responses is addressed when one uses a standard Newton-Raphson solver or the arc-length one for solving a boundary value problem.

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Section: A Numerical Example: An Asymmetrically Notched Specimenmentioning

confidence: 99%

“…Finally, the damage threshold Y 0 can be set to zero since, for the PF formulation, the threshold does not exist. One can refer to the cohesive phase-field formulations see [4,5], or the work of [16] in order to incorporate damage threshold in the phase-field formulation. In the scope of this work, Y 0 ≈ 0 is considered.…”

Section: Ge At2 Pf Connectionmentioning

confidence: 99%

A comparative study between phase‐field and micromorphic gradient‐extended damage models for brittle fracture

Harandi

Tabib

Alatassi

et al. 2023

Proc Appl Math and Mech

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“…In the work of Lorentz et al [33,34] and Wu et al [56], a rational degradation function was proposed. It is shown that the material response for this formulation converges to the sharp interface behavior (cohesive zone) as 0 decreases [43]. The specific form of the length-scale-insensitive model is taken in this work.…”

Section: Temperature-dependent Phase-field Fracture Modelmentioning

confidence: 99%

A thermo-mechanical phase-field fracture model: application to hot cracking simulations in additive manufacturing

Ruan¹,

Rezaei²,

Yang³

et al. 2022

Preprint

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Thermal fracture is prevalent in many engineering problems and is one of the most devastating defects in metal additive manufacturing. Due to the interactive underlying physics involved, the computational simulation of such a process is challenging. In this work, we propose a thermo-mechanical phase-field fracture model, which is based on a thermodynamically consistent derivation. The influence of different coupling terms such as damage-informed thermomechanics and heat conduction and temperature-dependent fracture properties, as well as different phase-field fracture formulations, are discussed. Finally, the model is implemented in the finite element method and applied to simulate the hot cracking in additive manufacturing. Thereby not only the thermal strain but also the solidification shrinkage are considered. As for thermal history, various predicted thermal profiles, including analytical solution and numerical thermal temperature profile around the melting pool, are regarded, whereas the latter includes the influence of different process parameters. The studies reveal that the solidification shrinkage strain takes a dominant role in the formation of the circumferential crack, while the temperature gradient is mostly responsible for the central crack. Process parameter study demonstrates further that a higher laser power and slower scanning speed are favorable for keyhole mode hot cracking while a lower laser power and quicker scanning speed tend to form the conduction mode cracking. The numerical predictions of the hot cracking patterns are in good agreement with similar experimental observations, showing the capability of the model for further studies.

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“…The main driving force for these developments is the possibility to handle complex fracture phenomena within numerical methods in two and three dimensions. In recent years, several brittle [5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27] and ductile [28,29,30,31,32,33,34,35,36,37,38,39,40,41] phase-field fracture formulations have been proposed in the literature. These studies range from the modeling of Figure 1: Offshore Wind Turbine (source: germanoffshorewind.org) with different concrete microstructures.…”

Section: Introductionmentioning

confidence: 99%

Probabilistic failure mechanisms via Monte Carlo simulations of complex microstructures

Noii,

Khodadadian,

Aldakheel

2022

Preprint

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A probabilistic approach to phase-field brittle and ductile fracture with random material and geometric properties is proposed within this work. In the macroscopic failure mechanics, materials properties and exactness of spatial quantities (of different phases in the geometrical domain) are assumed to be homogeneous and deterministic. This is unlike the lower-scale with strong fluctuation in the material and geometrical properties. Such a response is approximated through some uncertainty in the model problem. The presented contribution is devoted to providing a mathematical framework for modeling uncertainty through stochastic analysis of a microstructure undergoing brittle/ductile failure. Hereby, the proposed model employs various representative volume elements with random distribution of stiff-inclusions and voids within the composite structure. We develop an allocating strategy to allocate the heterogeneities and generate the corresponding meshes in two-and three-dimensional cases. Then the Monte Carlo finite element technique is employed for solving the stochastic PDE-based model and approximate the expectation and the variance of the solution field of brittle/ductile failure by evaluating a large number of samples. For the prediction of failure mechanisms, we rely on the phase-field approach which is a widely adopted framework for modeling and computing the fracture phenomena in solids. Incremental perturbed minimization principles for a class of gradient-type dissipative materials are used to derive the perturbed governing equations. This analysis enables us to study the highly heterogeneous microstructure and monitor the uncertainty in failure mechanics. Several numerical examples are given to examine the efficiency of the proposed method.

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An anisotropic cohesive fracture model: Advantages and limitations of length-scale insensitive phase-field damage models

Cited by 27 publications

References 73 publications

A comparative study between phase‐field and micromorphic gradient‐extended damage models for brittle fracture

A comparative study between phase‐field and micromorphic gradient‐extended damage models for brittle fracture

A thermo-mechanical phase-field fracture model: application to hot cracking simulations in additive manufacturing

Probabilistic failure mechanisms via Monte Carlo simulations of complex microstructures

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