A Thermo-mechanical gradient enhanced damage method for fracture

Sarkar, Subrato; Singh, I.V.; Mishra, B.K.

doi:10.1007/s00466-020-01908-z

Cited by 28 publications

(7 citation statements)

References 43 publications

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“…Gradient damage model, peridynamic and phase-field model, etc., are some of the popular continuum-based approaches. Localizing gradient damage model (LGDM) [16] was used for thermoelastic brittle fracture by Sarkar et al [17]. Recently, using the mathematical similarity between damaged material and Riemannian manifold a new continuum-based damage model has been proposed by Das et al [18].…”

Section: Introductionmentioning

confidence: 99%

A phase-field model for thermo-mechanical fracture

Prakash

Behera

Rahaman

2022

Mathematics and Mechanics of Solids

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In this article, we propose a thermodynamically consistent phase-field model for thermo-mechanical fracture and provide an open-source implementation of the proposed model using a recently developed finite element toolbox, Gridap in Julia. Here, we have derived the balance equations for the thermo-mechanical fracture by invoking the virtual power principle and determined the constitutive relations for the thermodynamic fluxes based on the satisfaction of the thermodynamic laws. Our proposed formulation provides an equation of temperature evolution that can easily accommodate dissipative effects such as viscous damping. We provide very compact and user-friendly open-source codes for implementing the proposed model using Gridap in Julia that requires very low memory usage and gives a high degree of flexibility to the users in defining weak forms of the governing partial differential equations (PDEs). We have validated the proposed model and its implementation against such standard results available in the literature as crack propagation in the cruciform shape material, single edge notched plate, bi-material beam, and a quenching test.

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Section: Introductionmentioning

confidence: 99%

A phase-field model for thermo-mechanical fracture

Prakash

Behera

Rahaman

2022

Mathematics and Mechanics of Solids

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“…Then, more studies on parameters, especially those accounting for temperature-dependent characteristics, are of importance for practical and realistic engineering applications. Furthermore, in order to obtain a relatively sharp and thin damage profile within the gradient damage framework, several approaches, for example, the conceptual transient length effect model, 46,47 the localizing gradient damage approach 36,[48][49][50] and the gradient damage model based on a micromorphic extension, 51,52 can be considered for further developments.…”

Section: Discussionmentioning

confidence: 99%

Thermomechanical fatigue life prediction of metallic materials by a gradient‐enhanced viscoplastic damage approach

Yin

Zreid

Zhao

et al. 2022

Numerical Meth Engineering

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Fatigue failure plays an important role in engineering applications, especially when structural components experience significant cyclic thermal loading and complex force loading simultaneously. During the last decades, several post-processing techniques have been developed based on empirical investigations of experimental evidence to predict the fatigue life of materials. The work at hand postulates a conventional continuum damage theory for thermomechanical fatigue failure modeling. In particular, an implicit gradient-enhanced approach is employed to address the ill-posedness of the partial differential equation system when the damage onsets. An internal fatigue variable is phenomenologically defined based on the accumulation of viscoplasticity. In the sequel, a regularized fatigue variable is obtained to further yield the damage softening function, which straightforwardly applies to the stress, material tangent, and viscoplastic dissipation. A multi-field problem, consisting of the strain field, the temperature, and the non-local variable, is taken into consideration, leading to a fully coupled system. This numerical methodology is consistently derived and implemented into the context of the finite element method. Several representative and demonstrative examples are performed, which yield good numerical stability and agreement with experimental data. Conclusive findings and further perspectives close this article.

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“…the gradient parameter (c) and the interaction parameter (g). The significance of these parameters is discussed extensively in the author's previous work (Sarkar et al, 2019a, Sarkar et al, 2020b and thus avoided here for brevity. However, the expressions for the damage law (D), macro equivalent strain (𝜀 eq ) and interaction function (g) used in the present work are defined in Appendix A.…”

Section: Localizing Gradient Damage Methods (Lgdm)mentioning

confidence: 99%