Thermoelastic fracture modelling in 2D by an adaptive cracking particle method without enrichment functions

Ai, Weilong; Augarde, Charles E.

doi:10.1016/j.ijmecsci.2019.06.033

Cited by 19 publications

(4 citation statements)

References 59 publications

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“…Meshless approaches [13] have also been used that removes the difficulties involved with the discretization of the domain. Ai and Augarde [14] used the meshless method using adaptive cracking particle method that requires some visibility criteria to model the discontinuities. Recently Greco et al [15] used the moving mesh strategy to model the crack propagation in the FEM framework.…”

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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“…An illustration is shown in Figure 1 . There are several previous works that address thermal fracturing using PFM [ 26 , 28 , 29 , 30 , 31 ]. In particular, Miehe et al [ 23 ] developed a theory of thermomechanical fracture with a diffusive crack model including various nonlinear effects and demonstrated several interesting numerical examples.…”

Section: Introductionmentioning

confidence: 99%

Phase Field Models for Thermal Fracturing and Their Variational Structures

Alfat

Kimura

2022

Materials

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It is often observed that thermal stress enhances crack propagation in materials, and, conversely, crack propagation can contribute to temperature shifts in materials. In this study, we first consider the thermoelasticity model proposed by M. A. Biot and study its energy dissipation property. The Biot thermoelasticity model takes into account the following effects. Thermal expansion and contraction are caused by temperature changes, and, conversely, temperatures decrease in expanding areas but increase in contracting areas. In addition, we examine its thermomechanical properties through several numerical examples and observe that the stress near a singular point is enhanced by the thermoelastic effect. In the second part, we propose two crack propagation models under thermal stress by coupling a phase field model for crack propagation and the Biot thermoelasticity model and show their variational structures. In our numerical experiments, we investigate how thermal coupling affects the crack speed and shape. In particular, we observe that the lowest temperature appears near the crack tip, and the crack propagation is accelerated by the enhanced thermal stress.

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“…Meshless approaches [15] have also been used that removes the difficulties involved with the discretization of the domain. Ai and Augarde [16] used the meshless method using adaptive cracking particle method that requires some visibility criteria to model the discontinuities. Recently Greco et al [17] used the moving mesh strategy to model the crack propagation in the FEM framework.…”

Section: Introductionmentioning

confidence: 99%