Fracture of thermo-elastic solids: Phase-field modeling and new results with an efficient monolithic solver

A phase-field model for thermo-mechanical fracture with an open-source implementation of it using Gridap in Julia

“…the crack propagates diagonally. The obtained crack propagation directions shows similar trend to that obtained by Duflot [13], Prasad et al [49], and Mandal et al [30].…”

“…The resulting displacement can be directly obtained by using the governing equation corresponding to the displacement field. This is similar to the one adopted by Mandal et al [30] wherein the load has been applied in the form of temperature strain based on the temperature change. The crack propagates because of thermal stresses due to the different coefficients of thermal expansion.…”

“…The problem has been introduced by Prasad et al [49], and since then, it has been considered as a benchmark problem for numerical analysis of thermo-mechanical fracture. We have taken L as 50 mm and chosen material properties from [49] and [30], which are E = 218400 N/m 2 , ν = 0.2, G c = 0.0002 N/m, ρ = 0.0, α = 6 × 10 −4 ℃, k 0 = 1.0W /m℃, c = 1.0J/kg ℃ . For numerical simulations, we have assumed plane stress condition similar to Mandal et al [30], and we have discretized the domain using CST elements.…”

“…We have taken L as 50 mm and chosen material properties from [49] and [30], which are E = 218400 N/m 2 , ν = 0.2, G c = 0.0002 N/m, ρ = 0.0, α = 6 × 10 −4 ℃, k 0 = 1.0W /m℃, c = 1.0J/kg ℃ . For numerical simulations, we have assumed plane stress condition similar to Mandal et al [30], and we have discretized the domain using CST elements. The Julia code for creating the mesh file for a particular case is given in Julia code for meshing of cruciform shape notched plate.…”

“…To simulate the realistic crack propagation under dynamic loading in a thermoelastic solid Chu et al [4] proposed a new elastic energy density and derived the coupling equations based on the energy balance principle. Mandal et al [30] extended the work of Wu [31] and Wu and Nguyen [32] for the thermoelastic case including a monolithic BFGS (Broyden-Fletcher-Goldfarb-Shanno) algorithm to solve the coupling equations. Wang et al [33] provided an Abaqus implementation of the thermoelastic problem using explicit time integration, as well as source code that can be used to adapt it to other multifield problems by researchers.…”