Quantum mechanics

Phase (matter)

Engineering

Pure mathematics

Materials science

Cohesive zone model

Field (mathematics)

Mathematical optimization

Solver

Physics

Finite element method

Mathematics

Cracking

Phase field models

Composite material

Structural engineering

Fracture (geology)

Mechanics

Fracture mechanics

Computer Methods in Applied Mechanics and Engineering

Thermally induced cracking occurs in many engineering problems such as drying shrinkage cracking of concrete, thermal shock induced fracture, micro cracking of two-phase composite materials etc. The computational simulation of such a fracture is complicated, but the use of phase-field models (PFMs) is promising as they can seamlessly model complex crack patterns like branching, merging, and fragmentation by treating the crack discontinuity as thin band of diffuse damage. Despite the success of phase-field models there are two major issues in previous PFMs of thermally induced fracture. Firstly, these models, which are mostly based on a PFM using a simple quadratic degradation function without any user-defined parameters, provide solutions that are sensitive to a length scale. Secondly, they are limited to brittle fracture only. As a solution, we extend the phase-field regularized cohesive zone model (PF-CZM) of Wu [JMPS, 103 (2017)], with a rational degradation function dependent on elasticity and fracture related material parameters, to thermoelastic solids. Furthermore, we present a monolithic BFGS algorithm to solve the three-field (displacements, phase-field and temperature) coupling equations altogether. Multiple thermally induced fracture problems, simulated within the framework of the finite element method, are presented with predictions in good agreement with previous findings and experiments. The proposed model is shown to give better performance in capturing the physics of thermally induced fracture: it provides length scale insensitive responses. And the monolithic solver is 4∼5 times faster than the conventional alternating minimization solver.

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