An extended deep energy method for thermo-mechanical crack propagation

2026-10-07

AI Summary

This study addresses the challenge of unifying transient heat conduction and crack growth modeling within neural network solvers for thermo-mechanical crack propagation. To this end, an extended deep energy method is proposed, employing dual networks to represent temperature and displacement fields separately. A scalar embedding function implicitly describes sharp cracks, enabling the treatment of field discontinuities without a regularization length parameter. Coupled solutions are achieved via a staggered minimization strategy, while Williams asymptotic expansions enrich the crack-tip displacement field and hierarchical Monte Carlo integration enhances computational accuracy. Experimental results demonstrate that the stress intensity factor error is merely 0.11%, with predicted crack paths exhibiting excellent agreement with reference solutions, thereby validating the accuracy and effectiveness of the proposed approach under complex loading conditions.

Abstract

Thermo-mechanical fracture couples transient heat conduction on a cracked domain with a crack that grows as the temperature and the displacement evolve. Neural energy solvers have been proposed for phase-field fracture and later extended to represent a sharp crack through the network input, but heat conduction on the cracked domain and crack propagation under the resulting thermal stresses have not yet been treated together in these solvers. We present an extended deep energy method for thermo-mechanical crack propagation in which the crack remains a sharp polyline. Two networks represent the temperature and the displacement and receive the crack through a scalar embedding function, discontinuous across the crack and smooth elsewhere, so that both fields can jump across it without a regularization length, and the displacement is enriched near the tip by the Williams expansion with trainable amplitudes. The two fields are obtained by minimizing an incremental conduction functional and the thermoelastic potential energy in a staggered sequence, with Monte Carlo integration on points stratified over background elements, densified near the tip and redrawn during training. The stress intensity factors are extracted by the interaction integral with the area term of Wilson and Yu and checked by a sweep of the contour radius, and the crack advances at the maximum hoop stress angle when the energy release rate of the kink reaches the critical value at the crack-tip temperature. On a stationary thermal edge crack the extracted stress intensity factor agrees with the published value to 0.11%, in a functionally graded shear test initiation agrees with an independent sharp-crack finite element solution to within one load step, and on a notched cruciform specimen the crack paths follow the published solutions under mechanical, thermal and combined loading.

Problem

• thermo-mechanical fracture
• crack propagation
• deep energy method
• transient heat conduction
• sharp crack

Innovation

• Deep energy method
• Thermo-mechanical fracture
• Sharp crack
• Physics-informed neural networks
• Williams expansion