An extended deep energy method for thermo-mechanical crack propagation
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.
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BibTeX
@misc{zhang2026extended,
title = {{An extended deep energy method for thermo-mechanical crack propagation}},
author = {Han Zhang and Mehrisadat Makki Alamdari and Babak Shahbodagh and Mohammad Vahab and Cosmin Anitescu and Timon Rabczuk and Elena Atroshchenko},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.09433},
eprint = {2610.09433},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.09433},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - An extended deep energy method for thermo-mechanical crack propagation
AU - Han Zhang
AU - Mehrisadat Makki Alamdari
AU - Babak Shahbodagh
AU - Mohammad Vahab
AU - Cosmin Anitescu
AU - Timon Rabczuk
AU - Elena Atroshchenko
PY - 2026
DA - 2026/10/07
PB - arXiv
DO - 10.48550/arxiv.2610.09433
UR - https://arxiv.org/abs/2610.09433
AB - 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.
ER -