Matrix-free phase-field modeling of fracture in micromechanical testing simulations of inelastic materials
Abstract
Resolving steep damage gradients across diffuse cracks in the phase-field modeling of fracture favors the use of high-order finite elements, for which matrix-free methods can provide superior performance and scalability. Here, we implement the Peric & Dettmer constitutive framework for visco-elastoplastic materials in an open source solid mechanics library supporting matrix-free operators for high-order finite elements with p-multigrid preconditioning on GPUs. We introduce a rheological fracture element assembled in series with the Peric & Dettmer block, keeping fracture and inelastic material properties mutually independent. We conduct numerical simulations of tensile and compressive quasistatic tests on synthetic particle-matrix microstructures using an El Capitan high-performance computing prototype. The results reproduce representative inelastic responses and fracture patterns, including X-shaped cracking observed in polymer-bonded explosives and cup-and-cone fracture in ductile metals.
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BibTeX
@misc{gioacchino2026matrixfree,
title = {{Matrix-free phase-field modeling of fracture in micromechanical testing simulations of inelastic materials}},
author = {Fabio Di Gioacchino and Rezgar Shakeri and Zachary Atkins and Karen Stengel and Layla Ghaffari and Jeremy Thompson and Jed Brown},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2607.21150},
eprint = {2607.21150},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.21150},
}
RIS
TY - UNPB
TI - Matrix-free phase-field modeling of fracture in micromechanical testing simulations of inelastic materials
AU - Fabio Di Gioacchino
AU - Rezgar Shakeri
AU - Zachary Atkins
AU - Karen Stengel
AU - Layla Ghaffari
AU - Jeremy Thompson
AU - Jed Brown
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2607.21150
UR - https://arxiv.org/abs/2607.21150
AB - Resolving steep damage gradients across diffuse cracks in the phase-field modeling of fracture favors the use of high-order finite elements, for which matrix-free methods can provide superior performance and scalability. Here, we implement the Peric & Dettmer constitutive framework for visco-elastoplastic materials in an open source solid mechanics library supporting matrix-free operators for high-order finite elements with p-multigrid preconditioning on GPUs. We introduce a rheological fracture element assembled in series with the Peric & Dettmer block, keeping fracture and inelastic material properties mutually independent. We conduct numerical simulations of tensile and compressive quasistatic tests on synthetic particle-matrix microstructures using an El Capitan high-performance computing prototype. The results reproduce representative inelastic responses and fracture patterns, including X-shaped cracking observed in polymer-bonded explosives and cup-and-cone fracture in ductile metals.
ER -