A phase-field fracture formulation for generalized standard materials: The interplay between thermomechanics and damage

Journal Article · Tue May 06 00:00:00 EDT 2025 · Journal of the Mechanics and Physics of Solids

DOI:https://doi.org/10.1016/j.jmps.2025.106154· OSTI ID:2566435

Svolos, Lampros ^[1]; Tran, Quoc-Thai ^[2]; Boureima, Ismael Djibrilla ^[2]; Anghel, Veronica ^[2]; Garikipati, Krishna ^[3]; Mourad, Hashem Mohamed ^[2]

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1. Univ. of Vermont, Burlington, VT (United States)
2. Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
3. Univ. of Southern California, Los Angeles, CA (United States)

Accurately modeling fracture of ductile materials poses open challenges in the field of computational mechanics due to the multiphysics nature of their failure processes. Integrating the interplay between thermodynamics and damage into ductile fracture models is vital for predicting critical failure modes. Here, in this paper, we develop a versatile phase-field (PF) framework for modeling ductile fracture, taking into account finite-strain elasto-plasticity. The framework stems from a variational formulation of constitutive relations for generalized standard materials (GSMs), whose response is described by a Helmholtz free energy and a dissipation pseudo-potential. Its variational structure is based on a minimum principle for a functional that expresses the sum of power densities for reversible and irreversible processes. By minimizing this functional with a constraint on a von Mises yield function, we derive the evolution equation for the equivalent plastic strain and an associative flow rule. This constrained optimization problem is analytically solved for a wide class of thermo-viscoplasticity models. The key innovations of the current work include (i) a cubic plastic degradation function that accounts for a non-vanishing damage-dependent yield stress, (ii) closed-form expressions of the Helmholtz free energy and dissipation pseudo-potential for three thermo-viscoplasticity models, (iii) an extended Johnson–Cook plasticity model with a nonlinear hardening law, and (iv) a plastic work heat source that depends on the plastic degradation function and a variable Taylor–Quinney (TQ) coefficient. The capabilities of the proposed framework are tested with the aid of four ductile fracture problems, including the Sandia Fracture Challenge. In each of these problems, we examine the evolution of relevant field variables such as the PF order parameter, the equivalent plastic strain, the temperature, and the internal power dissipation density, in addition to the overall structural response quantified by the force–displacement curve. These numerical studies demonstrate that the proposed framework effectively represents ductile fracture, yielding computational results that exhibit good agreement with experimental data.

• Research Organization: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
• Sponsoring Organization: USDOE National Nuclear Security Administration (NNSA)
• Grant/Contract Number: 89233218CNA000001
• OSTI ID: 2566435
• Report Number(s): LA-UR--24-29912
• Journal Information: Journal of the Mechanics and Physics of Solids, Journal Name: Journal of the Mechanics and Physics of Solids Vol. 201; ISSN 0022-5096
• Publisher: Elsevier
• Country of Publication: United States
• Language: English

Related Subjects

36 MATERIALS SCIENCE
Ductile fracture
Generalized standard materials
Phase-field modeling
Thermo-viscoplasticity