Neural Networks Meet Phase-Field: A Hybrid Fracture Model
Publikation: Vorabdruck/Dokumentation/Bericht › Vorabdruck (Preprint)
Beitragende
Abstract
We present a hybrid phase-field model of fracture at finite deformation and its application to the quasi-incompressible, hyperelastic behaviour of rubber. The key idea is to combine the predictive capability of the well-established phase-field approach to fracture with a physics-augmented neural network (PANN) that serves as a flexible, high-fidelity model of the response of the bulk material. To this end, recently developed neural network approaches are modified to better meet specific requirements of the phase-field framework. In particular, a novel architecture for a hyperelastic PANN is presented, that enables a decoupled description of the volumetric and the isochoric response based on a corresponding additive decomposition of the Helmholtz free energy. This is of particular interest when modelling fracture of soft quasi-incompressible solids with the phase-field approach, where a weakening of the incompressibility constraint in fracturing material may be required. Moreover, such an additive decomposition of free energy is a prerequisite for the application of several split methods, i.e. decompositions of free energy into degraded and non-degraded portions, which can improve model behaviour under multiaxial stress states. For the formulation of the hybrid model, we define a pseudo-potential, in which the phase-field ansatz for fracture dissipation is combined with a polyconvex PANN model of the isochoric response. The PANN is formulated in isochoric invariants. As a result, it can be proven that the PANN fulfils all desirable properties of hyperelastic potentials by construction. Moreover, a classical mixed displacement-pressure formulation of incompressibility based on the perturbed Lagrangian approach is included. Thereby, a relaxation of the incompressibility constraint in fracturing material is applied, in order to prevent numerical issues, for which the proposed PANN architecture is a crucial ingredient. The model is implemented in the finite element framework FEniCSx and studied by means of several numerical examples.
Details
Originalsprache | Englisch |
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Publikationsstatus | Veröffentlicht - 24 Dez. 2024 |
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Externe IDs
ORCID | /0000-0003-3358-1545/work/175219691 |
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Schlagworte
Schlagwörter
- Physics-augmented neural networks, Volumetric-isochoric split, Fracture, Phase-field, Incompressibility, Finite deformations