Gastvortrag aus UC Berkeley: ''Phase-Field Fracture Modeling at Finite Strains – Prospects and Challenges''

Der Lehrstuhl für Technische Mechanik lädt herzlich zum Kolloquium für Mechanik ein. Dr.-Ing. Paras Kumar von der University of California, Berkeley, wird in seinem Vortrag “Phase-Field Fracture Modeling at Finite Strains – Prospects and Challenges” aktuelle Forschungsentwicklungen auf dem Gebiet der Phasenfeldmodellierung von Rissprozessen vorstellen.

Abstract:

The phase-field approach to fracture modeling involves diffuse approximation via an auxiliary crack phase-field variable and hence offers itself as a suitable candidate for the development of a unified framework capable of dealing with both crack nucleation as well as propagation; see [1, Chapter 4]  and the references therein for instance. However, there still remain several open questions, particularly with regards to robustness and efficiency of the numerical solution procedure employed for incremental solution of the coupled system of equations at each load step. For instance, the diffuse approximation of a sharp crack, however, necessitates the usage of extremely fine finite element meshes in order to adequately resolve the diffuse crack zone. Furthermore, sufficiently small load increments are required, even more so in case of large strain problems, for accurate description of the fracture process.[2] Moreover, within the context of the commonly adopted staggered solution scheme, the degree of coupling between the displacement and damage fields varies strongly as cracks evolve, thereby adversely impacting regularity of the underlying, highly nonlinear displacement sub-problem. Extensive numerical studies highlight the critical nature of this issue in finite strain problems as the displacement stiffness matrix tends to lose its positive definiteness during brutal crack propagation, thus leading to non-convergence of the standard Newton-Raphson scheme for this sub-problem. Consequently, despite the rapid development of the phase-field fracture models in the last two decades, simulation of crack propagation in complex geometries, especially in three-dimensions, still remains a challenge.[3] In this talk, I will introduce two different nonlinear solvers tailor-made for the problem at hand. The first one entails a modification of the standard Newton-Raphson method by means of a coercion procedure and a line search algorithm to ensure convergence for a certain class of hyperelastic materials. The second one, based on the trust-region method [4], caters to the class of slightly incompressible hyperelastic materials involving a volumetric-isochoric split of the strain energy function. The current capabilities, computational cost, and limitations of the proposed nonlinear solvers are depicted by means of appropriate numerical examples. Further, efficient linear solvers and preconditioners for the inner solves within the coerced Newton-Raphson scheme will be explored to render large scale 3D phase-field fracture simulations of soft material computationally feasible.

References

[1]  P. Kumar. “Enhanced Computational Homogenization and Phase-Field Fracture Approaches for Polymer Nano-Composites”. PhD Thesis. Friedrich-Alexander-Universität Erlangen-Nürnberg, 2024. doi: 10.25593/open-fau-422.

[2]  M. Rohracker, P. Kumar, P. Steinmann, and J. Mergheim. “Efficient phase-field fracture simulations for fracture analysis in heterogeneous materials”. Computational Mechanics 77 (2026), pp. 707–727. doi: 10.1007/s00466-025-02685-3.

[3]  Z. Chafia et al. “Massively parallel phase field fracture simulations on supercomputers: towards multi-billion degree-of-freedom computations”. Advanced Modeling and Simulation in Engineering Sciences 11 (2024). doi: 10.1186/s40323-024-00280-4.

[4]  A. R. Conn, N. I. M. Gould, and P. L. Toint. Trust Region Methods. Society for Industrial and Applied Mathematics, 2000.