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The computational analysis of fiber network fracture is an emerging fieldwith application to paper, rubber-like materials, hydrogels, soft biologicaltissue, and composites. Fiber networks are often described as probabilisticstructures of interacting one-dimensional elements, such as truss-bars andbeams. Failure may then be modeled as strong discontinuities in thedisplacement field that are directly embedded within the structural finiteelements. As for other strain-softening materials, the tangent stiffness matrixcan be non-positive definite, which diminishes the robustness of the solutionof the coupled (monolithic) two-field problem. Its uncoupling, and thus the useof a staggered solution method where the field variables are solvedalternatingly, avoids such difficulties and results in a stable, butsub-optimally converging solution method. In the present work, we evaluate thestaggered against the monolithic solution approach and assess theircomputational performance in the analysis of fiber network failure. We thenpropose a hybrid solution technique that optimizes the performance androbustness of the computational analysis. It represents a matrix regularizationtechnique that retains a positive definite element stiffness matrix whileapproaching the tangent stiffness matrix of the monolithic problem. Theapproach is general and may also accelerate the computational analysis of otherfailure problems.

Hybrid of monolithic and staggered solution techniques for the computational analysis of fracture, assessed on fibrous network mechanics