  The computational analysis of fiber network fracture is an emerging field
with application to paper, rubber-like materials, hydrogels, soft biological
tissue, and composites. Fiber networks are often described as probabilistic
structures of interacting one-dimensional elements, such as truss-bars and
beams. Failure may then be modeled as strong discontinuities in the
displacement field that are directly embedded within the structural finite
elements. As for other strain-softening materials, the tangent stiffness matrix
can be non-positive definite, which diminishes the robustness of the solution
of the coupled (monolithic) two-field problem. Its uncoupling, and thus the use
of a staggered solution method where the field variables are solved
alternatingly, avoids such difficulties and results in a stable, but
sub-optimally converging solution method. In the present work, we evaluate the
staggered against the monolithic solution approach and assess their
computational performance in the analysis of fiber network failure. We then
propose a hybrid solution technique that optimizes the performance and
robustness of the computational analysis. It represents a matrix regularization
technique that retains a positive definite element stiffness matrix while
approaching the tangent stiffness matrix of the monolithic problem. The
approach is general and may also accelerate the computational analysis of other
failure problems.
