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. Given the problems investigated in this work, the hybrid solution approach is up to 30 times faster than the staggered approach, where its superiority is most pronounced at large loading increments. The approach is general and may also accelerate the computational analysis of other failure problems.

Abstract To model fiber failures in random fiber networks, we have developed an elastoplastic Timoshenko beam finite element with embedded discontinuities. The method is based on the theory of strong discontinuities where the generalized displacement field is enhanced by a jump. The continuum mechanics formulation accounts for a fracture process zone and a bulk material while retaining traction continuity across the discontinuity. The additional degrees of freedom that are associated with the discontinuity are represented by a midpoint node, which is statically condensed to enable the implementation in commercial software through the user element interface . We propose a quasi-brittle fracture model, where the failure-related deformation is uncoupled from the plastic deformation in the bulk material. To retain the positive definite finite element stiffness matrix of the bulk material, we neglect the fracture-related softening of the discontinuity and employ a modified Newton iteration in the strain softening domain. Our implementation facilitates the integration into commercial finite element software and examples illustrate the robustness of the method. The FORTRAN source code is freely available to benchmark our model. We show that fiber failures contribute to the nonlinear stress–strain response of paper. Together with fiber–fiber bond failures, they can potentially explain the nonlinear stress–strain response of paper and nanopaper.

We develop a thermodynamically consistent continuum damage micromechanics model for the compressive failure of flax fiber composites. We used a micromechanics-based constitutive model reported recently [1]. It describes the microstructure of a unidirectional composite and captures the material behavior of the fiber and matrix constituents, respectively. The description has been formulated in the reference configuration (i.e. the undeformed state of the composite) and is therefore independent of fiber rotations that may appear during the deformation of the composite. A hyperelastic finite deformation plasticity with power law hardening [3] mimics the compressive elastic-plastic stress-strain response of the fiber (reported in [2]) and the matrix. The model has been extended to account for fiber damage, resulting in a thermodynamically consistent continuum damage micromechanics model. Our results indicate that fiber damage plays an utmost role in the compressive failure of flax fiber composites – it is a major determinant of the material’s compressive stress-strain response. X-ray Computed Tomography and Scanning Electron Microscopy show that fiber damage can be attributed to intra-fiber splitting and elementary fiber crushing.