Journal
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
Volume 384, Issue -, Pages -Publisher
ELSEVIER SCIENCE SA
DOI: 10.1016/j.cma.2021.113964
Keywords
Fiber network; Multi-fracturing solids; Embedded Discontinuity Finite Element Method (ED-FEM); Enhanced finite elements; Beams; Strong discontinuity
Funding
- European Union's Horizon 2020 research and innovation program under the Marie SkodowskaCurie [764713]
- Swedish National Infrastructure for Computing (SNIC) at HPC2N [SNIC 2020/5-428, SNIC 2021/651]
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A new elastoplastic Timoshenko beam finite element method with embedded discontinuities has been developed to model fiber failures in random fiber networks. The formulation accounts for a fracture process zone in the bulk material and retains traction continuity across the discontinuity. The method proposes a quasi-brittle fracture model and neglects fracture-related softening to maintain the positive definite finite element stiffness matrix of the bulk material.
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. (C) 2021 The Author(s). Published by Elsevier B.V.
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