Modeling multi-fracturing fibers in fiber networks using elastoplastic Timoshenko beam finite elements with embedded strong discontinuities — Formulation and staggered algorithm
| Autor: | Artem Kulachenko, Vedad Tojaga, T. Christian Gasser, Sören Östlund |
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| Rok vydání: | 2021 |
| Předmět: |
Timoshenko beam theory
Continuum mechanics Computer science business.industry Mechanical Engineering Computational Mechanics General Physics and Astronomy Structural engineering Classification of discontinuities Finite element method Computer Science Applications Discontinuity (linguistics) Mechanics of Materials Displacement field Fracture (geology) business Stiffness matrix |
| Zdroj: | Computer Methods in Applied Mechanics and Engineering |
| ISSN: | 0045-7825 |
| DOI: | 10.1016/j.cma.2021.113964 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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