Modeling multi-fracturing fibers in fiber networks using elastoplastic Timoshenko beam finite elements with embedded strong discontinuities — Formulation and staggered algorithm

Tojaga, Vedad; Kulachenko, Artem; Gasser, Thomas C.

doi:10.1016/j.cma.2021.113964

Cited by 20 publications

(17 citation statements)

References 58 publications

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“…The cantilever beam is discretized with one and ten evenly spaced finite elements, where the ultimate tensile force is lowered by 1% in the most left element. Otherwise, the homogenous stress field of the problem would have resulted in an ambiguous failure pattern, see Section 3 elsewhere [39]. Figure 1 presents the force-displacement response of our structural problem for three different fracture energies 𝐺 𝑓 , a property also expressed as the area under the curve.…”

Section: Mesh Independencementioning

confidence: 99%

“…In-plane it covers the area 𝑊 × 𝐻 = 18 × 6 𝑚𝑚 2 and the displacement 𝛿 0 = 9.0 𝑚𝑚 is prescribed along one edge, while all six DOFs at the opposite edge are fixed. Out-of-plane displacements and rotations are prevented, and all information on how the mesh has been generated is reported elsewhere [55] together with the ANSYS input file [39]. A quasi-static failure analysis was computed through the incremental application of the prescribed displacement 𝛿 0 .…”

Section: Tensile Test Of a Fibrous Tissue Specimenmentioning

confidence: 99%

“…The E-FEM has received significant attention in the description of failure in truss-bars, beams, and structures thereof [32][33][34][35][36][37][38][39][40][41][42][43][44][45][46]. No crack-tracking algorithm is then needed [47].…”

Section: Introductionmentioning

confidence: 99%

“…The E-FEM framework allows static condensation of the additional DOF associated with the fracture kinematics [33] directly at the element level, resulting in an operator-splitting method [34] for the evaluation of these DOF. As with the phase-field method, a staggered solution method may be used, and the continuous and discontinuous fields are minimized alternatively [39]. In the present work, we expand these ideas and propose a hybrid method to optimize the performance and robustness of the E-FEM models in the analysis of fiber network failure [39,48].…”

Section: Introductionmentioning

confidence: 99%

“…As with the phase-field method, a staggered solution method may be used, and the continuous and discontinuous fields are minimized alternatively [39]. In the present work, we expand these ideas and propose a hybrid method to optimize the performance and robustness of the E-FEM models in the analysis of fiber network failure [39,48]. The hybrid solution approach is general and may also be applied to other fracture mechanics problems.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

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

Tojaga,

Kulachenko,

Ostlund

et al. 2022

Preprint

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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.

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Section: Mesh Independencementioning

confidence: 99%

Section: Tensile Test Of a Fibrous Tissue Specimenmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

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

Tojaga,

Kulachenko,

Ostlund

et al. 2022

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

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

et al. 2022

Self Cite

View full text Add to dashboard Cite

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.

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Iterative method for large-scale Timoshenko beam models assessed on commercial-grade paperboard

Görtz,

Kettil,

Målqvist

et al. 2024

Comput Mech

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Large-scale structural simulations based on micro-mechanical models of paper products require extensive numerical resources and time. In such models, the fibrous material is often represented by connected beams. Whereas previous micro-mechanical simulations have been restricted to smaller sample problems, large-scale micro-mechanical models are considered here. These large-scale simulations are possible on a non-specialized desktop computer with 128GB of RAM using an iterative method developed for network models and based on domain decomposition. Moreover, this method is parallelizable and is also well-suited for computational clusters. In this work, the proposed memory-efficient iterative method is numerically validated for linear systems resulting from large networks of Timoshenko beams. Tensile stiffness and out-of-plane bending stiffness are simulated and validated for various commercial-grade three-ply paperboards consisting of layers composed of two different types of paper fibers. The results of these simulations show that a linear network model produces results consistent with theory and published experimental data

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Modeling multi-fracturing fibers in fiber networks using elastoplastic Timoshenko beam finite elements with embedded strong discontinuities — Formulation and staggered algorithm

Cited by 20 publications

References 58 publications

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

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

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

Iterative method for large-scale Timoshenko beam models assessed on commercial-grade paperboard

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