On the use of non-iterative methods in cohesive fracture

Alfaiate, J.; Sluys, L.J.

doi:10.1007/s10704-018-0270-2

Cited by 12 publications

(3 citation statements)

References 23 publications

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“…However, there is no correlation between the observed “one real root” case and the onset of redistribution in any of the steps resulting in the intermittent proportional loading . The need for such a redistribution in a quasi‐static setup of SLA for non‐proportional SLA simulations is currently being investigated for cases when the constant load continues to drop gradually to very low values, indicating structural failure as has been previously interpreted and comparisons are being carried out between the available redistribution strategies() in literature, in a smeared crack setup. Nevertheless, the constant load in this study of ST4 is restored to its full value after each set of these redistribution steps.…”

Section: Validation Studies Against Experimental Benchmarksmentioning

confidence: 99%

“…The method is a proven alternative for applications in masonry, reinforced concrete, and glass . Advancements in SLA include contributions to make the procedure mesh objective,() saw‐tooth laws for extremely brittle materials with snap back at constitutive level like glass, extension to non‐proportional loading situations,() stepwise secant Coulomb friction laws, combined incremental‐total approaches like non‐iterative energy–based method and the automatic method, SLA in a stochastic setting, combining SLA with crack tracking technique, and mesh‐free SLA . Despite the active contributions of several researchers, the topic of non‐proportional loading in SLA continues to be a debated one.…”

Section: Introductionmentioning

confidence: 99%

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Non‐proportional loading in sequentially linear analysis for 3D stress states

Pari

Hendriks

Rots

2019

Numerical Meth Engineering

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Summary Sequentially linear analysis (SLA), a non‐incremental‐iterative approach towards finite element simulation of quasi‐brittle materials, is based on sequentially identifying a critical integration point in the model, to reduce its strength and stiffness, and the associated critical load multiplier (λcrit), to scale the linear analysis results. In this article, two novel methods are presented to enable SLA simulations for non‐proportional loading situations in a three‐dimensional fixed smeared crack framework. In the first approach, the cubic function in the load multiplier is analytically solved for real roots using trigonometric solutions or the Cardano method. In the second approach, the load multiplier is expressed as a function of the inclination of a potential damage plane and is deduced using a constrained optimization approach. The first method is preferred over the second for the validation studies due to computational efficiency and accuracy reasons. A three‐point bending beam test, with and without prestress, and an RC slab tested in shear, with and without axial loads, are used as benchmarks. The proposed solution method shows good agreement with the experiments in terms of force‐displacement curves and damage evolution.

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Section: Validation Studies Against Experimental Benchmarksmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Non‐proportional loading in sequentially linear analysis for 3D stress states

Pari

Hendriks

Rots

2019

Numerical Meth Engineering

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“…It has been a proven alternative to traditional incremental‐iterative methods for NLFEA of quasi‐brittle structures. SLA, thus far, has had contributions in the contexts of mesh‐objectivity, saw‐tooth laws for extremely brittle materials with snap‐back at constitutive level like glass, extension to non‐proportional loading situations, stepwise secant Coulomb friction laws, creep‐induced cracking, combined incremental‐total approaches like Non‐Iterative Energy‐based Method (NIEM) and the automatic method, combining SLA with a crack tracking technique and non‐proportional loading strategies for three‐dimensional (3D) stress states.…”

Section: Introductionmentioning

confidence: 99%

Two solution strategies to improve the computational performance of sequentially linear analysis for quasi‐brittle structures

Pari

Swart

Gijzen

et al. 2020

Numerical Meth Engineering

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Summary Sequentially linear analysis (SLA), an event‐by‐event procedure for finite element (FE) simulation of quasi‐brittle materials, is based on sequentially identifying a critical integration point in the FE model, to reduce its strength and stiffness, and the corresponding critical load multiplier (λcrit), to scale the linear analysis results. In this article, two strategies are proposed to efficiently reuse previous stiffness matrix factorisations and their corresponding solutions in subsequent linear analyses, since the global system of linear equations representing the FE model changes only locally. The first is based on a direct solution method in combination with the Woodbury matrix identity, to compute the inverse of a low‐rank corrected stiffness matrix relatively cheaply. The second is a variation of the traditional incomplete LU preconditioned conjugate gradient method, wherein the preconditioner is the complete factorisation of a previous analysis step's stiffness matrix. For both the approaches, optimal points at which the factorisation is recomputed are determined such that the total analysis time is minimised. Comparison and validation against a traditional parallel direct sparse solver, with regard to a two‐dimensional (2D) and three‐dimensional (3D) benchmark study, illustrates the improved performance of the Woodbury‐based direct solver over its counterparts, especially for large 3D problems.

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Modelling fracture due to corrosion and mechanical loading in reinforced concrete

Alfaiate,

Sluys,

Costa

2023

Int J Fract

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Corrosion in reinforced concrete is an important feature which can lead to increased deformation and cracking, as well as to premature failure. In the present work, macro-mechanical modelling of corrosion is performed, namely the degradation of bond–slip between concrete and steel. A mixed-mode damage model is adopted, in which the interaction between the bond–slip law and the stress acting in the neighbourhood of the concrete–steel bar interface is taken into account. Bond–slip degradation is modelled using an evolutionary bond–slip relationship, which depends on the level of corrosion. Different relevant loading cases are studied. Special attention is given to the evolution of corrosion in time, under constant load. This is done by adopting a Total Iterative Approach, in which the structure is reevaluated each time step, upon damage increase due to corrosion. Pullout tests are presented to illustrate the performance of the model. Bending tests are also performed to evaluate the influence of corrosion at structural level.

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On the use of non-iterative methods in cohesive fracture

Cited by 12 publications

References 23 publications

Non‐proportional loading in sequentially linear analysis for 3D stress states

Non‐proportional loading in sequentially linear analysis for 3D stress states

Two solution strategies to improve the computational performance of sequentially linear analysis for quasi‐brittle structures

Modelling fracture due to corrosion and mechanical loading in reinforced concrete

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