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Article
Publication date: 1 February 1988

Gilles Pijaudier‐Cabot, Zdeněk P. Bažant and Mazen Tabbara

This paper presents a comparison of various models for strain‐softening due to damage such as cracking or void growth, as proposed recently in the literature…

Abstract

This paper presents a comparison of various models for strain‐softening due to damage such as cracking or void growth, as proposed recently in the literature. Continuum‐based models expressed in terms of softening stress—strain relations, and fracture‐type models expressed in terms of softening stress—displacement relations are distinguished. From one‐dimensional wave propagation calculations, it is shown that strainlocalization into regions of finite size cannot be achieved. The previously well‐documented spurious convergence is obtained with continuum models, while stress—displacement relations cannot model well smeared‐crack situations. Continuum models may, however, be used in general if a localization limiter is implemented. Gradient‐type localization limiters appear to be rather complicated; they require solving higher‐order differential equations of equilibrium with additional bourdary conditions. Non‐local localization limiters, especially the non‐local continuum with local strain, in which only the energy dissipating variables are non‐local, is found to be very effective, and also seems to be physically realistic. This formulation can correctly model the transition between homogeneous damage states and situations in which damage localizes into small regions that can be viewed as cracks. The size effect observed in the experimental and numerical response of specimens in tension or compression is shown to be a consequence of this progressive transition from continuum‐type to fracture‐type formulations.

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Engineering Computations, vol. 5 no. 2
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 1 April 1991

RENÉ DE BORST

Classical continuum models, i.e. continuum models that do not incorporate an internal length scale, suffer from pathological mesh‐dependence when strain‐softening models…

Abstract

Classical continuum models, i.e. continuum models that do not incorporate an internal length scale, suffer from pathological mesh‐dependence when strain‐softening models are employed in failure analyses. In this contribution the governing field equations are regularized by adding rotational degrees‐of‐freedom to the conventional translational degrees‐of‐freedom. This so‐called elasto‐plastic Cosserat continuum model, for which an efficient and accurate integration algorithm and a consistent tangent operator are also derived in this contribution, warrants convergence of the load—deflection curve to a unique solution upon mesh refinement and a finite width of the localization zone. This is demonstrated for an infinitely long shear layer and a biaxial test of a strain‐softening elasto‐plastic von Mises material.

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Engineering Computations, vol. 8 no. 4
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 8 March 2011

Sebastian D'hers and Eduardo N. Dvorkin

The purpose of this paper is to model the strain localization in J2 materials with damage evolution using embedded strong discontinuity modes.

Abstract

Purpose

The purpose of this paper is to model the strain localization in J2 materials with damage evolution using embedded strong discontinuity modes.

Design/methodology/approach

In this procedure, an heuristic bandwidth scale is adopted to model the damage evolution in the shear bands. The bifurcation triggering conditions and band growth directions are studied for these materials.

Findings

The resulting formulation does not require a specific mesh refinement to model a localization, provides mesh independent results also insensitive to element distortions and allows calibration of the model response using experimental data. The formulation capability is shown embedding the strong discontinuity modes into quadrilateral and higher order elements.

Originality/value

The work described in this paper extends the use of strong discontinuity modes to materials with damage evolution.

Details

Engineering Computations, vol. 28 no. 2
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 18 April 2017

Hongxiang Tang, Yuhui Guan, Xue Zhang and Degao Zou

This paper aims to develop a finite element analysis strategy, which is suitable for the analysis of progressive failure that occurs in pressure-dependent materials in…

Abstract

Purpose

This paper aims to develop a finite element analysis strategy, which is suitable for the analysis of progressive failure that occurs in pressure-dependent materials in practical engineering problems.

Design/methodology/approach

The numerical difficulties stemming from the strain-softening behaviour of the frictional material, which is represented by a non-associated Drucker–Prager material model, is tackled using the Cosserat continuum theory, while the mixed finite element formulation based on Hu–Washizu variational principle is adopted to allow the utilization of low-order finite elements.

Findings

The effectiveness and robustness of the low-order finite element are verified, and the simulation for a real-world landslide which occurred at the upstream side of Carsington embankment in Derbyshire reconfirms the advantages of the developed elastoplastic Cosserat continuum scheme in capturing the entire progressive failure process when the strain-softening and the non-associated plastic law are involved.

Originality/value

The permit of using low-order finite elements is of great importance to enhance computational efficiency for analysing large-scale engineering problems. The case study reconfirms the advantages of the developed elastoplastic Cosserat continuum scheme in capturing the entire progressive failure process when the strain-softening and the non-associated plastic law are involved.

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Engineering Computations, vol. 34 no. 2
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 15 June 2015

Wenxiong Huang and Ke Xu

Cosserat continuum models are motivated by modeling size effects in materials with micro-structure. While elastic Cosserat continuum models can reproduce size effects in…

Abstract

Purpose

Cosserat continuum models are motivated by modeling size effects in materials with micro-structure. While elastic Cosserat continuum models can reproduce size effects in deformation stiffness, inelastic models are often used to capture localization and post failure behavior of materials. In application of inelastic Cosserat models, parameter determination is a difficult issue not fully addressed. The purpose of this paper is to discuss parameter-related characteristic lengths in Cosserat continuum modeling of granular materials.

Design/methodology/approach

Based on a Cosserat continuum extension of a hypoplastic model for granular media, interpretation of additional parameters are sought through analysis of simple one-dimensional shear. Governing equations are obtained, respectively, for small strain shear formation and for stead flow state in localized zone.

Findings

Two characteristic lengths are obtained analytically for granular materials: one governs the size effect near boundaries in shear deformation, the other scales the thickness of shear band in failure. While both characteristic lengths are proportional to the micro-structure length (the mean grain diameter), the former is related to the micro-stiffness parameter, and the latter depends on the micro-strength parameter. The results reveal a connection between size effects, the micro-structure length and the material properties. The work also provides a new perspective to inelastic Cosserat continuum models, as well as a possible way for determination micro-deformation and strength parameters.

Originality/value

The results reveal a connection between size effects, the micro-structure length and the material properties. The work provides a new perspective and an interpretation to the micro-deformation and strength parameters of inelastic Cosserat continuum models, as well as a possible way for determination of these parameters.

Details

Engineering Computations, vol. 32 no. 4
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 1 August 1998

Jaroslav Mackerle

This paper gives a review of the finite element techniques (FE) applied in the area of material processing. The latest trends in metal forming, non‐metal forming, powder…

Abstract

This paper gives a review of the finite element techniques (FE) applied in the area of material processing. The latest trends in metal forming, non‐metal forming, powder metallurgy and composite material processing are briefly discussed. The range of applications of finite elements on these subjects is extremely wide and cannot be presented in a single paper; therefore the aim of the paper is to give FE researchers/users only an encyclopaedic view of the different possibilities that exist today in the various fields mentioned above. An appendix included at the end of the paper presents a bibliography on finite element applications in material processing for 1994‐1996, where 1,370 references are listed. This bibliography is an updating of the paper written by Brannberg and Mackerle which has been published in Engineering Computations, Vol. 11 No. 5, 1994, pp. 413‐55.

Details

Engineering Computations, vol. 15 no. 5
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 1 November 1997

S. Glaser and F. Armero

Presents recent advances obtained by the authors in the development of enhanced strain finite elements for finite deformation problems. Discusses two options, both…

Abstract

Presents recent advances obtained by the authors in the development of enhanced strain finite elements for finite deformation problems. Discusses two options, both involving simple modifications of the original enhancement strategy of the deformation gradient as proposed in previous works. The first new strategy is based on a full symmetrization of the original enhanced interpolation fields; the second involves only the transposed part of these fields. Both modifications lead to a significant improvement of the performance in problems involving high compressive stresses, showing in particular a mode‐free response, while maintaining a simple and efficient (strain driven) numerical implementation. Demonstrates these properties with a number of numerical benchmark simulations, including a complete modal analysis of the elements.

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Engineering Computations, vol. 14 no. 7
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 1 August 2001

Jaroslav Mackerle

Gives a bibliographical review of the error estimates and adaptive finite element methods from the theoretical as well as the application point of view. The bibliography…

Abstract

Gives a bibliographical review of the error estimates and adaptive finite element methods from the theoretical as well as the application point of view. The bibliography at the end contains 2,177 references to papers, conference proceedings and theses/dissertations dealing with the subjects that were published in 1990‐2000.

Details

Engineering Computations, vol. 18 no. 5/6
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 26 February 2020

Gianluca Mazzucco, Beatrice Pomaro, Giovanna Xotta, Carmelo E. Maiorana and Valentina A. Salomoni

The purpose of this paper is the numerical assessment of concrete behaviour close to failure, via the development of robust elastoplastic models inclusive of damage…

Abstract

Purpose

The purpose of this paper is the numerical assessment of concrete behaviour close to failure, via the development of robust elastoplastic models inclusive of damage effects. If mesoscale investigations are to be considered, the model must take into account the local confinement effects because of the presence of aggregate inclusions in the cement paste and, correspondingly, the possibility to account for local 3D stress states even under uniaxial compression. Additionally, to enhance the predictive capabilities of a mesoscale representation, the reconstructed geometry must accurately follow the real one.

Design/methodology/approach

The work provides a procedure that combines a 3D digital image technique with finite element (FE) modelling thus maintaining the original 3D morphology of the composite.

Findings

The potentialities of the proposed approach are discussed, giving new insights to a FE modelling (FEM)-based approach applied together with a computer-aided design. Coupled mechanisms of mechanical mismatch and confinement, characterizing the combined cement matrix-aggregates effect, are captured and highlighted via the numerical tests.

Originality/value

The novelty of this research work lies in the proposal of a digitally based methodology for a precise concrete reconstruction together with the adoption of an upgraded elastic–plastic damage model for the cement paste.

Details

Engineering Computations, vol. 37 no. 7
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 1 February 1993

R. DE BORST, L.J. SLUYS, H.‐B. MUHLHAUS and J. PAMIN

Classical continuum models, i.e. continuum models that do not incorporate an internal length scale, suffer from excessive mesh dependence when strain‐softening models are…

Abstract

Classical continuum models, i.e. continuum models that do not incorporate an internal length scale, suffer from excessive mesh dependence when strain‐softening models are used in numerical analyses and cannot reproduce the size effect commonly observed in quasi‐brittle failure. In this contribution three different approaches will be scrutinized which may be used to remedy these two intimately related deficiencies of the classical theory, namely (i) the addition of higher‐order deformation gradients, (ii) the use of micropolar continuum models, and (iii) the addition of rate dependence. By means of a number of numerical simulations it will be investigated under which conditions these enriched continuum theories permit localization of deformation without losing ellipticity for static problems and hyperbolicity for dynamic problems. For the latter class of problems the crucial role of dispersion in wave propagation in strain‐softening media will also be highlighted.

Details

Engineering Computations, vol. 10 no. 2
Type: Research Article
ISSN: 0264-4401

Keywords

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