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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: 7 October 2019

Xikui Li, Songge Zhang and Qinglin Duan

This paper aims to present a novel scheme for imposing periodic boundary conditions with downscaled macroscopic strain measures of gradient Cosserat continuum on the…

Abstract

Purpose

This paper aims to present a novel scheme for imposing periodic boundary conditions with downscaled macroscopic strain measures of gradient Cosserat continuum on the representative volume element (RVE) of discrete particle assembly in the frame of the second-order computational homogenization methods for granular materials.

Design/methodology/approach

The proposed scheme is based on the generalized Hill’s lemma of gradient Cosserat continuum and the incremental non-linear constitutive relation condensed to the peripheral particles of the RVE of discrete particle assembly. The generalized Hill’s lemma conducts to downscale the macroscopic strain or stress measures and to impose the periodic boundary conditions on the RVE boundary so that the Hill-Mandel energy equivalence condition is ensured. Because of the incremental non-linear constitutive relation condensed to the peripheral particles of the RVE, the periodic boundary displacement and traction constraints together with the downscaled macroscopic strains and strain gradients, micro-rotations and curvatures are imposed in the point-wise sense without the need of introducing the Lagrange multipliers for enforcing the periodic boundary displacement and traction constraints in a weak sense.

Findings

Numerical results demonstrate that the applicability and effectiveness of the proposed scheme in imposing the periodic boundary conditions on the RVE. The results of the RVE subjected to the periodic boundary conditions together with the displacement boundary conditions in the second-order computational homogenization for granular materials provide the desired estimations, which lie between the upper and the lower bounds provided by the displacement and the traction boundary conditions imposed on the RVE respectively.

Research limitations/implications

Each grain in the particulate system under consideration is assumed to be rigid and circular.

Practical implications

The proposed scheme for imposing periodic boundary conditions on the RVE can be adopted solely for estimating the effective mechanical properties of granular materials and/or integrated into the frame of the second-order computational homogenization method with a nested finite element method-discrete element method solution procedure for granular materials. It will tend to provide, at least theoretically, more reasonable results for effective material properties and solutions of a macroscopic boundary value problem simulated by the computational homogenization method.

Originality/value

This paper presents a novel scheme for imposing periodic boundary conditions with downscaled macroscopic strain measures of gradient Cosserat continuum on the RVE of discrete particle assembly for granular materials without need of introducing Lagrange multipliers for enforcing periodic boundary conditions in a weak (integration) sense.

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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.

Details

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

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Article
Publication date: 4 January 2011

Jun Liu and Ming Huan

Traditional continuum theory is usually applied in analysis of a gravity dam and its foundation; as we all know, both analytic and numerical solution of traditional theory…

Abstract

Purpose

Traditional continuum theory is usually applied in analysis of a gravity dam and its foundation; as we all know, both analytic and numerical solution of traditional theory imply that stress concentration around the dam heel and toe is very severe. However, stress condition of the dam and its foundation seems better for it can work normally for decades. Since concrete masses have macroscopic inhomogeneity, a new model has been built in order to simulate the mechanics behaviour of dam and its foundation rationally as the influence of inhomogeneity of the material has been taken into consideration. The purpose of this paper is to describe the application of the Cosserat granular model to analyze the stress condition of a mass concrete structure.

Design/methodology/approach

Granular model of Cosserat theory has been built and adopted to model the gravity, considering the influence of the couple‐stresses, due to the inhomogeneity of the material.

Findings

The Cosserat results have been compared with the traditional numerical solution, and the outcome indicates that the distributions of the stresses and displacements are rational, and the stress concentration around dam hell and toe is less severe and closer to the reality when Cosserat theory adopted.

Originality/value

The granular model based on Cosserat theory has been used in modelling a dam body for the first time; because the model can reflect the influence of the inhomogeneity, it is more suitable than traditional continuum model under this condition.

Details

Engineering Computations, vol. 28 no. 1
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 15 June 2015

Ke Wan and Xikui Li

The purpose of this paper is to extend the bridge scale method (BSM) developed for granular materials with only the solid phase to that taking into account the effects of…

Abstract

Purpose

The purpose of this paper is to extend the bridge scale method (BSM) developed for granular materials with only the solid phase to that taking into account the effects of wetting process in porous continuum. The granular material is modeled as partially saturated porous Cosserat continuum and discrete particle assembly in the coarse and fine scales, respectively.

Design/methodology/approach

Based on the mass and momentum conservation laws for the three phases, i.e. the solid skeleton, the pore water and the pore air, the governing equations for the unsaturated porous Biot-Cosserat continuum model in the coarse scale are derived. In light of the passive air pressure assumption, a reduced finite element model for the model is proposed. According to the decoupling of the fine and coarse scale calculations in the BSM, the unsaturated porous Cosserat continuum model using the finite element method and the discrete element model using the discrete element method for granular media are combined.

Findings

The numerical results for a 2D example problem of slope stability subjected to increasing rainfall along with mechanical loading demonstrate the applicability and performance of the present BSM. The microscopic mechanisms of macroscopic shear band developed in the slope are demonstrated.

Research limitations/implications

Do not account for yet the effects of unsaturated pore water in the fine scale.

Originality/value

The novel BSM that couples the Biot-Cosserat porous continuum modeling and the discrete particle assembly modeling in both coarse and fine scales, respectively, is proposed to provide a micro-macro discrete-continuum two-scale modeling approach for numerical simulations of the hydro-mechanical coupling problems in unsaturated granular materials.

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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.

Details

Engineering Computations, vol. 34 no. 2
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

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Article
Publication date: 8 July 2019

Qing Xie, Yucai Hu, Yexin Zhou and Wanshui Han

Poor bending response is a major shortcoming of lower-order elements due to excessive representation of shear stress/strain field. Advanced finite element (FE…

Abstract

Purpose

Poor bending response is a major shortcoming of lower-order elements due to excessive representation of shear stress/strain field. Advanced finite element (FE) formulations for classical elasticity enhance the bending response by either nullifying or filtering some of the symmetric shear stress/strain modes. Nevertheless, the stress/strain field in Cosserat elasticity is asymmetric; consequently any attempt to nullify or filter the anti-symmetric shear stress/strain modes may lead to failure in the constant couple-stress patch test where the anti-symmetric shear stress/strain field is linear. This paper aims at enhancing the bending response of lower-order elements for Cosserat elasticity problems.

Design/methodology/approach

A four-node quadrilateral and an eight-node hexahedron are formulated by hybrid-stress approach. The symmetric stress is assumed as those of Pian and Sumihara and Pian and Tong. The anti-symmetric stress components are first assumed to be completely linear in order to pass the constant couple-stress patch test. The linear modes are then constrained with respect to the prescribed body-couple via the equilibrium conditions.

Findings

Numerical tests show that the hybrid elements can strictly pass the constant couple-stress patch test and are markedly more accurate than the conventional elements as well as the incompatible elements for bending problems in Cosserat elasticity.

Originality/value

This paper proposes a hybrid FE formulation to improve the bending response of four-node quadrilateral and eight-node hexahedral elements for Cosserat elasticity problems without compromising the constant couple-stress patch test.

Details

Engineering Computations, vol. 36 no. 6
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 1 June 1995

S. Nakamura and R.S. Lakes

Distributions of stress and strain in composite and cellular materialscan differ significantly from the predictions of classical elasticity. Forexample, concentration of…

Abstract

Distributions of stress and strain in composite and cellular materials can differ significantly from the predictions of classical elasticity. For example, concentration of stress and strain around holes and cracks is consistently less than classical predictions. Generalized continuum theories such as micropolar (Cosserat) elasticity offer improved predictive power. In this article Saint‐Venant end effects for self equilibrated external forces in micropolar solids are investigated in two dimensions. A two dimensional finite element analysis is used which takes into account the extra degrees of freedom, to treat the problem of localized end loads acting upon a strip. The rate of decay of strain energy becomes slower in a two dimensional strip as the micropolar characteristic length l is increased (for l sufficiently less than the strip width). For the strip geometry a Cosserat solid exhibits slower stress decay than a classical solid.

Details

Engineering Computations, vol. 12 no. 6
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 1 March 2004

G.A. D'Addetta, E. Ramm, S. Diebels and W. Ehlers

In this paper, a new homogenization technique for the determination of dynamic and kinematic quantities of representative elementary volumes (REVs) in granular assemblies…

Abstract

In this paper, a new homogenization technique for the determination of dynamic and kinematic quantities of representative elementary volumes (REVs) in granular assemblies is presented. Based on the definition of volume averages, expressions for macroscopic stress, couple stress, strain and curvature tensors are derived for an arbitrary REV. Discrete element model simulations of two different test set‐ups including cohesionless and cohesive granular assemblies are used as a validation of the proposed homogenization technique. A non‐symmetric macroscopic stress tensor, as well as couple stresses are obtained following the proposed procedure, even if a single particle is described as a standard continuum on the microscopic scale.

Details

Engineering Computations, vol. 21 no. 2/3/4
Type: Research Article
ISSN: 0264-4401

Keywords

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