Characteristic lengths in Cosserat continuum modeling of granular materials

Huang, Wenxiong; Xu, Ke

doi:10.1108/ec-02-2015-0031

Cited by 6 publications

(3 citation statements)

References 26 publications

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“…Since composite materials are heavily dependent on their microstructure, and several experiments have shown an inability of classical theory to capture these effects [10][11][12][13][14][15][16][17][18][19], a formulation of elasticity that accounts for microstructural effects must be considered. Adequate characterization of such materials necessitates non-classical continuum theories since size-dependent behaviour is inherent to them.…”

Section: Introductionmentioning

confidence: 99%

Finite element modelling of exponentially graded composites with microstructure

Barrage

Potapenko

Polak

2023

Mathematics and Mechanics of Solids

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Composite material properties are dependent on their microstructure. To adequately model these microstructural effects, a formulation of elasticity that accounts for microstructural effects must be considered. Size-dependent behaviour is an inherent property of such materials, resulting in a need for non-classical continuum theories for adequate characterization. A three-dimensional model for an exponentially graded composite with microstructural effects is developed under the framework of Cosserat elasticity. The mixed boundary value problem is formulated and solved through the finite element method, and implemented in the commercial software Abaqus through two user developed elements. Recovery of the classical limit for the Dirichlet problem is discussed as an initial model validation until complete experimental measurements can be conducted.

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Section: Introductionmentioning

confidence: 99%

Finite element modelling of exponentially graded composites with microstructure

Barrage

Potapenko

Polak

2023

Mathematics and Mechanics of Solids

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“…Classical elasticity theory is often regarded as inadequate to describe some of modern materials with granular, fibrous or lattice microstructures (Lakes, 1993; Huang and Xu, 2015). This leads to the development of generalized models of continuum such as the Cosserat theory.…”

Section: Introductionmentioning

confidence: 99%

Improving the bending response of four-node quadrilateral and eight-node hexahedral elements for Cosserat elasticity problems

Xie

Zhou

et al. 2019

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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.

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“…In the past decades, various problems of progressive localization of strain have been tackled using the Cosserat continuum model. Representative works include, but are not limited to, Muhlhaus (1989); Muhlhaus and Vardoulakis (1987); de Borst (1991); de Borst and Sluys (1991); de Borst (1993); Steinmann (1994; 1995); Iordache and Willam (1998); Ehlers and Volk (1998); Ebrahimian et al (2012); Bauer et al (2012); Huang et al (2014); Huang and Xu (2015). In geomechanics, Li and Tang (2005), Tang and Li (2007), Tang et al (2013) developed a consistent algorithm for handling problems involving pressure-dependent elastoplastic materials in the framework of Cosserat continuum theory, in which a closed form of the consistent elastoplastic tangent modulus matrix was derived, and the resulting algorithm was applied for modelling strain localization phenomena because of strain-softening.…”

Section: Introductionmentioning

confidence: 99%

Low-order mixed finite element analysis of progressive failure in pressure-dependent materials within the framework of the Cosserat continuum

Tang

Guan

Xue

et al. 2017

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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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Characteristic lengths in Cosserat continuum modeling of granular materials

Cited by 6 publications

References 26 publications

Finite element modelling of exponentially graded composites with microstructure

Finite element modelling of exponentially graded composites with microstructure

Improving the bending response of four-node quadrilateral and eight-node hexahedral elements for Cosserat elasticity problems

Low-order mixed finite element analysis of progressive failure in pressure-dependent materials within the framework of the Cosserat continuum

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