The role of a realistic volume constraint in modelling a two dimensional granular assembly

Chandler, H.W.; Sands, C.M.

doi:10.1016/j.jmps.2007.01.002

Cited by 13 publications

(16 citation statements)

References 36 publications

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“…As _ a a is a variable akin to strain rate, it can be included in the dilatancy rule. A sophisticated dilatancy rule presented elsewhere (Chandler & Sands, 2007b) is extended for use in this model, such that…”

Section: Incorporation Of Self-cancelling Shear Strainsmentioning

confidence: 99%

“…Together, the terms including n i and n r produce the volume changes associated with small cyclic shear strains and large monotonic shear strain and predict non-coaxiality of shear stress and shear strain rate when the principal axes rotate (Chandler & Sands, 2007b). In order to do this, n i and n r are constructed as functions of the current density and evolve as deformation progresses.…”

Section: Incorporation Of Self-cancelling Shear Strainsmentioning

confidence: 99%

“…where c 1 is assumed to be a material constant (Chandler & Sands, 2007b). The parameters ', k, n i and n r evolve as deformation progresses.…”

Section: Incorporation Of Self-cancelling Shear Strainsmentioning

confidence: 99%

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Simulating pressure-induced compaction by grain rearrangement

Sands¹,

Chandler²

2012

Géotechnique Letters

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This article presents a novel model of the compaction of loose sand, or other granular material, incorporating two dilatancy terms. One is negative, reflecting the general tendency of an assembly to collapse under a combination of shear stress and pressure. The other develops during shear straining and, at the critical state, is sufficiently large and positive to counter the negative contribution. The existence of a term producing negative dilatancy, however, suggests the concept of 'self-cancelling shear deformation'. These shears contribute to the shear-volume coupling, producing densification, but not to the macroscopic shear deformation. They only occur when there is a small amount of damage. This produces pressure-induced densification by granule rearrangement, resulting in a model where compaction is possible under a hydrostatic load but the model can still simulate cyclic deformation and critical state behaviour.

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Section: Incorporation Of Self-cancelling Shear Strainsmentioning

confidence: 99%

Section: Incorporation Of Self-cancelling Shear Strainsmentioning

confidence: 99%

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Simulating pressure-induced compaction by grain rearrangement

Sands¹,

Chandler²

2012

Géotechnique Letters

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“…More interestingly, (i) a cap is generated ending at p/ = 1 and (ii) the evolving dilatancy term produces rotational kinematic hardening [19]. Typical yield surfaces, found from Equation (6), and strain rate directions, found from Equation (5), are shown in Figure 4, using model parameters shown in Table I.…”

Section: An Illustrative Applicationmentioning

confidence: 99%

“…A useful model for such a dilation rule in applications to cyclic deformation [19] is one where the rate of volume strain (˙ =ė K K ) is related to the components of deviatoric strain rate. This is achieved by first constructing a (9×1) vector of deviatoric strain (d G K ) representing the evolving anisotropy of the dilatational response.…”

Section: An Illustrative Applicationmentioning

confidence: 99%

Including friction in the mathematics of classical plasticity

Chandler

Sands

2009

Num Anal Meth Geomechanics

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SUMMARYIn classical plasticity there are clear mathematical links between the dissipation function and the consequent yield function and flow rule. These links help to construct constitutive equations with the minimum of adjustable parameters. Modelling granular materials, however, requires that the dissipation function depends on the current stress state (frictional plasticity) and this changes the mathematical structurealtering the links and invalidating the associated flow rule. In this paper we show, for a large family of dissipation functions, how much of the structure remains intact when frictional dissipation is included. The surviving links are examined using straightforward physically based graphical insight and well-established mathematical techniques leading to a central result, which provides a mathematical justification for the procedural features of hyperplasticity. This should allow hyperplasticity to be used more widely and certainly with increased confidence.As an example of the effectiveness of the general method, two specific dissipation functions are constructed from the simple physical concepts of sliding friction and granule damage. One is based on a Drucker-Prager cone and the other a Matsuoka-Nakai cone, both incorporate kinematic hardening and a compactive cap. In each Case a single smooth yield function with consistent flow rules is produced. The computational usefulness of an inequality derived in the paper is demonstrated in the generation of the figures showing yield surfaces and flow directions by means of a simple maximization procedure.

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Developing elasto‐plastic models without establishing any expression for the yield function

Sands

Chandler

Guz

2011

Num Anal Meth Geomechanics

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SUMMARYThis paper presents a procedure for developing elasto-plastic material models from a dissipation function and kinematic constraint that obviates the need to establish an expression for the yield function. This method could be applied to a wide range of different materials, but it is particularly suitable for testing new models of granular materials. This is because there is often a difficulty associated with finding an algebraic expression for the yield function for appropriate dissipation functions combined with realistic dilatancy rules. The procedure presented in this paper allows the approach to fulfill its potential for the easy incorporation of physical insight into the dissipation function and kinematic constraint without being hindered by algebraic complexity. The method is applied to the familiar von Mises model and also to a model for granular materials that incorporates a realistic dilatancy rule and extends into three dimensions a model presented in earlier work.

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The role of a realistic volume constraint in modelling a two dimensional granular assembly

Cited by 13 publications

References 36 publications

Simulating pressure-induced compaction by grain rearrangement

Simulating pressure-induced compaction by grain rearrangement

Including friction in the mathematics of classical plasticity

Developing elasto‐plastic models without establishing any expression for the yield function

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