Non-Associated Flow Rules in Description of Plastic Flow of Granular Materials

Mróz, Z.; Szymański, Cz.

doi:10.1007/978-3-7091-4352-0_2

Cited by 7 publications

(8 citation statements)

References 8 publications

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“…Experiments on soils clearly demonstrate that the associated flow rule predicts excessive dilation for granular soils, and for this reason alternative flow rules, including (coaxial) non-associated and non-coaxial flow rules (cf. [19]), have been utilized. While these alternative flow rules in most cases model the behavior of soils more accurately than the associated flow rule, they also complicate the analysis considerably.…”

Section: Punch Indentationmentioning

confidence: 99%

“…The simple and robust numerical scheme used to solve this system is based on the Euler (forward) method. In this procedure, numerical values at the beginning of the finite difference step ( j , l j , j , and j ) were first used with Equation (19) to determine the value l j +1 corresponding to the end of the step, calculated based on the standard Euler method. Next, the value of at the end of the increment ( j +1 ) was calculated from Equation (1) using values of and l at the end of the increment ( j +1 and l j +1 ) and the value of at the beginning of the increment ( j ).…”

Section: Cylinder Indentationmentioning

confidence: 99%

“…No exact solution to Equation (19) could be found, but in this section an approximate closed-form solution to Equation (19) is derived by examining the limiting (asymptotic) behavior at /r = 0. This solution is obtained by rewriting (19) as yet unknown constant. Upon rewriting Equation (19) in terms of dimensionless variables and substituting l = asym , the following expression is obtained:…”

Section: Asymptotic Solution For Cylindermentioning

confidence: 99%

“…This solution is obtained by rewriting (19) as yet unknown constant. Upon rewriting Equation (19) in terms of dimensionless variables and substituting l = asym , the following expression is obtained:…”

Section: Asymptotic Solution For Cylindermentioning

confidence: 99%

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Approximate model for blunt objects indenting cohesive‐frictional materials

Hambleton

Drescher

2011

Num Anal Meth Geomechanics

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SUMMARYAn approximate two-dimensional model for indentation of blunt objects into various types of rigid-perfectly plastic cohesive-frictional material is derived. Particular emphasis is placed on considering indentation as a process involving evolution of the boundary of material displaced by the indenter. Force-penetration relationships are obtained by an incremental approach utilizing key kinematic and static information from indentation of a flat punch. Albeit approximate, the proposed model applies to arbitrary indenter geometry and weightless or ponderable cohesive-frictional materials exhibiting associated or non-associated plastic flow. Two specific indenter geometries, the cylinder and blunt wedge, are explored in detail. Favorable agreement is found between the analytic results and those obtained using the finite element method (FEM). For both the wedge and cylinder, it is further shown that accurate analytic expressions relating indentation force explicitly to penetration can be derived. In the case of the wedge and weightless material, predictions of indentation force obtained from the derived expressions are very close to those computed from implicit equations available in the literature. Copyright ᭧ 2011 John Wiley & Sons, Ltd. Penetration of a rigid object into plastically deforming material commonly occurs in a number of applications. Tests for evaluating strength of metallic materials, for example, are usually based on indentation of spheres, cones, and pyramids [1]. Likewise, indentation of conical and non-conical objects into soils is a well-recognized practical methodology for determining in situ properties [2]. Indentation also represents a fundamental mode of operation in soil-machine interaction (SMI), where components of agricultural and earth-moving machinery of various types penetrate the soil [3,4]. Additional areas where penetration of an object may be of interest are sediment-object interaction in marine environments and processing of bulk materials.This paper is concerned with theoretically modeling the process of quasi-static normal indentation of blunt, two-dimensional (plane strain) objects into rigid-perfectly plastic cohesive-frictional material. Concentration on the process rather than a particular state necessitates consideration of the evolving contact interface between the indenter and material as well as the evolution of the lips forming next to the indenter, which possess a geometry that is unknown beforehand. Accordingly, the problem belongs to the class of unknown boundary type for which solutions may be non-unique [5,6]. The term 'blunt' implies that the ratio of penetration depth to contact length * Correspondence to: J. P. Hambleton,

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Section: Punch Indentationmentioning

confidence: 99%

Section: Cylinder Indentationmentioning

confidence: 99%

Section: Asymptotic Solution For Cylindermentioning

confidence: 99%

Section: Asymptotic Solution For Cylindermentioning

confidence: 99%

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Approximate model for blunt objects indenting cohesive‐frictional materials

Hambleton

Drescher

2011

Num Anal Meth Geomechanics

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“…However, associated ‡ow rules proved too restrictive to account for experimental properties of granular materials and attention turned to using a plastic potential function distinct from the yield function, i.e. a non-associated ‡ow rule, Mroz et al (1979).…”

Section: Introductionmentioning

confidence: 99%

A hyperbolic augmented elasto-plastic model for pressure-dependent yield

Harris

2014

Acta Mech

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A three-dimensional elasto-plastic model for the deformation and ‡ow of granular materials which generalises the plastic potential model and contains an additional term analogous to that appearing in the double shearing model is presented. It is shown that for planar ‡ows the resulting system of …rst order partial di¤erential equations is hyperbolic. This is in distinct contrast to the non-associated plastic potential model rule and the double shearing model, both of which fail to be hyperbolic. The ill-posedness of the planar double shearing model is due to the presence of the rotation-rate of the principal axes of stress. The ill-posedness of the non-associated plastic potential model is due to distinct quasi-static spatial stress and velocity characteristics. The present model attains wellposedness by replacing the planar rotation-rate of the principal stress axes by the vector intrinsic spin of a Cosserat continuum and using it to ensure identical spatial stress and velocity characteristics. Flows in which the intrinsic spin vector is constant in both space and time correspond to ‡ows in an ordinary continuum. The model governing such ‡ows is embedded into a Cosserat model in such a way that the characteristic structure is preserved.

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Analytical solution for high-pressure torsion in the framework of geometrically nonlinear non-associative plasticity

Sevastyanov

2020

International Journal of Solids and Structures

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Non-Associated Flow Rules in Description of Plastic Flow of Granular Materials

Cited by 7 publications

References 8 publications

Approximate model for blunt objects indenting cohesive‐frictional materials

Approximate model for blunt objects indenting cohesive‐frictional materials

A hyperbolic augmented elasto-plastic model for pressure-dependent yield

Analytical solution for high-pressure torsion in the framework of geometrically nonlinear non-associative plasticity

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