A continuum theory for granular materials

Goodman, M.A.; Cowin, Stephen C.

doi:10.1007/bf00284326

Cited by 668 publications

(286 citation statements)

References 22 publications

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“…In the microdilatation model described in [41,57,58] The proposed more specific form of the free energy potential is 15) where the relative strain measure e := ε eq − χ involves the equivalent strain measure, ε eq , function of the three invariants of the strain tensor ε 16) where ψ α related to hardening is left unspecified and can be non-quadratic. Accordingly,…”

Section: (B) Scalar Microstrainmentioning

confidence: 99%

Nonlinear regularization operators as derived from the micromorphic approach to gradient elasticity, viscoplasticity and damage

Forest¹

2016

Proc. R. Soc. A.

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International audienceThe construction of regularization operators presented in this work is based on the introduction of strain or damage micromorphic degrees of freedom in addition to the displacement vector and of their gradients into the Helmholtz free energy function of the constitutive material model. The combination of a new balance equation for generalized stresses and of the micromorphic constitutive equations generates the regularization operator. Within the small strain framework, the choice of a quadratic potential w.r.t. the gradient term provides the widely used Helmholtz operator whose regularization properties are well known: smoothing of discontinuities at interfaces and boundary layers in hardening materials, and finite width localization bands in softening materials. The objective is to review and propose nonlinear extensions of micromorphic and strain/damage gradient models along two lines: the first one introducing nonlinear relations between generalized stresses and strains; the second one envisaging several classes of finite deformation model formulations. The generic approach is applicable to a large class of elastoviscoplastic and damage models including anisothermal and multiphysics coupling. Two standard procedures of extension of classical constitutive laws to large strains are combined with the micromorphic approach: additive split of some Lagrangian strain measure or choice of a local objective rotating frame. Three distinct operators are finally derived using the multiplicative decomposition of the deformation gradient. A new feature is that a free energy function depending solely on variables defined in the intermediate isoclinic configuration leads to the existence of additional kinematic hardening induced by the gradient of a scalar micromorphic variable

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Section: (B) Scalar Microstrainmentioning

confidence: 99%

Nonlinear regularization operators as derived from the micromorphic approach to gradient elasticity, viscoplasticity and damage

Forest¹

2016

Proc. R. Soc. A.

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“…Eringen (1970) and Nowacki (1966)developed the linear theory of micropolar thermoelasticity which are known as micropolar coupled thermoelasticity to include thermal effects. Goodman and Cowin (1972) established a continuum theory for granular materials, whose matrix material (or skeletal) is elastic and interstices are voids and they introduced the concept of distributed body, which represents a continuum model for granular materials (sand, grain, powder, etc) as well as porous materials (rock, soil, sponge, pressed powder, cork, etc.). Nunziato and Cowin (1979), developed the non-linear theory of elastic materials with void, underlying the basic concept that the bulk density of the material is written as the product of two fields, the density field of the matrix material and the volume fraction field (the ratio of volume occupied by grains to the bulk volume at a point of the material) Kumar and Gupta (2010)].…”

Section: Latin American Journal Of Solids and Structures 12 (2015) 14mentioning

confidence: 99%

Two-Dimensional Fractional Order Generalized Thermoelastic Porous Material

Abbas

Youssef

2015

Lat. Am. j. solids struct.

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In the work, a two-dimensional problem of a porous material is considered within the context of the fractional order generalized thermoelasticity theory with one relaxation time. The medium is assumed initially quiescent for a thermoelastic half space whose surface is traction free and has a constant heat flux. The normal mode analysis and eigenvalue approach techniques are used to solve the resulting non-dimensional coupled equations. The effect of the fractional order of the temperature, displacement components, the stress components, changes in volume fraction field and temperature distribution have been depicted graphically.

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“…Our approach is close to that of the volume fraction concept as the latter reduces to the former once a suitable constraint among the enlarged set of state parameters is assumed [34]. For example, for an incompressible solid constituent, it is easy to see [25] how a mixture model endowed with the volume fraction concept transforms into a binary mixture whose solid constituent has second gradient constitutive relations. After formulating a general problem, we study deformations of a porous hollow linear elastic cylinder filled with a perfect fluid.…”

Section: Introductionmentioning

confidence: 95%

Static Deformations of a Linear Elastic Porous Body Filled with an Inviscid Fluid

Sciarra

Batra²,

Dell’Isola³

2003

Journal of Elasticity

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Abstract. We study infinitesimal deformations of a porous linear elastic body saturated with an inviscid fluid and subjected to conservative surface tractions. The gradient of the mass density of the solid phase is also taken as an independent kinematic variable and the corresponding higher-order stresses are considered. Balance laws and constitutive relations for finite deformations are reduced to those for infinitesimal deformations, and expressions for partial surface tractions acting on the solid and the fluid phases are derived. A boundary-value problem for a long hollow porous solid cylinder filled with an ideal fluid is solved, and the stability of the stressed reference configuration with respect to variations in the values of the coefficient coupling deformations of the two phases is investigated. An example of the problem studied is a cylindrical cavity leached out in salt formations for storing hydrocarbons.Key words: solid-fluid mixture, conservative tractions, principle of virtual power, partial tractions, fluid-filled cylindrical cavity, stability analysis. R.C. Batra dedicates this work with deep respect and admiration to

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A continuum theory for granular materials

Cited by 668 publications

References 22 publications

Nonlinear regularization operators as derived from the micromorphic approach to gradient elasticity, viscoplasticity and damage

Nonlinear regularization operators as derived from the micromorphic approach to gradient elasticity, viscoplasticity and damage

Two-Dimensional Fractional Order Generalized Thermoelastic Porous Material

Static Deformations of a Linear Elastic Porous Body Filled with an Inviscid Fluid

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