Rational approach to anisotropy of sand

Wu, Wei

doi:10.1002/(sici)1096-9853(1998110)22:11<921::aid-nag948>3.0.co;2-j

Cited by 55 publications

(22 citation statements)

References 19 publications

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“…Inherent anisotropy has already been implemented to hypoplasticity (Wu 1998) to modify the nonlinear part of (25). Tensor N has been replaced by A : N wherein A is the fourth order tensor of transverse isotropy.…”

Section: Introductionmentioning

confidence: 79%

Anisotropic effects in hypoplasticity

Niemunis¹

2003

Deformation Characteristics of Geomaterials / Comportement Des Sols Et Des Roches Tendres

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Isochoric response of the hypoplastic constitutive model is improved by means of small modifications in the linear stiffness tensor and in the barotropy function. Comparisons with the Rowe theory of dilatancy and with the experimental results by Pradhan et al. are presented. The essential modification consists in increasing of shear stiffness. Moreover two anisotropic effects have been implemented: one in the linear part and one in the definition of barotropy factor. The modified hypoplastic model is presented using isomorphic variables P, Q. INTRODUCTIONHypoplastic constitutive models originate from a formalism alternative to elastoplasticity. First models were formulated independently in Karlsruhe (Kolymbas 1978) and in Grenoble (Chambon 1982) in late seventies. Numerous versions, improvements and applications have made evident the attractiveness of this approach. The 'Karlsruhe'-hypoplastic models for sand are based on a single equation (25), or similar, expressing the stress rateT as a nonlinear function of stretching D, stress T and of the void ratio e. Readers familiar with the endochronic theory may discover that hypoplasticity is closely related with the early Valanis models (Valanis 1971a; Valanis 1971b) with a single kernel and with an expression for stress written directly in the rate form. Equations of a contemporary hypoplastic model (Gudehus 1996;Wolffersdorf 1997) are given in Appendix 2. An extensive discussion of this model is given in the monography (Niemunis 2003). Notation is explained in Appendix 1.The reference model presented in Appendix 2 has no inherent anisotropy. All material constants are independent of the orientation of the coordinate system. The only tensorial state variable is stress T which induces incremental orthotropy with the planes of symmetry given by the eigenvectors of T. Choosing the initial stress to be isotropic, T 0 ∼ 1, the total hypoplastic response can be considered isotropic. Otherwise it is orthotropic with symmetry planes given by eigenvectors of T 0 .In elastoplasticity the back-stress anisotropy is usually implemented by means of nested loading sub-

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Section: Introductionmentioning

confidence: 79%

Anisotropic effects in hypoplasticity

Niemunis¹

2003

Deformation Characteristics of Geomaterials / Comportement Des Sols Et Des Roches Tendres

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“…For a refined modeling of the mechanical properties of granular materials the tensor functions L and in (2.3) may also depend on additional scalar-and tensor-valued state variables. For instance, the influence of pressure and on the incremental stiffness can be taken into account by scaling L and with a pressure-dependent stiffness factor and densityfactor [19,20,40,41]; rate-dependent properties can be introduced in the nonlinear part of the constitutive relation [42,43], and with additional structure tensors initial anisotropy [44,45], cohesion [46] and a so-called inter-granular strain [47] can be modeled. In order to also take into account particle rotation and couple stresses the nonpolar constitutive relation (2.3) was extended to a micro-polar continuum [28,30,31], which is discussed in more detail in the next section.…”

Section: The Concept Of Hypoplasticitymentioning

confidence: 99%

Initial response of a micro-polar hypoplastic material under plane shearing

Bauer

2005

J Eng Math

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The behavior of an infinite strip of a micro-polar hypoplastic material located between two parallel plates under plane shearing is investigated. The evolution equation of the stress tensor and the couple-stress tensor is described using tensor-valued functions, which are nonlinear and positively homogeneous of first order in the rate of deformation and the rate of curvature. For the initial response of the sheared layer an analytical solution is derived and discussed for different micro-polar boundary conditions at the bottom and top surfaces of the layer. It is shown that polar quantities appear within the shear layer from the beginning of shearing with the exception of zero couple stresses prescribed at the boundaries.

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“…Transversely isotropic material properties are included with a certain invariant form of a tensor function given by Boehler and Sawczuk (1977). The tensor function depends on the stress tensor and on a second order structure tensor and it is incorporated in the non-linear part of the constitutive equation according to the concept proposed by Wu (1998). While the coefficients of anisotropy are assumed to be constant in the earlier version by Wu (1998), an evolution of anisotropy depending on the relative density is considered in the present version.…”

Section: Introductionmentioning

confidence: 99%

“…The tensor function depends on the stress tensor and on a second order structure tensor and it is incorporated in the non-linear part of the constitutive equation according to the concept proposed by Wu (1998). While the coefficients of anisotropy are assumed to be constant in the earlier version by Wu (1998), an evolution of anisotropy depending on the relative density is considered in the present version. It is assumed that the influence of the initial anisotropy decreases for large shearing and it is swept out in critical-states (Bauer and Huang, 1999).…”

Section: Introductionmentioning

confidence: 99%