A note on non‐linear elasticity of isotropic overconsolidated clays

SUMMARYExperimental evidence shows that soil stiffness at very small strains is strongly anisotropic and depends on the stress level and void ratio. In particular, stiffness anisotropy varies considerably in sand when subjected to cyclic loading, following the stress cycles applied. To model this behaviour, an innovative hyperelastic formulation based on the elastoplastic coupling is incorporated in a new kinematic hardening elastoplastic model. The proposed hyperelastic-plastic model is the first to be capable of correctly simulating all aspects of the small-strain behaviour of granular materials subjected to monotonic and cyclic loads. This hyperelastic formulation is generally applicable to any elastoplastic model.

mentioning

confidence: 99%

Hyperelastic modelling of small‐strain stiffness anisotropy of cyclically loaded sand

Gajo

2009

“…Alternatively, a different formulation in terms of complementary free-energy density may be given in the following form: APPENDIX C: AN ALGEBRAIC FORM FOR TENSORIAL PRODUCTS (27) Taking into account the relationship existing between symmetric second-order tensors, fourth-order tensors having minor symmetries and vectors of dimension 6, and 6 × 6 matrices, respectively, the following vectorial representation can be given to every second-order symmetric tensor C:…”

mentioning

confidence: 99%

A model for stress and plastic strain induced nonlinear, hyperelastic anisotropy in soils

Gajo

Bigoni

2007

SUMMARYThe experimental evidence that cohesive and granular soils possess an elastic range in which the elasticity is both nonlinear and anisotropic-with stiffness and directional characteristics strongly dependent on stress and plastic strain (the so-called 'stress history')-is given a formulation based on hyperelasticity. This is accomplished within the framework of elastoplastic coupling, through a new proposal of elastic potentials and a combined use of a plastic-strain-dependent fabric tensor and nonlinear elasticity. When used within a simple elastoplastic framework, the proposed model is shown to yield very accurate simulations of the evolution of elastic properties from initial directional stiffening to final isotropic degradation. Within the proposed constitutive framework, it is shown that predictions of shear band formation and evolution become closer to the existing experimental results, when compared to modelling in which elasticity does not evolve.

“…Comparing tensor coefficients of Eqn () and Eqn (), and because the basis tensors

E^{iso}

and

E^{sd}

are not expressible as linear combinations of

\bar{γ} δ

δ \bar{γ}

\bar{γ} \bar{γ}

\bar{h} δ

\overset{h}{true}

\bar{h} \bar{γ}

\bar{γ} \bar{h}

, and

\bar{h} \bar{h}

, an isotropic material will have an isotropic stiffness if and only if μ is independent of the deformation measure, and the bulk modulus varies at most with

J_{1}^{\bar{ε}}

. Hueckel arrived at the same conclusion with respect to the secant bulk and shear moduli , and, using the right Cauchy–Green stretch tensor as a deformation measure, Marsden gave a similar representation of the elastic stiffness to that of Eqn (). Thus, an isotropic material will generally have an anisotropic stiffness if the shear modulus varies with deformation.…”

Section: Thermodynamic Requirement Of Reversible Deformation‐induced mentioning

confidence: 86%

On the effects of deformation induced anisotropy in isotropic materials

Fuller

Brannon

2012

SUMMARYEffects of recoverable deformation induced anisotropy in the elastic stiffness of isotropic materials are described. In isotropic materials, thermodynamics predicts coupling of hydrostatic and deviatoric responses. It is shown that the coupling of the two responses is more significant than previously recognized in the literature. Properly accounting for the coupling of hydrostatic and deviatoric responses requires re-evaluating elastic materials characterization data, allowing for the coupled response. The result is an apparent decrease in the pressure sensitivity of the elastic shear modulus. The decrease in the pressure sensitivity of the shear modulus leads to stress paths that are more tangential to the yield surface in stress space, resulting in an increase in predicted elastic strain at each step of an elastic-plastic stress update. Consequently, predicted plastic strains and, in particular, volumetric plastic strains, are smaller than if recoverable deformation induced anisotropy had been neglected. The result is an associated plasticity model, which appears to be non-associated.