Abstract
In this paper, modelling of the superposition of stress-induced and inherent anisotropy of soil small strain stiffness is presented in the framework of hyperelasticity. A simple hyperelastic model, capable of reproducing variable stress-induced anisotropy of stiffness, is extended by replacement of the stress invariant with mixed stress–microstructure invariant to introduce constant inherent cross-anisotropic component. A convenient feature of the new model is low number of material constants directly related to the parameters commonly used in the literature. The proposed description can be incorporated as a small strain elastic core in the development of some more sophisticated hyperelastic-plastic models of overconsolidated soils. It can also be used as an independent model in analyses involving small strain problems, such as dynamic simulations of the elastic wave propagation. Various options and features of the proposed anisotropic hyperelastic model are investigated. The directional model response is compared with experimental data available in the literature.
Highlights
An elastic stress–strain relation is the core of all the elastoplastic constitutive models
In this paper, modelling of the superposition of stress-induced and inherent anisotropy of soil small strain stiffness is presented in the framework of hyperelasticity
A simple anisotropic hyperelastic model is presented in this paper
Summary
An elastic stress–strain relation is the core of all the elastoplastic constitutive models. Based on the experimental observations, Graham and Houlsby [21] proposed a simplification of the five-parameter cross-anisotropic stiffness They reduced the number of material constants to three independent parameters leaving Ev and mhh, denoted by EÃ and mÃ; respectively, and introducing the anisotropy coefficient a that imposes the following condition: rffiffiffiffiffi a 1⁄4 Eh 1⁄4 mhh 1⁄4 Ghh ; ð1Þ. The general framework of incorporating inherent anisotropy based on the microstructure within the hyperelasticity has been recently presented by Houlsby et al [29] and validated with the experimental evidence by Amorosi et al [2] Another notable works on anisotropic hyperelastic models for soils have been reported in the literature by Gajo and Bigoni [17, 18] and Xiao et al [54]. An interesting method of incorporating inherent cross-anisotropy into hyperelastic model by scaling of stiffness has been shown by Niemunis et al [44]
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