Abstract
Micromechanical studies of granular materials have demonstrated the importance of their microstructure to their behaviour. This microstructure is often characterized by fabric tensors. Experimental and computational studies have shown that the fabric can change significantly during deformation. Therefore, the evolution of fabric is important to constitutive modelling. Current fabric evolution laws for granular materials have generally been developed for continuum-mechanical models, and use a loading index multiplier associated with a yield surface. Such evolution laws can not be employed with micromechanical models that do not involve an explicit macro-scale yield surface.This study develops an evolution law for fabric anisotropy, based on observations from experiments and Discrete Element Method simulations from literature. The proposed evolution law considers the effects of inherent anisotropy, void ratio, stress ratio, loading direction and intermediate principal stress ratio. In the critical state, the value of the fabric anisotropy depends only on the Lode angle. The predicted evolution of fabric anisotropy is in good agreement with results of Discrete Element Method simulations, showing both hardening and softening behaviour and describing the influence of the initial void ratio.The proposed evolution law can be embedded into micromechanics-based constitutive relations as well as conventional continuum-mechanical models. As an example, a well-established micromechanical model (in which the fabric is considered as constant) has been extended by accounting for the variations in fabric, in combination with the proposed fabric evolution law. The performance of this enhanced micromechanical model has been demonstrated by a comparison between the predicted behaviour and experimental results from literature for Toyoura sand under various loading conditions.
Highlights
The mechanical behaviour of granular materials is important in many disciplines of engineering and science
Since the expressions for the average stress and strain and for the “localisation operator” involve the actual fabric tensor F, the CH micromechanical model can be extended in a straightforward manner by employing the actual fabric, where the actual fabric is given by the proposed fabric evolution law, Eq (13)
It is crucial to account for fabric evolution in constitutive modelling of granular materials subjected to large deformations, preferably consistent with the framework of ACST such that the unique critical state of granular materials is retained
Summary
The mechanical behaviour of granular materials is important in many disciplines of engineering and science. Micromechanics-based constitutive models for granular materials have recently been developed with homogenization methods (Chang and Hicher, 2005; Kruyt and Rothenburg, 2004; Misra and Singh, 2014; Nicot and Darve, 2011; Xiong et al, 2017; Yin and Chang, 2009; Zhao et al, 2018, 2019) In this micromechanical approach, the force-displacement relationship is specified at the micro-scale level of interparticle contacts and the stress-strain behaviour at the continuum, macro-scale level is obtained by averaging over all contact orientations.
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