Abstract
The structure of the contact network in granular assemblies can evolve due to either dissipative mechanisms such as sliding at contact points, or non-dissipative mechanisms through the phenomenon of contact gain and loss. Being associated with negligible deformations, non-dissipative mechanisms is actually active even in the small strain range of ~ 10−3 , especially in the case of densely packed assemblies. Hence, from a constitutive modelling point of view, it is crucial to be able to estimate such non-dissipative evolutions since both elastic and plastic properties of granular assemblies highly depend on contact network characteristics. The current study proposes an analytical scheme that allows us to estimate the non-dissipative contact gain/loss regime in terms of directional changes in the average contact force. The probability distribution of contact forces is used to compute the number of lost contact for each direction. Similarly, the number of newly formed contacts is estimated by considering the probability distribution of the gap between neighbouring particles. Based on the directional contact gain/loss computed, the changes in coordination number and fabric anisotropy can be found which, together with statistical treatments of Love-Weber stress expression, form a complete system of equations describing the evolution of other controlling microvariables. Finally, the results of the calculations have been compared with DEM simulations which verify the accuracy of the proposed scheme.
Highlights
The internal structure of jammed granular materials can change under external loading according to various mechanisms that can be classified into three broad categories: Non-dissipative- reversible (e): which refers to the socalled elastic deformation at interparticle contact points
From a constitutive modelling point of view, it is crucial to be able to calculate the evolution of internal structure mainly because almost all micromechanical models heavily depends on the structure of contacts often expressed in terms of coordination number and fabric anisotropy
The current study proposes an analytical scheme to compute the change in fabric anisotropy and coordination number due to non-dissipative/irreversible mechanisms
Summary
The internal structure of jammed granular materials can change under external loading according to various mechanisms that can be classified into three broad categories:. Non-dissipative- reversible (e): which refers to the socalled elastic deformation at interparticle contact points Such processes conserve energy, contribute to overall strain, and are recoverable upon load reversal. Dissipative- irreversible (p): which includes the plastic deformation associated with sliding at contact points Such processes dissipate energy, contribute to overall strain, and are, by nature, irrecoverable upon load reversal. Non-dissipative- irreversible (δ): which includes the changes in contact network topology due to contact gain and loss events These events do not contribute to overall strain, nor do they dissipate energy. From a constitutive modelling point of view, it is crucial to be able to calculate the evolution of internal structure mainly because almost all micromechanical models (including models for elasticity of granular materials) heavily depends on the structure of contacts often expressed in terms of coordination number and fabric anisotropy. The calculation procedure, can be extended to be applicable to more general cases
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