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Constitutive relationships for granular solids with particle slidings and fabric changes
A constitutive relationship is developed for granular materials from a micro-mechanical point of approach accounting for heterogeneity of deformation field, inter-particle sliding and packing structure change. The granular system is idealized to be composed of circular particles with same stiffness properties and inter-particle friction angle. The granular assembly supports the imposed load through resistance at inter-particle contacts. The deformation at inter-particle contact is represented by springs which connect particles at the inter-particle contact. With this simplified picture of the granular, the continuum variables such as stress and strain are defined for a particle (local or micro level) and for a collection of particles (overall or macro level). A definition of strain tensor which accounts for the particle rotation is introduced. A local stress-strain law is defined to describe the mechanical behavior of a particle interacting with its neighbors. The local stress-strain law is established by considering the following relationships: between the stress and contact force; and between the strain and relative displacement of the particles. The local stress-strain law is cast in terms of nominal stress increments in order to account for packing configuration change due to finite strains. Geometric non-linearity due to loss of existing contacts is included. A concept of over-shooting force is described which accounts for the effect of material nonlinearity due to inter-particle sliding and separation. The overall stress-strain law is defined for a representative volume of granular media. The representative volume of the granular material is taken to consist of a large number of particles such that it is considered to be equivalent to a point in a continuum media. The overall stress and strains are determined as volume averages of corresponding local quantities. A 'concentration' tensor is defined to relate the overall strain to the local strain. Using the 'concentration' tensor, and the definition of overall stress and strain as volume averages, the overall stiffness tensor is established. The overall stress-strain behavior is determined through a numerical effort. The stress-strain relationship developed in this study can reduce the discrete granular system to an equivalent continuum system which is mathematically and computationally more tractable. Example results are presented to show that the model captures all-the salient features features of mechanical behavior of granular materials such as: nonlinearity, elasto-plasticity, stress/strain path dependency, dilatancy-contractancy, failure and strain softening under post-peak loading.
Misra, Anil, "Constitutive relationships for granular solids with particle slidings and fabric changes" (1991). Doctoral Dissertations Available from Proquest. AAI9120921.