Modelling of cohesive-frictional materials : proceedings of by P A Vermeer
By P A Vermeer
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Extra resources for Modelling of cohesive-frictional materials : proceedings of 2nd International Symposium on Continuous and Discontinuous Modelling of Cohesive-Frictional Materials, CDM 2004, Stuttgart, 27-28 September 2004
2 Stress and energetics The conventional expression for granular (Cauchy) stress as dipolar force density can be expressed in terms of edge contributions as (8) where fe is interparticle force at the particle contact represented by edge e. The latter requires additional work terms to account higherorder moment (CosseratMindlin) stresses and velocity gradients (Chang and Lun 1991; Chang and Gao 1995; Goddard 1997), and will not be considered further here. While P(z) may depend on time, we restrict attention here to spatially homogeneous systems, such that P(z) and dΩ(z) are independent of spatial position.
Finally, it offers a brief elaboration on a virtualthermomechanics associated with granular entropy (Goddard 2004). Also, the thermomechanical formalism requires no direct appeal to the concept of (static) granular temperature favored in certain statisticalphysics literature, although one can introduce a parameter that could play a vague similar role. 1, a graph based on Delaunay triangulation (Goddard 1998). Solid lines represent real granular contacts and dotted lines latent contacts. Basis vectors g i, foreshortened for clarity, have same length as corresponding edges.
7 (material 2). 7 (material 2). 2) it is also possible to define scalar bA from tensor Aij. In these tests q=σ1−σ2 and p= (σ1+σ2)/2. This critical state corresponds to values of q/p, void ratio e and anisotropy measured by bH independent of the initial states (density and anisotropy). So for this kind of material (polygonal particles with important elongation ratio) the critical state seems to be very difficult to reach even for very large strain. 7 (material 2). This means that particles rotate throughout the test with a main value of rotation which remains equal to 0.