By P A Vermeer
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Extra info 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
Example text
Hill 1998) and will be of ratetype. In analogy, we split κ and τ into elastic and plastic parts, viz. κ:=κe+κp , τ:=τe+τp . (Hill 1998)) to the stress(like) quantities s, m, λ and s as well as to the softening (or hardening) function h, and read as follows: (13) (14) (15) (16) (17) Above, is a Lagrange multiplier whose appearance is due to the principle of maximal plastic dissipation. It is moreover remarked that micropolar elastoplastic material behavior as considered in (Steinmann 1995) can also be regained from the present material model by assigning α1=1/l2, α2=α3=0.
While we mainly are concerned with 3D granular assemblies, it seems evident that the above ideas could be extended to arbitrary dimensions d, perhaps most naturally by means of exterior (Grassmann) algebra (Frankel 1999). 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.
AddisonWesley. International Journal of Solids & Structures 40(13–14), 3537–3556. International Journal of Solids & Structures 39(3), 571–583. International Journal of Engineering Science 30(10), 1525–1533. Focusing on two kinds of microstructured materials (gradient continua, micromorphic continua), an attempt is thus made to identify their role and their potential with regard to numerical implementations in a generic theory. be modeled by applying a mixed variational principle to a micromorphic continuum.