Including friction in the mathematics of classical plasticity

Abstract

SUMMARYIn classical plasticity there are clear mathematical links between the dissipation function and the consequent yield function and flow rule. These links help to construct constitutive equations with the minimum of adjustable parameters. Modelling granular materials, however, requires that the dissipation function depends on the current stress state (frictional plasticity) and this changes the mathematical structurealtering the links and invalidating the associated flow rule. In this paper we show, for a large family of dissipation functions, how much of the structure remains intact when frictional dissipation is included. The surviving links are examined using straightforward physically based graphical insight and well-established mathematical techniques leading to a central result, which provides a mathematical justification for the procedural features of hyperplasticity. This should allow hyperplasticity to be used more widely and certainly with increased confidence.As an example of the effectiveness of the general method, two specific dissipation functions are constructed from the simple physical concepts of sliding friction and granule damage. One is based on a Drucker-Prager cone and the other a Matsuoka-Nakai cone, both incorporate kinematic hardening and a compactive cap. In each Case a single smooth yield function with consistent flow rules is produced. The computational usefulness of an inequality derived in the paper is demonstrated in the generation of the figures showing yield surfaces and flow directions by means of a simple maximization procedure.

Smooth Yield Surface Constitutive Modeling for Granular Materials

“…In the transition between granular and fully dense states of a given material, the constitutive formulation faces the challenging problem of granular and dense materials having completely different mechanical behaviors, e.g., nonlinear elastic properties, cohesion, interparticle friction, pressure-sensitive yielding, plastic flow, hardening laws, crack/fracture induced damage, differences in strength in triaxial extension versus compression, and the Bauschinger effect. Capturing these behaviors typically necessitates the use of fairly complicated and expensive nonlinear material models [2][3][4][5][6][7][8][9][10][11].…”

Experimental and Numerical Investigation of Sand Compression Peculiarities

“…Such primary investigations prescribe the parameters of particles to be considered (Cavarretta 2009), namely: particle shape, form coefficient, area, perimeter, roundness, angularity and sphericity. The friction between individual particles should be also properly evaluated (Chandler, Sands 2010).…”