Granular hypoplasticity with Cosserat effects

Abstract

Abstract. This paper provides an extension to Cosserat mechanics of a recently proposed version of hypoplasticity [1], and this extension is achieved economically by means of a novel complex-variable formulation of Cosserat theory.The present work represents a compact synthesis and theoretical framework for both non-polar and polar hypoplasticity, and it encompasses various special cases considered in the literature, as discussed in the recent monograph by Tejchman [2].The current approach offers a perspective on granular dilatancy, elastoplastic yield, and energy dissipation which differs from the standard hypoplasticity and which serves to establish a connection to classical incremental plasticity. In contrast to the classical theory, the present approach, based entirely on the concept of pseudo-linear forms, admits but does require elastoplastic potentials to describe plastic flow. When such potentials are assumed, it is shown that they can be related to the plastic moduli of the present formulation.It is also shown that hypoplasticity allows for a distinction between active and passive internal variables, with the latter serving to define parameters. Finally, the known forms for linear isotropic Cosserat elasticity are employed to represent isotropic hypoplasticity, and the resulting formulae appear to encompass several empiricisms found in the literature.

A local constitutive model with anisotropy for ratcheting under 2D axial-symmetric isobaric deformation

“…The original reason for this behavior becomes clear looking at Figs. 4(g) and 4(h), where the variation of the contractancy/dilatancy ratio AS/2B (during initial loading (0) and the odd reversal points (1,3,5,7,9)) is shown for the two different β A . At the beginning (0), the quantity becomes always negative due to the initial decrease of A: that is, the system always shows initial dilatancy, see path 0 − 1 in 4(e) and 4(f).…”

“…Only few theories, see e.g. [2,7,15,[18][19][20]22] and references therein, involve an anisotropy state variable. The influence of the micromechanics on the noncoaxiality of stress, strain and anisotropy of soils is described e.g.…”

On material velocities and non-locality in the thermo-mechanics of continua

“…Because of the small length scales, such effects are expected to be relatively weak in the molecular system, other than in liquid crystals or in experiments involving high-frequency (large k, s) response. The situation is different at larger particle scales in fields such as granular mechanics and rotational seismology [20,35,17,14], where gradient effects can be much more important. Setting aside non-linear (amplitude) effects, the non-local model of viscoelasticity (34), which is also applicable to anisotropic materials, is readily modified to incorporate couple-stress effects.…”

“…A recently proposed complex-variable representation [14], with complex stress T + ıM and complex velocity v + ıx giving a single balance for linear and angular momentum, is readily implemented in (35) and (36) on replacingŝ ij byŝ ij þ ıl ij ;v k byv k þ ıx k and A, B, . .…”

Micro-macro and jamming transition of polydisperse granular materials

“…In the majority of the models, the stress increment is related to the actual stress state of the granular system and its density. This is the case for hypoplasticity [64,68,94,192], where a single non-linear tensorial equation relates the Jaumann stress-rate with strain-rate and stress tensors. Later versions [145] also involve an explicit relation with the structure of the contact network.…”