Micromechanics based second gradient continuum theory for shear band modeling in cohesive granular materials following damage elasticity

Abstract

a b s t r a c tGradient theories, as a regularized continuum mechanics approach, have found wide applications for modeling strain localization failure process. This paper presents a second gradient stress-strain damage elasticity theory based upon the method of virtual power. The theory considers the strain gradient and its conjugated double stresses. Instead of introducing an intrinsic material length scale into the constitutive law in an ad hoc fashion, a microstructural granular mechanics approach is applied to derive the higher-order constitutive coefficients such that the internal length scale parameter reflects the natural granularity of the underlying material microstructure. The derivations of the required damage constitutive relationships, the strong form governing equations as well as its weak form for the second gradient model are described. The recently popularized Element-Free Galerkin (EFG) method is then employed to discretize the weak form equilibrium equation for accommodating the resultant higher-order continuity requirements and further handling the mesh sensitivity problem. Numerical examples for shear band simulations show that the proposed second gradient continuum model can produce stable, accurate as well as mesh-size independent solutions without a priori assumption of the shear band path.

“Fast” and “slow” pressure waves electrically induced by nonlinear coupling in Biot-type porous medium saturated by a nematic liquid crystal

“…Due to the high porosity, the Biot model should probably be modified, see e.g. [50][51][52][53][54][55][56][57][58], by adding a correction term which takes into account the microstructural effect [48,[59][60][61][62][63][64]. Strain gradient models (see e.g.…”

Using a penalty term to deal with spurious oscillations in second gradient finite elements

“…This was soon followed with several applications for plane strain shear banding 20 , 21 , 22 , 23 mostly in soils, using constitutive models based on plasticity. Similar approaches were also recently used in the framework of damage mechanics combined with homogenization techniques by 24 , 25 , see also 26 , 27 , 28 and 29 for application in concrete structures.…”

Homogenization of periodic graph-based elastic structures

“…. Their very rich behavior allows for instance to regularize and thus to study precisely the parts of materials where the deformation tends to concentrate, [56], [32] (inter-phases, [41], [24], [34], [51], porous media, [50], fractures, [2], [3], damage and plasticity, [57], [48]). However the second gradient properties are scarcely measured directly, [9], [10], [35] nor rigorously interpreted from a microscopic point of view.…”