Propagation of Localization Instability Under Active and Passive Loading

Abstract

Abstract:The mechanical response of a solid continuum changes drastically as the deformation evolves from a diffuse state to a highly localized state. For this reason the subject of strain localization has received much research attention lately. This paper investigates the impact of strain localization in the form of strong discontinuity, or displacement jump, on the limit strengths of retaining walls supporting an elastoplastic backfill. The analysis focuses on the propagation of strong instability in active and passive loading using a recently developed strong discontinuity finite element model where the elements are enhanced to accommodate the presence of displacement jumps. Specifically, the analysis applies to dilative frictional material that is susceptible to shear banding. For the retaining wall problem, strong instability is shown to initiate at the ground surface and propagate downward at an angle that depends on the state of stress at the onset of localization.

Finite element simulation of strain localization with large deformation: capturing strong discontinuity using a Petrov–Galerkin multiscale formulation

“…Following standard lines [24][25][26][27]31,34,35], elastic unloading outside the band can be captured by assuming H to take the form…”

“…Such treatment is not limited to the kinematical description of deformation alone but may also include characterization of the bifurcated constitutive response inside the localization band [23][24][25][26][27]. An example of a bifurcated constitutive response is the accelerated softening behavior exhibited by the granular material inside a crack or fault as compared to that exhibited by the parent rock [28].…”

Critical state plasticity. Part VI: Meso-scale finite element simulation of strain localization in discrete granular materials

“…For this reason, much experimental work has been conducted to gain a better understanding of the localization process in these materials [1][2][3][4][5][6][7][8][9][10][11]. The subject also has spurred considerable interest in the theoretical and computational modeling fields [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29]. It is important to recognize that the material response observed in the laboratory is a result of many different micro-mechanical processes, such as mineral particle rolling and sliding in granular soils, micro-cracking in brittle rocks, and mineral particle rotation and translation in the cement matrix of soft rocks.…”

Mechanical aspects of thrust faulting driven by far-field compression and their implications for fold geometry

“…In the context of finite element (FE) analysis, there are many alternative approaches that one can possibly pursue to model thrust faulting, including: (a) the embedded discontinuity approach [9,11,15,16]; (b) the extended finite element approach, or XFEM [29,40,57]; and (c) the contact mechanics technique [5,20,31,44,58,73,93]. All of these approaches entail some form of regularization to characterize the thickness of the fault.…”