A C2 continuous approximation to the Mohr–Coulomb yield surface

Abbo, Andrew J.; Lyamin, A. V.; Sloan, Scott W.; Hambleton, J.P.

doi:10.1016/j.ijsolstr.2011.06.021

Cited by 76 publications

(62 citation statements)

References 10 publications

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“…An explicit forward Euler stress integration scheme was used with adaptive sub-stepping and error control as described by Sloan [19] and Abbo [1]. Full C2 rounding of the Mohr-Coulomb yield surface was also implemented as described by Abbo et al [2]. It was found that the implementation of C2 rounding, particularly in the meridional plane, was very helpful in improving model convergence.…”

Section: Constitutive Model Implementationmentioning

confidence: 99%

A numerical study into factors affecting stress and pore pressure in free draining mine stopes

Doherty

2015

Computers and Geotechnics

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Section: Constitutive Model Implementationmentioning

confidence: 99%

A numerical study into factors affecting stress and pore pressure in free draining mine stopes

Doherty

2015

Computers and Geotechnics

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“…Many numerical algorithms have been proposed and demonstrated to be effective for treating this singularity problem. Examples of these algorithms are the smoothing of Mohr‐Coulomb yield surface corners, linearisation of the yield surface, hyperbolic approximation of the sharp corners, C1 and C2 continuous treatment of the model . In this work, the approach proposed by Chen and Mizuno is adapted for implementing the Mohr‐Coulomb model in SPH.…”

Section: Constitutive Modelmentioning

confidence: 99%

A generic approach to modelling flexible confined boundary conditions in SPH and its application

Zhao

Bui

Lemiale

et al. 2019

Num Anal Meth Geomechanics

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Summary In this paper, a new approach to applying confining stress to flexible boundaries in the smoothed particle hydrodynamics (SPH) method is developed to facilitate its applications in geomechanics. Unlike the conventional SPH methods that impose confining boundary conditions by creating extra boundary particles, the proposed approach makes use of kernel truncation properties of SPH approximations that occur naturally at free‐surface boundaries. Therefore, it does not require extra boundary particles and, as a consequence, can be utilised to apply confining stresses onto any boundary with arbitrary geometry without the need for tracking the curvature change during the computation. This enables more complicated problems that involve moving confining boundaries, such as confining triaxial tests, to be simulated in SPH without difficulties. To further enhance SPH applications in elasto‐plastic computations of geomaterials, a robust numerical procedure to implement Mohr‐Coulomb plasticity model in SPH is presented for the first time to avoid difficulties associated with corner singularities in Mohr‐Coulomb model. The proposed approach was first validated against two‐dimensional finite element (FE) solutions for confining biaxial compression tests to demonstrate its predictive capability at small deformation range when FE solutions are still valid. It is then further extended to three‐dimensional conditions and utilised to simulate triaxial compression experiments. Simulation results predicted by SPH show good agreement with experiments, FE solutions, and other numerical results available in the literature. This suggests that the proposed approach of imposing confining stress boundaries is promising and can handle complex problems that involve moving confining boundary conditions.

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“…The sharp edges of the yield surface are smoothed with a C2 approximation [1]. The elastic regime is assumed to fulfil a linear model between the Kirchhoff stress and the elastic Hencky Strain: For the coupled hydro-mechanical analysis, a Modified Cam Clay model is used [6,29].…”

Section: Constitutive Relationsmentioning

confidence: 99%

Performance of mixed formulations for the particle finite element method in soil mechanics problems

et al. 2016

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This paper presents a computational framework for the numerical analysis of fluid-saturated porous media at large strains. The proposal relies, on one hand, on the Particle Finite Element Method (PFEM), known for its capability to tackle large deformations and rapid changing boundaries, and, on the other hand, on constitutive descriptions well-established in current geotechnical analyses (Darcy's law; Modified Cam Clay; Houlsby hyper-elasticity). An important feature of this kind of problem is that incompressibility may arise either from undrained conditions or as a consequence of material behavior; incompressibility may lead to volumetric locking of the low-order elements that are typically used in PFEM. In this work, two different three-field mixed formulations for the coupled hydro-mechanical problem are presented, in which either the effective pressure or the Jacobian are considered as nodal variables, in addition to the solid skeleton displacement and water pressure. Additionally, several mixed formulations are described for the simplified single-phase problem due to its formal similitude to the poromechanical case and its relevance in geotechnics, since it may approximate the saturated soil behavior under undrained conditions. In order to use equal order interpolants in displacements and scalar fields, stabilization techniques are used in the mass conservation equation of the biphasic medium and in the rest of scalar equations. Finally, all mixed formulations are assessed in some benchmark problems and their performances are compared. It is found that mixed formulations that have the Jacobian as a nodal variable perform better.

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A C2 continuous approximation to the Mohr–Coulomb yield surface

Cited by 76 publications

References 10 publications

A numerical study into factors affecting stress and pore pressure in free draining mine stopes

A numerical study into factors affecting stress and pore pressure in free draining mine stopes

A generic approach to modelling flexible confined boundary conditions in SPH and its application

Performance of mixed formulations for the particle finite element method in soil mechanics problems

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