The mixed complementarity problem arising from non-associative plasticity with non-smooth yield surfaces

Zheng, Hong; Tan, Zhen; Wang, Qiusheng

doi:10.1016/j.cma.2019.112756

Cited by 26 publications

(18 citation statements)

References 36 publications

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“…Suppose the set of solutions to MiCP (f I , f E ) is not empty [25]; based on the Gauss-Seidel iteration, we designed a projection-contraction algorithm, abbreviated by GSPC. GSPC is unnecessary to (i) test if the elastic trial stress point σ e , defined in Equation ( 13), is outside the elastic domain E σ ; (ii) find the intersection between the elastic path σ 0 -σ e and the yielding surface; (iii) guess which yielding patches are active; and (iv) form the Hesse matrix of any potential function g i .…”

Section: The Mixed Complementarity Problemmentioning

confidence: 99%

Location of Tension Cracks at Slope Crests in Stability Analysis of Slopes

et al. 2022

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Over the conventional limit equilibrium method and limit analysis method, the finite element method is advantageous, especially for slopes involving complex failure mechanisms where the critical slip surfaces cannot be represented by log spirals and other similarities. In the presence of tension cracks at slope crests, however, the finite element method encounters difficulties in convergence while handling Mohr–Coulomb’s yielding surfaces with tensile strength cut-off. Meanwhile, the commonly used load-controlled method for the system of nonlinear equilibrium equations is hard to bring the slope into the limit equilibrium state. The two drawbacks drag down the finite element method in more extensive applications. By reducing the constitutive integration of plasticity with non-smooth yielding surfaces to the mixed complementarity problem, the convergence in numerical constitutive integration is established for arbitrarily large incremental strains. In order to bring the slope to the limit equilibrium state, a new displacement-controlled algorithm is designed for the system of nonlinear equilibrium equations, which is far more efficient than the load-controlled method. A procedure is proposed to locate tension cracks. Corresponding to the Mohr–Coulomb failure criterion with and without tensile strength cut-off, the failure mechanisms differ significantly, while the difference in the factor of safety might be ignorable.

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Section: The Mixed Complementarity Problemmentioning

confidence: 99%

Location of Tension Cracks at Slope Crests in Stability Analysis of Slopes

et al. 2022

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“…The original GSPC is invoked in this way by Zheng et al 41

\begin{equation} (N,x)=\mbox{GSPC}(N^0,x^0,f_I,f_E) \end{equation}

where

(N^0,x^0)

is the initial guess value of GSPC algorithm,

f_I

is the inequality condition in MiCP,

f_E

is the equality condition in the MiCP.…”

Section: Comparison Between R‐gspc and Gspcmentioning

confidence: 99%

“…The GSPC is a PCA based on Gauss-Seidel, Allevi et al 40 introduced the extended Gauss-Seidel method to solve the multivalued problem of mixed complementarity. The GSPC method was firstly applied to solve the elastoplastic problem of nonsmooth yield surface by Zheng et al, 41 then the method was used for elastic-plastic shear band problems by Fan et al 42 It can be found that the GSPC algorithm can be extended to a large class of complementary problems, such as the contact problem discussed in this paper later, owing to the contact complementarity problem and the elastic-plastic complementarity problem have similar mathematical forms.…”

Section: Introductionmentioning

confidence: 99%

Improved Gauss Seidel based projection–contraction algorithm for the mixed complementarity problem in contact problem

Zeng

Zheng

Liu

et al. 2022

Num Anal Meth Geomechanics

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The GSCP (Gauss–Seidel based projection‐contraction) algorithm has been well established in solving elastoplastic mixed complementarity problems (MiCPs) or other problems which have similar mathematical form. However, the stability problems in the GSPC algorithm may cause nonconvergence or program crashes. Thus, the method of constructing and analyzing counterexamples is adopted to study the reasons for the instability of the GSPC algorithm. The R‐GSPC algorithm was developed by modifying the part of the GSPC algorithm that caused the crash to make the algorithm stable. In addition, this paper analyzes the convergence, compatibility, and initial value impact of R‐GSPC, and finds that the R‐GSPC algorithm greatly improves the robustness and stability without losing accuracy. This paper allows the GSPC algorithm to be better extended to more fields and to be suitabled for being introduced into commercial programs.

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“…However, laboratory investigations still suffer from difficulty in capturing the complex microscopic behaviors of unsaturated soils even with some advanced experimental techniques such as the photoelasticity technique 19 and X‐ray computerized tomography 20 . As an alternative tool, numerical methods, 21 which can conveniently deal with complex model geometry and boundary conditions, 22,23 are widely adopted to investigate the mechanical behavior of unsaturated soils. Due to the discontinuity of soil skeleton and complexity of capillary action, continuum‐based numerical methods represented by the finite element method (FEM), 24 which are often applied for macroscopic behavior analysis, 25–28 can hardly realistically reflect the micro‐mechanism of unsaturated soils.…”

Section: Introductionmentioning

confidence: 99%

An extended numerical manifold method for unsaturated soil‐water interaction analysis at micro‐scale

Sun

Zheng

et al. 2021

Num Anal Meth Geomechanics

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To investigate unsaturated soil‐water interaction at micro‐scale, this study extends the numerical manifold method (NMM) by incorporating a soil‐water coupling model considering specific capillary water distribution and capillary force calculation. The soil skeleton is constructed by a soil skeleton generation algorithm with random polygons. To more realistically capture the interaction between soil grains and capillary water, a capillary mechanics‐based geometric algorithm is proposed to iteratively calculate the capillary water distribution. The capillary forces corresponding to the capillary water distribution are calculated based on the Young‐Laplace equation. The proposed capillary water solving framework is first verified by reproducing the soil‐water characteristic curve and the capillary water distribution of an ideal contact‐disk model against analytical solutions. To further validate the ability of the capillary water solving framework to predict hydraulic behavior of the real soil, a laboratory test on the Toyoura sand is reproduced numerically. Then an ideal direct shear test is performed to further validate the two‐way soil‐water coupling procedure, in which a comparison between the numerical and analytical results regarding the shear strength and matric suction is presented. Finally, microscopic hydraulic and compression tests are conducted on two soil specimens with the same porosity and mean grain diameter but different uniformity coefficients. The results elucidate that the extended method is a potential tool to explore unsaturated soil behaviors at micro‐scale.

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The mixed complementarity problem arising from non-associative plasticity with non-smooth yield surfaces

Cited by 26 publications

References 36 publications

Location of Tension Cracks at Slope Crests in Stability Analysis of Slopes

Location of Tension Cracks at Slope Crests in Stability Analysis of Slopes

Improved Gauss Seidel based projection–contraction algorithm for the mixed complementarity problem in contact problem

An extended numerical manifold method for unsaturated soil‐water interaction analysis at micro‐scale

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