An unconstrained stress updating algorithm with the line search method for elastoplastic soil models

Zhou, Xin; Lu, Dechun; Su, Cancan; Gao, Zhiwei; Du, Xiuli

doi:10.1016/j.compgeo.2021.104592

Cited by 13 publications

(4 citation statements)

References 51 publications

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“…To this end, the KKT conditions in Equation (20) 4 are replaced equivalently by the Fischer-Burmeister smooth function. 19…”

Section: Unconstrained Implicit Stress Update Based On the Line Searc...mentioning

confidence: 99%

“…The solving process is also known as the “plastic correction.” The loading/unloading estimation is required at each increment step, which increases the complexity of the model implementation. To this end, the KKT conditions in Equation (20) 4 are replaced equivalently by the Fischer–Burmeister smooth function 19

$$\begin{equation}\left\{ { \def\eqcellsep{&}\begin{array}{@{}*{1}{c}@{}} {{f}_1}\\[15pt] {{f}_2}\\[15pt] {{f}_3}\\[15pt] {{f}_4} \end{array} } \right\} = \left\{ { \def\eqcellsep{&}\begin{array}{@{}*{1}{c}@{}} {{p}_{n + 1} - {p}_n\exp \left( {{c}_\kappa \Delta \varepsilon _{{\rm{v, }}n + 1}^{\rm{e}}} \right) = 0}\\[15pt] {{q}_{n + 1} - \sqrt {\dfrac{3}{2}} \dfrac{{\left\| {{{{\bf s}}}_n + 2\bar{G}\Delta {{{\bm \gamma }}}_{n + 1}} \right\|}}{{1 + c}} = 0}\\[15pt] {{p}_{{\rm{c}},n + 1} - {p}_{{\rm{c}},n}\exp \left( {{c}_{\rm{p}}\Delta \varepsilon _{{\rm{v, }}n + 1}^{\rm{p}}} \right) = 0}\\[15pt] {\sqrt {{{\left( {{c}_{\rm{d}}\Delta {\phi }_{n + 1}} \right)}}^2 + f_{n + 1}^2 + 2\beta } - {c}_{\rm{d}}\Delta {\phi }_{n + 1} + {f}_{n + 1} = 0} \end{array}...

…”

Section: Unconstrained Implicit Stress Update Based On the Line Searc...mentioning

confidence: 99%

“…Therefore, attempts have been made to improve the efficiency of the implicit stress integration method. For instance, one can use the smoothing function to replace the inequality constraints [19][20][21][22][23] or the penalty function 24 to bypass loading/unloading judgment. The nonlinear equations can be solved by the homotopy method, 25 the line search method, 18,19 or the trust region method 19 instead of the Newton method.…”

Section: Introductionmentioning

confidence: 99%

“…Therefore, attempts have been made to improve the efficiency of the implicit stress integration method. For instance, one can use the smoothing function to replace the inequality constraints 19–23 or the penalty function 24 to bypass loading/unloading judgment. The nonlinear equations can be solved by the homotopy method, 25 the line search method, 18,19 or the trust region method 19 instead of the Newton method.…”

Section: Introductionmentioning

confidence: 99%

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A robust stress update algorithm for elastoplastic models without analytical derivation of the consistent tangent operator and loading/unloading estimation

Zhang

Zhou

et al. 2023

Num Anal Meth Geomechanics

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A robust and concise implicit stress integration algorithm of elastoplastic models is presented. It does not require the loading/unloading estimation and analytical derivation operation for the stress update. First, the elastoplastic stress update problem is recast into an unconstrained minimization problem by utilizing the smooth function to bypass the loading/unloading estimation. Then, the object problem is solved by the line search method instead of the Newton method for better convergence. The consistent tangent operator is evaluated by the complex step derivative approximation without the subtraction cancellation error, which provides the quadratic convergence rate of global iteration. The rationality of the numerical consistent tangent operator is validated by the one obtained by the analytical derivation. A recently developed non-orthogonal elastoplastic (NEP) clay model is implemented using the new algorithm. The algorithm is confirmed through comparing the numerical solution and the analytical one for a cavity expansion problem. The algorithm performance is assessed based on a series of geotechnical boundary value problems. It is found that the new algorithm is more robust than the one employed by ABAQUS. The source code of the model implementation can be downloaded from https://github.com/zhouxin615.

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“…To this end, the KKT conditions in Equation (20) 4 are replaced equivalently by the Fischer-Burmeister smooth function. 19…”

Section: Unconstrained Implicit Stress Update Based On the Line Searc...mentioning

confidence: 99%

$$\begin{equation}\left\{ { \def\eqcellsep{&}\begin{array}{@{}*{1}{c}@{}} {{f}_1}\\[15pt] {{f}_2}\\[15pt] {{f}_3}\\[15pt] {{f}_4} \end{array} } \right\} = \left\{ { \def\eqcellsep{&}\begin{array}{@{}*{1}{c}@{}} {{p}_{n + 1} - {p}_n\exp \left( {{c}_\kappa \Delta \varepsilon _{{\rm{v, }}n + 1}^{\rm{e}}} \right) = 0}\\[15pt] {{q}_{n + 1} - \sqrt {\dfrac{3}{2}} \dfrac{{\left\| {{{{\bf s}}}_n + 2\bar{G}\Delta {{{\bm \gamma }}}_{n + 1}} \right\|}}{{1 + c}} = 0}\\[15pt] {{p}_{{\rm{c}},n + 1} - {p}_{{\rm{c}},n}\exp \left( {{c}_{\rm{p}}\Delta \varepsilon _{{\rm{v, }}n + 1}^{\rm{p}}} \right) = 0}\\[15pt] {\sqrt {{{\left( {{c}_{\rm{d}}\Delta {\phi }_{n + 1}} \right)}}^2 + f_{n + 1}^2 + 2\beta } - {c}_{\rm{d}}\Delta {\phi }_{n + 1} + {f}_{n + 1} = 0} \end{array}...

…”

Section: Unconstrained Implicit Stress Update Based On the Line Searc...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…Therefore, attempts have been made to improve the efficiency of the implicit stress integration method. For instance, one can use the smoothing function to replace the inequality constraints 19–23 or the penalty function 24 to bypass loading/unloading judgment. The nonlinear equations can be solved by the homotopy method, 25 the line search method, 18,19 or the trust region method 19 instead of the Newton method.…”

Section: Introductionmentioning

confidence: 99%

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