An open-source unconstrained stress updating algorithm for the modified Cam-clay model

This paper presents an unconstrained stress updating algorithm for a critical state plastic model of clay soil, where the loading/unloading estimations and the consideration of the stress behaviour transition from elasticity to plasticity can be bypassed by using the Fischer–Burmeister smoothing fun...

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Bibliographic Details
Published in:Computer methods in applied mechanics and engineering Vol. 390; p. 114356
Main Authors: Zhou, Xin, Lu, Dechun, Zhang, Yaning, Du, Xiuli, Rabczuk, Timon
Format: Journal Article
Language:English
Published: Amsterdam Elsevier B.V 15.02.2022
Elsevier BV
Subjects:
Algorithms
Clay soils
Computational efficiency
Computing time
Consistent tangent operator
Constitutive equations
Constitutive model integration
Constitutive relationships
Cyclic loads
Finite element method
Mathematical models
Modified Cam-clay model
Newton methods
Operators (mathematics)
Robustness (mathematics)
Smoothing
Smoothing function
Source code
Trust region method
UMAT
Modified Cam-clay model
Smoothing function
UMAT
Constitutive model integration
Consistent tangent operator
Trust region method
ISSN:0045-7825, 1879-2138
Online Access:Get full text
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Summary:This paper presents an unconstrained stress updating algorithm for a critical state plastic model of clay soil, where the loading/unloading estimations and the consideration of the stress behaviour transition from elasticity to plasticity can be bypassed by using the Fischer–Burmeister smoothing function instead of the Kuhn–Tucker complementarity conditions. A smoothing tangent operator consistent with the unconstrained stress updating strategy is derived from preserving the quadratic convergence speed for the global solution. Specifically, the relationship and difference between the consistent and continuum tangent operators are analysed from the perspectives of algebra and geometry. In addition, the nonlinear constitutive equations obtained by the backward Euler integration scheme are solved by the double dogleg trust region method (improved by non-monotonic technology), where a larger strain increment than that of the newton method is allowed for the stress updating. Then, the modified Cam-clay model for soil is implemented in ABAQUS/Standard by the proposed algorithm. The results of numerical examples show that the algorithm has significant advantages in terms of computation efficiency and robustness in contrast to the ABAQUS/Standard default integration algorithm, especially for the condition of large load increments and cyclic loadings. More than twice the computational efficiency of the ABAQUS/Standard default integration algorithm can be observed in the representative numerical examples. The source code of the proposed algorithm is freely available at https://github.com/zhouxin615/NMTR_Method. •Non-smoothness of MCC model is eliminated by unconstrained stress updating strategy.•Implicit integration equations is solved by non-monotonic region method.•Smoothing consistent tangent operator is derived.•Convergence of proposed algorithm is superior to that of ABAQUS algorithm.
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ISSN:0045-7825
1879-2138
DOI:10.1016/j.cma.2021.114356