An improved return-map stress update algorithm for finite deformation analysis of general isotropic elastoplastic geomaterials

• Published in: International journal for numerical and analytical methods in geomechanics Vol. 38; no. 6; pp. 636 - 660
• Main Authors: Huang, Junjie, Peng, Qi, Chen, Ming-Xiang
• Format: Journal Article
• Language: English
• Published: Chichester Blackwell Publishing Ltd 25.04.2014; Wiley; Wiley Subscription Services, Inc
• Subjects: Algorithms; Applied sciences; Buildings. Public works; constitutive equations; Constitutive relationships; Decomposition; Elastoplasticity; Exact sciences and technology; finite strain elastoplasticity; geomechanics; Geotechnics; Mapping; Mathematical analysis; Mathematical models; return mapping algorithm; Soil investigations. Testing; Soil mechanics. Rocks mechanics; Strain; Strength of materials (elasticity, plasticity, buckling, etc.); stress-point integration; Structural analysis. Stresses; tensor function representation theorem; Tensors; Constitutive equation; Stress analysis; Slope stability; Mapping; Finite strain; Algorithm; Modeling; geomechanics; Finite element method; constitutive equations; return mapping algorithm; tensor function representation theorem; Elastoplasticity; Example; finite strain elastoplasticity; Numerical simulation; stress-point integration; Application; Isotropic material; Geomaterial
• ISSN: 0363-9061; 1096-9853; 1096-9853
• DOI: 10.1002/nag.2244

SUMMARY This paper develops a novel return mapping algorithm for the numerical integration of general isotropic finite strain elastoplastic constitutive models for geomaterials. The constitutive formulation is founded on multiplicative decomposition of the deformation gradient. The logarithmic strain measure as well as the exponential approximation of the plastic flow rule is utilized to restore the standard infinitesimal format return mapping algorithm. Central to the algorithm is the exploitation of a set of three mutually orthogonal unit base tensors for the representation of constitutive relations and the corresponding integration of the rate form of the constitutive equations. The base tensors constitute a local cylindrical coordinate system in the principal space, which allows to formulate the return mapping algorithm in the three‐dimensional space and reduce the dimension of the problem to be analyzed from six down to three. With the proposed approach, direct determination of the principal axes and the transformation procedure between the general space and the principal space, as required in traditional spectral decomposition, are avoided. Furthermore, the matrices that are involved in the inversion evaluation take simple forms, leading to extremely easy inverse computation. As a result, the consistent tangent operator can be streamlined into a form simpler and more compact than those by conventional integration methods. Following the formulation of the integration procedure, a numerical experiment is performed to assess the accuracy and efficiency of the proposed algorithm. Copyright © 2014 John Wiley & Sons, Ltd.