Efficient algorithm for 3D bimodulus structures

The bimodulus material is a classical model to describe the elastic behavior of materials with tension–compression asymmetry. Due to the inherently nonlinear properties of bimodular materials, traditional iteration methods suffer from low convergence efficiency and poor adaptability for large-scale...

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Bibliographic Details
Published inActa mechanica Sinica Vol. 36; no. 1; pp. 143 - 159
Main Authors Pan, Qinxue, Zheng, Jianlong, Wen, Pihua
Format Journal Article
LanguageEnglish
Published Beijing The Chinese Society of Theoretical and Applied Mechanics; Institute of Mechanics, Chinese Academy of Sciences 01.02.2020
Springer Nature B.V
EditionEnglish ed.
Subjects
Algorithms
Classical and Continuum Physics
Computational Intelligence
Computer simulation
Constitutive equations
Constitutive relationships
Convergence
Elasticity
Engineering
Engineering Fluid Dynamics
Error analysis
Finite element method
Iterative methods
Numerical analysis
Research Paper
Shear modulus
Stability analysis
Theoretical and Applied Mechanics
Finite element method
3D complemented algorithm
Elastic theory
Generalized elastic law
General 3D shear modulus
Bimodulus material
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Summary:The bimodulus material is a classical model to describe the elastic behavior of materials with tension–compression asymmetry. Due to the inherently nonlinear properties of bimodular materials, traditional iteration methods suffer from low convergence efficiency and poor adaptability for large-scale structures in engineering. In this paper, a novel 3D algorithm is established by complementing the three shear moduli of the constitutive equation in principal stress coordinates. In contrast to the existing 3D shear modulus constructed based on experience, in this paper the shear modulus is derived theoretically through a limit process. Then, a theoretically self-consistent complemented algorithm is established and implemented in ABAQUS via UMAT; its good stability and convergence efficiency are verified by using benchmark examples. Numerical analysis shows that the calculation error for bimodulus structures using the traditional linear elastic theory is large, which is not in line with reality.
ISSN:0567-7718
1614-3116
DOI:10.1007/s10409-019-00909-3