Efficient algorithm for 3D bimodulus structures

• Published in: Acta mechanica Sinica Vol. 36; no. 1; pp. 143 - 159
• Main Authors: Pan, Qinxue, Zheng, Jianlong, Wen, Pihua
• Format: Journal Article
• Language: English
• Published: Beijing The Chinese Society of Theoretical and Applied Mechanics; Institute of Mechanics, Chinese Academy of Sciences 01.02.2020; Springer Nature B.V
• Edition: English 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
• DOI: 10.1007/s10409-019-00909-3
• ISSN: 0567-7718

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.