Algorithmic tangent modulus at finite strains based on multiplicative decomposition

• Published in: Applied mathematics and mechanics Vol. 35; no. 3; pp. 345 - 358
• Main Author: 李朝君 冯吉利
• Format: Journal Article
• Language: English
• Published: Heidelberg Shanghai University 01.03.2014; State Key Laboratory for Geomechanics and Deep Underground Engineering, Beijing 100083, P.R.China; School of Mechanics and Civil Engineering, China University of Mining and Technology(Beijing), Beijing 100083, P.R.China
• Subjects: algorithmic; Algorithms; Applications of Mathematics; Classical Mechanics; Decomposition; Elastoplasticity; expression;finite; Fluid- and Aerodynamics; Mathematical analysis; Mathematical Modeling and Industrial Mathematics; Mathematical models; Mathematics; Mathematics and Statistics; modulus;matrix; Nonlinearity; Partial Differential Equations; Strain; strain;multiplicative; tangent; Tangent modulus; algorithmic tangent modulus; O344.1; matrix expression; 74B20; finite strain; multiplicative decomposition
• ISSN: 0253-4827; 1573-2754
• DOI: 10.1007/s10483-014-1795-6

The algorithmic tangent modulus at finite strains in current configuration plays an important role in the nonlinear finite element method. In this work, the exact tensorial forms of the algorithmic tangent modulus at finite strains are derived in the principal space and their corresponding matrix expressions are also presented. The algorithmic tangent modulus consists of two terms. The first term depends on a specific yield surface, while the second term is independent of the specific yield surface. The elastoplastic matrix in the principal space associated with the specific yield surface is derived by the logarithmic strains in terms of the local multiplicative decomposition. The Drucker-Prager yield function of elastoplastic material is used as a numerical example to verify the present algorithmic tangent modulus at finite strains.