Abstract
The main objective of this contribution is the development of a thermodynamically consistent and modular formulation of anisotropic multiplicative elasto-plasticity. Based on the framework of standard dissipative materials, we introduce as a key-ingredient additional symmetric arguments — typically structural tensors — into the relevant scalar-valued isotropic tensor functions. Then the fundamental covariance relation allows a set up directly in terms of spatial fields and a convenient implementation within any numerical setting.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Boehler, J. (1987). Applications of Tensor Functions in Solid Mechanics, 292, CISM Courses and Lectures, Springer.
Ericksen, J. (1960). Tensor Fields. In Flügge, S. (ed.), Encyclopedia of Physics, Springer, III/1, 794–858.
Halphen, B. and Nguyen, Q. (1975). Sur les materiaux standards generalises. Journal de Mecanique, 14, 39–62.
Haupt, P. (2000). Continuum Mechanics and Theory of Materials, Advanced Texts in Physics, Springer.
Lodge, A. (1974). Body Tensor Fields in Continuum Mechanics (With Application to Polymer Rheology), Academic Press.
Lu, J. and Papadopoulos, P. (2000). A covariant constitutive description of anisotropic non-linear elasticity. Zeit. Angew. Mat. Phys., 51, 204–217.
Marsden J. and Hughes, T. (1994). Mathematical Foundations of Elasticity, Dover.
Menzel, A. and Steinmann, P. (2000). On she spatial formulation of anisotropic hyperplasticity. Technical Report, J00–09, UKL/LTM.
Menzel, A. and Steinmann, P. (2001). On she spatial formulation of anisotropic multiplicative elasto-plasticity. Technical Report, J01–07, UKL/LTM.
Murnaghan, F. (1937). Finite deformations of an elastic solid. Am. J. Math., 59, 235–260.
Simo, J. and Miehe, C. (1992). Associated coupled thermoplasticity at finite strains: Formulation, numerical analysis and implementation. Comp. Meth. Appl. Mech. Engr., 98, 41–104.
Spencer, A. (1984). Constitutive theory of strongly anisotropic solids. In Spencer, A. (ed) Continuum Theory of the Mechanics of Fibre-Reinforced Composites, 282, CISM Courses and Lectures, Springer.
Truesdell, C. and Noll, W. (1992). The Non-Linear Field Theories of Mechanics, Springer, 2nd edition.
Weiss, J., Maker, B. and Govindjee, S. (1996). Finite element implementation of incompressible, transversely isotropic hyperelasticity. Comp. Meth. Appl. Mech. Engr.,135, 107–128.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer Science+Business Media Dordrecht
About this paper
Cite this paper
Menzel, A., Steinmann, P. (2003). Formulation and Computation of Geometrically Nonlinear Anisotropic Inelasticity. In: Miehe, C. (eds) IUTAM Symposium on Computational Mechanics of Solid Materials at Large Strains. Solid Mechanics and Its Applications, vol 108. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-0297-3_16
Download citation
DOI: https://doi.org/10.1007/978-94-017-0297-3_16
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-6239-0
Online ISBN: 978-94-017-0297-3
eBook Packages: Springer Book Archive