Algorithms for computation of stresses and elasticity moduli in terms of Seth-Hill's family of generalized strain tensors

Communications in Numerical Methods in Engineering

Volumn 17, Issue 5, 2001, Pages 337-353

  Miehe, Christian ^a   Lambrecht, Matthias ^a  

^a UNIVERSITY OF STUTTGART   (Germany)

Author keywords

Finite elasticity; Generalized strain measures; Isotropic tensor functions; Spectral decompositions

Indexed keywords

COMPUTATIONAL METHODS; EIGENVALUES AND EIGENFUNCTIONS; ELASTIC MODULI; ELASTICITY; FUNCTIONS; STRAIN; STRESSES; TENSORS;

CAUCHY-GREEN TENSOR;

ALGORITHMS;

STRESS;

EID: 0035337267     PISSN: 10698299     EISSN: None     Source Type: Journal    
DOI: 10.1002/cnm.404     Document Type: Article

References (19)

1. Seth BR. Generalized strain measure with application to physical problems. In: Second-Order Effects in Elasticity, Plasticity and Fluid Dynamics, Reiner M, Abir D (eds). Pergamon Press: Oxford, 1964; 162-172.
2. Hill R. On constitutive inequalities for simple materials - I. Journal of the Mechanics and Physics of Solids 1968; 16:229-242.
3. Ogden RW. Non-Linear Elastic Deformations. Ellis Horwood: Chichester, 1984.
4. Šilhavý M. The Mechanics and Thermodynamics of Continuous Media. Springer: Berlin, 1997.
5. Bowen RM, Wang C-C. Acceleration waves in inhomogeneous isotropic elastic bodies. Archive of Rational Mechanics and Analysis 1970; 38:13-45 with Corrigendum in vol. 40, 403.
6. Chadwick P, Ogden RW. A theorem of tensor calculus and its application to isotropic elasticity. Archive of Rational Mechanics and Analysis 1971b; 44:54-68.
7. Miehe C. Computation of isotropic tensor functions. Communications in Numerical Methods in Engineering 1993; 9:889-896.
8. Miehe C. Comparison of two algorithms for the computation of fourth-order isotropic tensor functions. Computers and Structures 1998; 66:37-43.
9. Miehe C. Aspects of the formulation and finite element implementation of large strain isotropic elasticity. International Journal for Numerical Methods in Engineering 1994; 37:1981-2004.
10. Papadopoulos P, Lu J. A general framework for the numerical solution of problems in finite elasto-plasticity. Computer Methods in Applied Mechanics and Engineering 1998; 159:1-18.
11. Perić D, Owen DRJ, Honnor ME. A model of finite strain elasto-plasticity based on logarithmic strains: computational issues. Computer Methods in Applied Mechanics and Engineering 1992; 94:35-61.
12. Cuitiño AM, Ortiz M. A material-independent method for extending stress update algorithms from small-strain plasticity to finite plasticity with multiplicative kinematics. Engineering Computations 1992; 437-451.
13. Simó, JC. Algorithms for static and dynamic multiplicative plasticity that preserve the classical return mapping schemes of the infinitesimal theory. Computer Methods in Applied Mechanics and Engineering 1992; 99: 61-112.
14. Miehe C, Stein E. A canonical model of multiplicative elastoplasticity: formulation and aspects of the numerical implementation. European Journal of Mechanics, A/Solids 1992; 11:25-43.
15. Miehe C. A formulation of finite elastoplasticity based on dual co- and contra-variant eigenvector triads normalized with respect to a plastic metric. Computer Methods in Applied Mechanics and Engineering 1998; 159:223-260.
16. Ball JM. Convexity conditions and existence theorems in nonlinear elasticity. Archive of Rational Mechanics and Analysis 1977; 63:337-403.
17. Ciarlet PG. Mathematical elasticity. Elsevier Science Publishers B.V.: Amsterdam, 1988.
18. Simó JC, Taylor RL. Quasi-incompressible finite elasticity in principal stretches. Continuum basis and numerical algorithms. Computer Methods in Applied Mechanics and Engineering 1991; 85:273-310.
19. Meyers A, Schiesse P, Bruhns TO. Some comments on objective rates of symmetric Eulerian tensors with application to Eulerian strain rates. Acta Mechanica 2000; 139:91-103.