A model of finite strain viscoplasticity based on unified constitutive equations. Theoretical and computational considerations with applications to shells

✍ Scribed by Carlo Sansour; Werner Wagner

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 727 KB
• Volume: 191
• Category: Article
• ISSN: 0045-7825
• DOI: 10.1016/s0045-7825(01)00282-1

✦ Synopsis

A model of multiplicative ®nite strain viscoplasticity is developed. Hereby the elastic internal potential is assumed to depend quadratically on the elastic strain measure C e by means of corresponding invariants. Hence, possible extension of the model to take anisotropy into account is straightforward. The evolution equation of the uni®ed type due to Bodner and Partom [ASME J. Appl. Mech. 42 (1975) 385] are modi®ed so as to ®t into the framework adopted. The numerical treatment of the problem is fully developed. Speci®cally, the algorithmic aspects of the resulting non-additive structure are intensively discussed. Hereby, the treatment of the exponential map of a non-symmetric argument is of a central importance. Two consistent methods are developed. Various applications to shell problems are considered. Hereby, a shell theory with seven degrees of freedom together with a 4-node enhanced strain ®nite element formulation are used. A central feature of the shell formulation is its eligibility to the application of a three-dimensional constitutive law.