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Computational methods for inverse deformations in quasi‐incompressible finite elasticity
Author(s) -
Govindjee Sanjay,
Mihalic Paul A.
Publication year - 1998
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/(sici)1097-0207(19981115)43:5<821::aid-nme453>3.0.co;2-c
Subject(s) - compressibility , inverse , mathematics , hyperelastic material , elasticity (physics) , inverse problem , constraint (computer aided design) , finite element method , mathematical analysis , geometry , physics , structural engineering , mechanics , engineering , thermodynamics
This paper presents a formulation for incorporating quasi‐incompressibility in inverse design problems for finite elastostatics where deformed configurations and Cauchy tractions are known. In the recent paper of Govindjee and Mihalic [1996, Comput. Methods Appl. Mech. Engng. , 136 , 47–57.] a method for solving this class of inverse problems was presented for compressible materials; here we extend this work to the important case of nearly incompressible materials. A displacement‐pressure mixed formulation is combined with a penalty method to enforce the quasi‐incompressible constraint without locking. Numerical examples are presented and compared to known solutions; further examples present practical applications of this research to active problems in elastomeric component design. © 1998 John Wiley & Sons, Ltd.