Computational methods for inverse deformations in quasi-incompressible finite elasticity

✍ Scribed by Sanjay Govindjee; Paul A. Mihalic

• Publisher: John Wiley and Sons
• Year: 1998
• Tongue: English
• Weight: 219 KB
• Volume: 43
• Category: Article
• ISSN: 0029-5981
• DOI: 10.1002/(sici)1097-0207(19981115)43:5<821::aid-nme453>3.0.co;2-c

✦ Synopsis

This paper presents a formulation for incorporating quasi-incompressibility in inverse design problems for ÿnite elastostatics where deformed conÿgurations 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.