On the variational foundations of assumed strain methods. (English) Zbl 0592.73019

Simo, J. C.; Hughes, T. J. R.

J. Appl. Mech. 53, 51-54 (1986).

Summary: So-called assumed strain methods are based on the a-priori assumption of an interpolation for the discrete gradient operator, not necessarily derivable from the displacement interpolation. It is shown that this class of methods falls within the class of variational methods based on the Hu-Washizu principle. The essential point of this equivalence lies in the statement of the appropriate stress recovery procedure compatible with this variational structure. It is noted that most currently existing assumed strain methods fail to perform the stress recovery in a manner consistent with the variational structure discussed herein. Application is made to recently proposed methods such as mode decomposition techniques.

MSC:

74S30

Other numerical methods in solid mechanics (MSC2010)

Keywords:

assumed strain methods; a-priori assumption; interpolation; discrete gradient operator; Hu-Washizu principle; appropriate stress recovery procedure