On the volumetric part of strain-energy functions used in the constitutive modeling of slightly compressible solid rubbers

✍ Scribed by Cornelius O. Horgan; Jeremiah G. Murphy

• Book ID: 104018400
• Publisher: Elsevier Science
• Year: 2009
• Tongue: English
• Weight: 352 KB
• Volume: 46
• Category: Article
• ISSN: 0020-7683
• DOI: 10.1016/j.ijsolstr.2009.04.007

✦ Synopsis

A popular model for the finite element simulation of slightly compressible solid rubber-like materials assumes that the strain-energy function can be additively decomposed into a volumetric part and a deviatoric part. Based on mathematical convenience, the volumetric part is usually assumed to be a finite polynomial in the volume change. Experimental evidence suggests that for solid rubbers in compression, this polynomial can be taken to be a simple quadratic for moderate deformations and that this function also adequately models the volume change and the stress/stretch relation for materials in simple tension, up to stretches of order 100%. For larger tensile deformations, however, experimental data suggest that the Cauchy stress-volume change relation has an increasingly large slope and therefore a truncated Taylor series expansion is not the most appropriate. A rational function approach is proposed here as an alternative.