Issue 48

R. Brighenti et alii, Frattura ed Integrità Strutturale, 48 (2019) 1-9; DOI: 10.3221/IGF-ESIS.48.01 3 Figure 1 : Cracked plate: main geometrical sizes and reference systems in the (a) undeformed and (b) deformed configuration. Constitutive models Constitutive models for polymers are usually defined in terms of the strain energy function ˆ  ; several models suitable for rubber-like materials have been proposed in the literature. Among them, the well-known neo-Hookean, Gent and Ogden models can be mentioned [17]. In particular, the following energy expression   r  for the deformation of a single chain is assumed by the neo-Hookean model, and the strain energy density follows the Gent model, respectively:     2 1 1 2 3 ,        ln 1 ˆ 6 2 B m m k T J E r r J J J Nb            (2) where B k is the Boltzmann constant and T the absolute temperature. Further, N is the number of Kuhn’s segments in a single polymer chain and b is their length, whereas E is the small strain Young modulus, 1 1 3 J I   is a stretch invariant, and m J is the limit value of 1 J . The energy per unit volume of the material  can be obtained from the following relationship:     Ω Ω ˆ d      r r (3)