Affine and non-affine microsphere models for chain scission in polydisperse elastomer networks

摘要

Under mechanical loading, elastomers undergo discrete chain rupture events in their network architecture which collectively contribute to macroscale failure. This phenomenon is expected to have a significant influence due to the polydispersity of elastomer networks, which occurs naturally due to the probabilistic nature of the chain polymerization process. To study the deterioration of the network due to polydispersity under loading, a set of micromechanically motivated constitutive models are developed. At the chain level, an extensible inverse Langevin model is utilized, accounting for the internal energy due to stretching of Kuhn segments. Further, chain scission is introduced following an energetic criterion for bond rupture. To obtain the macroscale response, affine and non-affine microsphere models are developed incorporating the effects of chain scission through a microscopic chain damage variable. Utilizing the microsphere for homogenization purposes allows for the connection of anisotropic microscale damage to the effective macroscopic response. The theory allowing for rupture of chains is first applied to an affine microsphere model where two variants are considered, assuming equal force and equal strain load sharing. A non-affine microsphere model is then subsequently developed that takes chain rupture into account. Interestingly, the resulting non-affine formulation, specialized for the monodisperse case in the absence of damage, is identical to the maximal advance path theory by Tkachuk and Linder (2012) despite the different assumptions in the development of each model. Through numerical simulations of uniaxial tension tests, the stress-stretch response and concurrent damage evolution are studied. The impact of microsphere quadrature order and chain damage evolution on stability is also studied. Stereographic projections of the microsphere visually display chain deformation and damage behavior as a function of load level and constitutive model assumptions.