Micro-sphere based viscoplastic constitutive model for uncured green rubber

Abstract

Uncured rubber exhibits strong viscoplastic flow without a distinct yield point accompanied by hardening. Classical hyperelastic models developed for crosslinked rubber do not apply to uncured rubber due to the lack of crosslinks which endow the material its elasticity. This paper presents a new constitutive model for the isothermal response of uncured green rubber. The kinematic structure of the proposed approach is based on the affine micro-sphere model. The computation of the stretch in the orientation direction follows the Cauchy-Born rule. The micro-sphere enables numerical integration over the unit sphere via finite summation over the orientation directions corresponding to the integration points over the sphere. This structure replaces the complex three-dimensional formulations of finite inelasticity based on the multiplicative split of the deformation gradient by a simpler and more attractive one-dimensional rheological representation at the orientation directions. The rheology of the model consists of two parts: (i) a part responsible for the rate-independent reponse and (ii) a part responsible for the rate-dependent response, respectively. The first branch consists of a spring connected to a modified Kelvin element, where the latter spring models the kinematic hardening. The dashpot describes a time-independent endochronic flow rule based solely on the deformation history. The second branch consists of a spring connected to a Maxwell element in parallel to a dashpot. The two dashpots in the latter branch model the ground-state viscoelasticity and rate-dependent hardening phenomenon. Albeit its apparent complexity, the proposed rheology and its numerical implementation are straightforward. The proposed model shows favorable results suitable for large scale finite element based simulations for forming process of uncured rubber components.