IWPDF 2019 1st International Workshop on Plasticity, Damage and Fracture of Engineering Materials, Ankara, Turkey, 22 - 23 August 2019, pp.1
Rubbery polymers are widely used in, e.g., the automotive, the aeronautical and
space industry. Rubbery polymers consist of network of long polymer chains responsible for
the elastic response and a secondary free chains superimposed to the elastic network in terms
of entanglements leading to the rate-dependent viscoelastic response. The fracture toughness
of rubbery polymers is a rate-dependent phenomenon which manifests itself in the sense of
monotonically increasing fracture toughness with rising crack velocity under tearing tests .
In order to communicate the above-mentioned phenomena, the ground state elasticity, in the
current study, is accounted by the eight-chain model of Arruda & Boyce , whereas the
superimposed viscous effects are incorporated into the model in terms of a number of
Maxwell elements . For the evolution of the viscous deformations, a new relaxation
kinetics is introduced without the multiplicative split of the deformation gradient, thereby
capturing the shear and volumetric creep deformations. As a novel aspect, local phase field
approach similar to damage mechanics formulation governs the failure of the superimposed
chains, while the degradation of the elastic network is governed by a rate-dependent phasefield
approach [4,5]. The model parameters are fitted to extant experimental data from the
literature. We, afterwards, demonstrate qualitative results of the proposed model by means of
representative numerical examples.
1. H. Dal and M. Kaliske (2009). A micro-continuum-mechanical material model for failure of
rubber-like materials: Application to aging induced fracturing, J. Mech. Phys. Solids, Vol. 57,
2. E. M. Arruda. and M.C. Boyce (1993). A three-dimensional model for the large stretch
behavior of rubber elastic materials. J. Mech. Phys. Solids, 41(2), pp. 389–412.
3. H. Dal and M. Kaliske (2009). Bergström-Boyce model for nonlinear finite rubber
viscoelasticity: Theoretical aspects and algorithmic treatment for FE method. Comp. Mech.,
4. L. Schänzel, H. Dal and C. Miehe (2013) On the micromechanically-based approaches to
failure in polymers, Proc. Appl. Math. Mech., Vol. 13, pp. 557–560.
5. L. Schänzel , H. Dal, and C. Miehe (2013). Phase-field modeling of fracture in rubbery
polymers, Const. Models for Rubber VIII, Taylor & Francis Group, London, pp. 335–341