George S. Whitby Award for Distinguished Teaching and Research - A Constitutive Tube Model of Rubber Elasticity: The Path from Polymer Network to the Rubber Component

The presentation introduces briefly into the rigorous (non-Gibbsian) molecular-statistical scenario for developing a theory of polymer networks with fixed topological constraints like permanent crosslinks and trapped entanglements (S. F. Edwards et al.). The specific features of mean-field approximations in the frame of a model of tube-like constraints of network chain conformations in stretched rubbers will be briefly explained (Heinrich, Straube et al.). Extensions of the model include the presence of reinforcing fillers and the effects of limited network chain extension (Vilgis, Heinrich). The so derived materials law of rubber elasticity is suitable for implementation into a finite element code (Kaliske, Heinrich). It is considered presently as one of the most powerful constitutive material law for rubbers (Verron et al.), and it is even of physical nature. Further extensions of this model include very specific details of nature and morphology of the fillers within the rubber matrix (Klüppel et al.).

Several examples will show applications of the material law with respect to large scale and FE directed modelling of rubber parts like engine mounts, sealings etc. (Kaliske et al; Freund, Ihlemann, Lorenz, Juhre, Klüppel). Very recent applications are related to the evaluation of crack propagation in rubber parts using the J-integral concept (Lombardi et al.).

The presented approach to solely physically based rubber material laws and their subsequent treatment and application can be considered as the only multi-scale approach that comprises consequently the route from statistical polymer mechanics via continuum mechanics to FE modeling, or in other words, from polymer network molecules to rubber parts.

An outlook discusses the present efforts to incorporate into the prevailing concept the time dependent viscoelasticity of rubber materials.