A model for the mechanical response of composites with thermoplastic-elastomer matrices

Constitutive equations are derived for the elastic response of composites with thermoplastic-elastomer matrices at arbitrary three-dimensional deformations with finite strains. With reference to the homogenization method, a composite is thought of as an incompressible network of strands bridged by permanent junctions (filler particles and micro-domains in the crystalline or glassy states). Unlike conventional models for rubber elasticity, excluded-volume interactions between segments are taken into account. An explicit expression is developed for the strain energy density of a network of flexible chains with weak self-repellent interactions, and a phenomenological equation is suggested for the mechanically induced evolution in strength of segment interactions. The stress-strain relations involve three to four material constants that are found by matching experimental data on thermoplastic elastomers reinforced with short fibres and in situ composites with liquid-crystalline fillers. Good agreement is demonstrated between the observations and the results of numerical simulation at uniaxial tension with elongation ratios up to 1300%. It is shown that (i) adjustable parameters in the constitutive equations are affected by thermo-mechanical factors in a physically plausible way, and (ii) the model can predict the elastic response at one deformation mode when its material parameters are determined by fitting observations at another mode.