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.