Dynamic effective properties of matrix composite materials with high volume concentrations of particles

A new approach is proposed to investigate the propagation of a plane compressional wave in matrix composite materials with high volume concentrations of particles. The theory of quasicrystalline approximation and Waterman’s T matrix formalism are employed to treat the multiple scattering resulting from the particles in composites. The addition theorem for spherical Bessel functions is used to accomplish the translation between different coordinate systems. The Percus–Yevick correlation function widely applied in the molecular theory of liquids is employed to analyze the interaction of the densely distributed particles. The analytical expression for the Percus–Yevick correlation function is also given. The closed form solution for the effective propagation constant is obtained in the low frequency limit. Only numerical solutions are obtained at higher frequencies. Numerical examples show that the phase velocities in the composite materials with low volume concentration are in good agreement with those in previous literatures. The effects of the incident wave number, the volume fraction and the material properties of the particles and matrix on the phase velocity are also examined.     

Constitutive modeling of isotropic hyperelastic materials in an exponential framework using a self-contained approach

In this paper, an exponential framework for strain energy density functions of elastomers and soft biological tissues is proposed. Based on this framework and using a self-contained approach that is different from a guesswork or combination viewpoint, a set strain energy density functions in terms of the first and second strain invariants is rebuilt. Among the constructed options for strain energy density, a new exponential and mathematically justified model is examined. This model benefits from the existence of second strain invariant, simplicity, stability of parameters, and the state of being accurate. This model can capture strain softening, strain hardening and is able to differentiate between various deformation-state dependent responses of elastomers and soft tissues undergoing finite deformation. The model has two material parameters and the mathematical formulation is simple to render the possibility of numerical implementations. In order to investigate the appropriateness of the proposed model in comparison to other hyperelastic models, several experimental data for incompressible isotropic materials (elastomers) such as VHB 4905 (polyacrylate rubber), two various silicone rubbers, synthetic rubber neoprene, two different natural rubbers, b186 rubber (a carbon black-filled rubber), Yeoh vulcanizate rubber, and finally porcine liver tissue (a very soft biological tissue) are examined. The results demonstrate that the proposed model provides an acceptable prediction of the behavior of elastomers and soft tissues under large deformation for different applied loading states.