Modeling micro-inertia in composite materials subjected to dynamic loading

A continuum model including micro-inertia for heterogeneous materials under high rate loading is proposed using the micromechanics method. The macro-strain and stress are defined as the volume averages of the strain and stress fields in the representative volume element (RVE). The macro equation of motion is derived by Hamilton's principle in which the macro strain energy density and kinetic energy density contains the micro-inertia terms.; The present model is used to study wave propagation in layered media. Using a simple linear displacement field for the RVE, the dispersion curve obtained from the present model agrees very well with the exact solutions for longitudinal and transverse waves propagating normal to the layers for a range of wavelengths. Similar results are obtained when the model is applied to investigate waves propagation in fiber reinforced composite materials.; As practical applications, the present model was also applied to simulate the dynamic responses of layered media and fiber reinforced composites under triangular and step stress loadings. The results of the present model and a finely-meshed finite element model in ABAQUS code agree very well. As a comparison, the effective modulus theory is also used to perform the analysis of the same problems. The effective modulus theory is much less accurate in predicting the results than the present model, especially when loading duration is short.; Finally, the dynamic micromechanics method proposed in this work was applied to viscous media. It was shown that the proposed model can properly describe the dynamic behavior in layered media of viscous materials.