Analysis of unbalanced laminate composites with imperfect interphase: Effective properties via asymptotic homogenization method

This work addresses the Asymptotic Homogenization Method (AHM) to find all the non-zero independent constants of the fourth-order elasticity tensor of a theoretically infinite periodically laminated composite. The concept of Unit Cell describes the domain, comprised of two orthotropic composite plies separated by an isotropic interphase. A general case with an unbalanced composite is considered. Thus, the coupled components of the tensor are expected. Both analytical and numerical solutions are derived. In addition, an interphase degradation model is proposed to evaluate its effect on the effective properties of the media. Two different stacking sequences are considered with five degrees of interphase imperfection each. The results show good agreement between the analytical and numerical solutions. In addition, it is clear that the more imperfect the interphase is, the more affected the effective properties of the media are, especially those dependent on the stacking direction.

Analytical external spherical solutions in entangled relativity

In this manuscript, we present analytical external spherical solutions of entangled relativity, which we compare to numerical solutions obtained in a Tolman–Oppenheimer–Volkoff framework. Analytical and numerical solutions match perfectly well outside spherical compact objects, therefore validating both types of solutions at the same time. The analytical external (hairy) solutions – which depend on two parameters only – may be used in order to easily compute observables – such as X-ray pulse profiles – without having to rely on an unknown equation of state for matter inside the compact object.

Heat Transfer Process with Solid-solid Interface: Analytical and Numerical Solutions

This work is aimed at the study and analysis of the heat transport on a metal bar of length L with a solid-solid interface. The process is assumed to be developed along one direction, across two homogeneous and isotropic materials. Analytical and numerical solutions are obtained under continuity conditions at the interface, that is a perfect assembly. The lateral side is assumed to be isolated and a constant thermal source is located at the left-boundary while the right-end stays free allowing the heat to transfer to the surrounding fluid by a convective process. The differences between the analytic solution and temperature measurements at any point on the right would indicate the presence of discontinuities. The greater these differences, the greater the discontinuity in the interface due to thermal resistances, providing a measure of its propagation from the interface and they could be modeled as temperature perturbations. The problem of interest may be described by a parabolic equation with initial, interface and boundary conditions, where the thermal properties, the conductivity and diffusivity coefficients, are piecewise constant functions. The analytic solution is derived by using Fourier methods. Special attention is given to the Sturm-Liouville problem that arises when deriving the solution, since a complicated eigenvalue equation must to be solved. Numerical simulations are conducted by using finite difference schemes where its convergence and stability properties are discussed along with physical interpretations of the results.