Couple-stress thermoelasticity of three-dimensional multilayered composites

Abstract

This work presents a comprehensive analysis of field solutions for three-dimensional multilayered composites within the framework of the couple-stress thermoelasticity. Using double Fourier series expansion solutions, the powerful and elegant mathematical Stroh formalism is extended to include the thermal coupling with the couple-stress elasticity theory to capture small-scale microstructural effects. The size-dependent layered approach leads to concise and general eigenrelations for each homogeneous orthotropic plate, while the unconditionally stable dual-variable technique is used to propagate the extended displacement/temperature fields and force-/tangential couple-tractions through the internal interfaces of the multilayered structures. Closed-form expressions are derived for the recursive layer-to-layer relations, as well as for the temperature, heat flux, displacement, stress and couple-stress field components, with respect to simply-supported structures subjected to combined thermal and mechanical loading. Application examples, including highly anisotropic fiber-reinforced composites, show significant deviations from the classical thermoelasticity, demonstrating the critical importance of considering the microstructural characteristics of interface-dominated materials. The results result come from a series of scenarios, covering mechanical and thermomechanical loading conditions, changes in aspect ratios and stacking sequences within multilayered systems, and the consequences of varying the number of sandwich plates.