Thermodynamics of fractional-order nonlocal continua and its application to the thermoelastic response of beams

This study presents a comprehensive framework for constitutive modeling of frame-invariant fractional-order approach to nonlocal thermoelasticity in solids. For this purpose, thermodynamic and mechanical balance laws are derived solids modeled using the continuum theory. includes revisiting Cauchy’s hypothesis surface traction vector order account long-range interactions across domain solid. Remarkably, it is shown that model allows rigorous localized application principles unlike existing integral approaches elasticity. Further, governing equations motion obtained here consistent with results from variational principles. These involve self-adjoint operators admit unique solutions, contrast analogous studies following local hypothesis. To illustrate efficacy framework, case-studies linear geometrically nonlinear responses beams subject combined thermomechanical loads considered here. Comparisons integer-order highlight softening response structures predicted by irrespective boundary loading conditions. latter aspect addresses an important incongruence often observed strain-based