Domain-independent thermoelastic coupling mechanism for multi-physical systems applications: a Bond Graph approach

In this paper, we propose a domain-independent nonlinear thermoelastic coupling element to enable the realization of a two-way dynamic coupling between the thermal and elastic domains. The implementation of the proposed coupling element in multi-physical systems modeling will provide reversibly conserved power transactions among the existing physical domains (thermal and elastic domains), which is a favorable demand in coupled field dynamic investigations. To guarantee a conserved and continuous power transmission between the thermal and elastic domains, by means of the Bond Graph notation, a reversible multi-dimensional storage element is designed, and the corresponding multi-dimensional constitutive equations are derived that satisfy the Maxwell reciprocity. The power network of each domain of interest is, also, represented in the Bond Graph notation, and the corresponding governing equation of each domain is extracted on the basis of physical system theory. The reversible connectivity of the thermal and elastic domains is then executed via replacing the storage elements of each of the domains with the proposed coupling element. The ensuing model will provide the thermoelastic behavior of the system from the reversible thermal and elastic domains’ energetic interactions, which preserves the fundamental physical natures of such phenomena in the model. The generated coupling element will allow the model of each physical domain to remain independent from other existing domains while they are dynamically coupled, which provides a unique benefit for multi-physical phenomena investigations.