A simple interface is a complicated energy exchanger in nature, can a complicated logic render simple connections?
Multifield Theories and Analogy
This is a unified analogy-based computation methodology, together with a concept of multifield, multifunctional sensing, from elasticity to electromagnetic-chemical-thermal fields, via utilizing the similarities of mechanical-electromagnetic-chemical-thermal (MEMCT) field variables, governing equations, and the material properties pertaining to each individual field. Three equivalences are systemized, which are the field-formulation equivalence, surface-value equivalence, and time scale comparison. Due to similarity, a number of thermal, electromagnetic, or chemical solutions can be obtained from the direct degeneration of existing mechanical solutions by making specified equivalences, as well as by setting Poisson’s ratio to be 0.5. These specified equivalences enable quick solutions to other fields directly from mechanics formulations, such as those in the forms of the Galerkin vectors and Papkovich-Neuber potentials, and field coupling, by means of analogy. This work has demonstrated that the field solutions of a layered half-space with imperfect thermal, electromagnetic, or chemical interfaces can be readily obtained from the elastic solutions involving interfacial imperfections via the formulation equivalence. A set of simple equations are derived to relate surface behaviors of different fields via the obtained surface-value equivalence.
Related Publications
- Zhang, X. and Wang, Q., 2022, “A Unified Analogy-Based Computation Methodology from Elasticity to Electromagnetic-Chemical-Thermal Fields and a Concept of Multifield Sensing,” ASME Open Journal of Engineering, invited, Inaugural issue. https://doi.org/10.1115/1.4053910
- Wang, Q. and Zhu, D., Dec. 2019, Interfacial Mechanics, Theories and Methods for Contact and Lubrication, CRC Press, ISBN: 978-1-4398-1510-6, 978-1-1387-4890-3 Boca Raton, London, New York.
Multifield, Multifunctional Sensing
The concept of multifield sensing means to measure one surface field via monitoring the change of another, e.g., sensing the thermal field via surface normal displacement monitoring at one location, or certain locations, by means of the analogy methodology, if the sources are linearly related, and the surface-value equivalence approach. The theory of convolution further shows that no matter the surface sources are concentrated or distributed, mechanical or others, the relationship of the responses at X still obeys that for concentrated sources as long as the corresponding distribution shapes are the same. This offers a great convenience for sensing, and one sensor, one calculation, applies to all types of loading with simple parameter conversions. An application patent has been applied.
Related Publications
- Zhang, X. and Wang, Q., 2022, “A Unified Analogy-Based Computation Methodology from Elasticity to Electromagnetic-Chemical-Thermal Fields and a Concept of Multifield Sensing,” ASME Open Journal of Engineering, invited, Inaugural issue. https://doi.org/10.1115/1.4053910.
- Wang, Q. and Zhang, X., Multifield, Multifunctional Sensors, in process; Provisional application, No.: 63/296,558, January 5, 2022
Multifield Galerkin Vectors for Inhomogeneous Materials
Galerkin vectors are building blocks for elastic solutions, especially for those to inhomogeneous materials. The multifield analogy theory offers a path to obtain “Galerkin vectors” in a general sense, for building solutions to other fields of inhomogeneous materials. Several sets of “Galerkin vectors” for the temperature field of homogeneous and inhomogeneous materials have been derives, which, by analogy, are the same in expressions as those for static electromagnetic fields and chemical diffusion problems in inhomogeneous materials, directly applicable to the analysis and modeling of systems like bearings, batteries, sensors, and energy harvesters.
Related Publications
- Shi, X., Wang, L., Zhou, Q., and Wang, Q., 2018, “A Fast Approximate Method for Heat Conduction in an Inhomogeneous Half Space Subjected to Frictional Heating,” Journal of Tribology, Vol. 140 (4), 041101, https://doi.org/10.1115/1.4038953.
- Shi, X., Wang, Q., and Wang, L., 2019, “New Galerkin-Vector Theory and Efficient Numerical Method for Analyzing Steady-State Heat Conduction in Inhomogeneous Bodies Subjected to a Surface Heat Flux,” Journal of Applied Thermal Engineering, Vol. 161, 113838. https://doi.org/10.1016/j.applthermaleng.2019.113838
- Zhang, X. and Wang, Q., 2022, “A Unified Analogy-Based Computation Methodology from Elasticity to Electromagnetic-Chemical-Thermal Fields and a Concept of Multifield Sensing,” ASME Open Journal of Engineering, invited, Inaugural issue. https://doi.org/10.1115/1.4053910.