The numerical manifold method for transient moisture diffusion in 2D functionally graded materials

A Unified Analogy-Based Computation Methodology From Elasticity to Electromagnetic-Chemical-Thermal Fields and a Concept of Multifield Sensing

“…1, i.e. electric potential φ ↔ magnetic potential ϕ ↔ temperature T (41) electrical flux i e ↔ magnetic flux i m ↔ heat flux q (42) permittivity ϖ 0 ↔ permeability μ 0 ↔ conductivity k 0 (43) free charge density ρ f ↔ heat source q 0 (44)…”

“…Actually, the concept analogy across mechanical field, thermal, and electric/magnetic fields can be dated back to how the related theories were developed, from Einstein who imagined a "flow" of electric charge or heat in analogy to a mechanical force [41], from Fourier's law for heat conduction and Ohm's law for electricity, which were primarily inspired by Newton's law of cooling, especially from Thompson [42], who derived the concepts of different physical fields from their mathematical analogy. The thought of analogy, for example, between heat flow and mass diffusion, has to enable the use of the solution methods for thermal or thermomechanical systems to analyze diffusion, poroelastic, or chemo-mechanical problems, among them are the numerical manifold method for transient moisture diffusion in graded materials [43] in analogy to the corresponding transient thermal analysis [26], the equivalent inclusion method for frictional heating in inhomogeneous half-spaces [29] in analogy to the corresponding inclusion problem in elasticity [44], the unified solution approach for poroelasticity and thermoelasticity [45,46], the prediction method for the conversion between a thermal-energy flow and a mass transport [47], the analogy between the shear stress in a twisted bar and a stretched soap film [48], and the analogy on material properties among electric, elastic, and piezoelectric parameters [49]. These investigations have intensively explored different facets of the MEMCT fields by analogies of their characters, but still involve resolving and re-deriving the field equations of the material systems under consideration.…”

Corrosion Enhancement for FGM Coolant Pipes Subjected to High-Temperature and Hydrostatic Pressure

“…The FGM mixture is based on the linear rule of mixture method [25][26][27]; the vo mixture for two-phase materials can be described as below, Vm: First-phase volume fraction, Vc: second-phase volume fraction, dG: distanc non-negative real numbers. Accordingly, the initial concentration and diffusion c cient can be taken as [25,26],…”

“…The FGM mixture is based on the linear rule of mixture method [25][26][27]; the volume mixture for two-phase materials can be described as below,…”

“…V m : First-phase volume fraction, V c : second-phase volume fraction, d G : distance, N: non-negative real numbers. Accordingly, the initial concentration and diffusion coefficient can be taken as [25,26],…”