Global sensitivity analysis of MGT thermo-magneto-microstretch media with reference-scaled thermal conductivity

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This paper presents a theoretical and numerical investigation of the coupled thermo-magneto-elastic behavior of a microstretch thermoelastic half-space subjected to mechanical and magnetic loading within the Moore–Gibson–Thompson (MGT) theory of thermoelasticity. The thermal conductivity is modeled by the reference-temperature family 𝜅 = 𝜅 ⁢ ₀ ⁢ ( 1 − 𝛼 𝜅 ⁢ 𝑇 ⁢ ₀ ) , where 𝛼 𝜅 is a material parameter and 𝑇 ⁢ ₀ is the reference temperature. It is emphasized at the outset that this family assigns a constant conductivity to each realization when 𝑇 ⁢ ₀ and 𝛼 𝜅 are fixed; the model therefore belongs to the class of constant-property families rather than to evolving-temperature closures such as 𝜅 ⁡ ( 𝜃 ) = 𝜅 ⁡ ₀ ⁢ ( 1 + 𝐾 ⁢ ₁ ⁢ 𝜃 ) . The Kirchhoff transformation consequently reduces to the exact linear rescaling 𝜓 = ( 1 − 𝛼 𝜅 ⁢ 𝑇 ⁢ ₀ ) ⁢ 𝜃 , which introduces no thermal nonlinearity and does not alter the underlying material coupling constants. The governing system constitutive relations, the MGT heat-conduction equation, dimensionless field variables, normal-mode expansion, and associated boundary conditions is derived in full. The normal-mode solution is validated against four independent limiting cases: (i) 𝐻 ⁡ ₀ → 0 (non-magnetic thermo-microstretch), (ii) 𝛼 𝜅 → 0 (constant-conductivity MGT), (iii) suppression of microstretch (MGT thermoelastic half-space), and (iv) comparison with a published MGT half-space solution. A global sensitivity analysis (GSA) based on Sobol first- and total-order indices, the Morris elementary-effect method, and partial rank correlation coefficients (PRCC) is then performed on a parameter set drawn directly from the governing equations: 𝑋 = [ 𝑃 , 𝐻 ⁡ ₀ , 𝛼 𝜅 , 𝜏 ⁢ ₀ , 𝑘 ̄ , 𝜆 ⁢ ₀ , 𝛼 ⁢ ₀ ] ⁢ ᵀ . The results show that 𝛼 𝜅 dominates the response of nearly all quantities of interest, while the micropolar coupling k̄ and microstretch coupling 𝜆 ⁢ ₀ exert secondary but non-negligible influence. The magnetic parameter H₀ and the microstretch modulus α₀ have small total-order indices. The GSA is consistent with the mathematical structure of the formulation and identifies the parameters that most strongly control near-surface field amplification in MGT thermo-magneto-microstretch media.