Global sensitivity analysis of Rayleigh wave propagation in functionally graded skin tissue: A fractional three-phase lag thermo-viscoelastic model

Abstract

The paper develops a complete fractional three-phase lag thermo-viscoelastic model in order to investigate Rayleigh wave propagation in the functionally graded human skin tissue. The proposed framework combines nonlocal elasticity, fractional memory effects, and depth-dependent material gradation-a key lacuna in the integration of multi-physics into biological wave modeling. Furthermore, it conducts the GSA using the variance-based Sobol method to quantify the influence of primary parameters, namely elastic nonlocality (ϵ1), thermal nonlocality ϵ2, fractional order (α), gradation parameter α*, phase lags τq,τT,τv, and hydrostatic stress (P) on phase velocity, attenuation, penetration depth, and specific heat loss. All phase velocities are normalized by a reference speed c0=10m/s (typical for skin) to present dimensionless results; the corresponding physical values lie in the range 100−1000m/s, consistent with elastography measurements. Results have demonstrated that wave characteristics are mainly controlled by thermal nonlocality ϵ2 with respect to heat loss, the fractional order (α) for penetration depth, while elastic nonlocality ϵ1 for phase velocity, and attenuation is the result of very complex synergistic interactions of all parameters. Herein, GSA provides a sound hierarchy for model simplification and parameter prioritization, providing needed insight into optimizing diagnostic elastography and thermal therapies in clinical applications.