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<p>Classical Fourier heat conduction and local elasticity theories are inadequate for capturing microstructural interactions and delayed thermal responses in porous materials, often leading to inaccurate predictions of thermoelastic dynamic behavior. This study develops a unified thermoelastic model for an infinite medium containing a cylindrical cavity by synthesizing three established theoretical frameworks: nonlocal elasticity of Klein-Gordon type, higher-order dual-phase-lag heat conduction, and Nunziato-Cowin void theory. The original contribution lies in the novel combination of these frameworks and their application to the cylindrical cavity geometry, enabling a systematic investigation of the coupled effects of nonlocality, thermal relaxation, and void dynamics. Eringen’s nonlocal elasticity is generalized via a Klein–Gordon-type (KG-type) spatiotemporal convolution, while stress, strain, and heat flux are expressed as memory-dependent integrals using the Boltzmann superposition principle, effectively representing long-range forces and finite thermal relaxation times. The coupled governing equations for voided thermoelastic media are derived and solved analytically for transient radial vibrations induced by harmonic thermal loading on the cavity surface. Employing Laplace transforms with exact time-domain inversion, the dynamic responses of radial displacement, stresses, temperature change, and void volume fraction are investigated. Numerical results demonstrate that smaller void sizes and higher pore density substantially attenuate vibration amplitudes and thermal disturbances, highlighting enhanced intrinsic damping and improved thermal diffusion. Nonlocal effects reduce effective structural stiffness and lower resonance frequencies, whereas higher-order phase lags in the DPL model promote slower thermal wave propagation and reduced stress magnitudes. This work presents a unified formulation that systematically couples nonlocal KG elasticity, higher-order DPL heat conduction, and void dynamics in a cylindrical configuration, extending the void-coupled thermoelastic models previously analyzed for cylindrical cavities by Sharma et al. [<CitationRef CitationID="CR49">49</CitationRef>] and others. The results emphasize the beneficial influence of microscale porosity in suppressing thermoelastic vibrations and increasing thermal shock resistance, with direct implications for the design of aerospace thermal protection systems, lightweight composite cylindrical structures, microelectronic packaging, biomedical porous implants, and energy-absorbing materials. The proposed model offers a robust predictive framework for optimizing the thermomechanical performance of advanced porous materials in engineering applications.</p>

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Thermoelastic response of a porous medium with a cylindrical cavity using Klein–Gordon nonlocal elasticity and a higher-order dual-phase-lag heat conduction model

  • 期刊论文

  • 发表日期：

    2026年5月18日

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  • Salman S. Alsaeed,
  • Nahar F. Alshammari

摘要

Classical Fourier heat conduction and local elasticity theories are inadequate for capturing microstructural interactions and delayed thermal responses in porous materials, often leading to inaccurate predictions of thermoelastic dynamic behavior. This study develops a unified thermoelastic model for an infinite medium containing a cylindrical cavity by synthesizing three established theoretical frameworks: nonlocal elasticity of Klein-Gordon type, higher-order dual-phase-lag heat conduction, and Nunziato-Cowin void theory. The original contribution lies in the novel combination of these frameworks and their application to the cylindrical cavity geometry, enabling a systematic investigation of the coupled effects of nonlocality, thermal relaxation, and void dynamics. Eringen’s nonlocal elasticity is generalized via a Klein–Gordon-type (KG-type) spatiotemporal convolution, while stress, strain, and heat flux are expressed as memory-dependent integrals using the Boltzmann superposition principle, effectively representing long-range forces and finite thermal relaxation times. The coupled governing equations for voided thermoelastic media are derived and solved analytically for transient radial vibrations induced by harmonic thermal loading on the cavity surface. Employing Laplace transforms with exact time-domain inversion, the dynamic responses of radial displacement, stresses, temperature change, and void volume fraction are investigated. Numerical results demonstrate that smaller void sizes and higher pore density substantially attenuate vibration amplitudes and thermal disturbances, highlighting enhanced intrinsic damping and improved thermal diffusion. Nonlocal effects reduce effective structural stiffness and lower resonance frequencies, whereas higher-order phase lags in the DPL model promote slower thermal wave propagation and reduced stress magnitudes. This work presents a unified formulation that systematically couples nonlocal KG elasticity, higher-order DPL heat conduction, and void dynamics in a cylindrical configuration, extending the void-coupled thermoelastic models previously analyzed for cylindrical cavities by Sharma et al. [49] and others. The results emphasize the beneficial influence of microscale porosity in suppressing thermoelastic vibrations and increasing thermal shock resistance, with direct implications for the design of aerospace thermal protection systems, lightweight composite cylindrical structures, microelectronic packaging, biomedical porous implants, and energy-absorbing materials. The proposed model offers a robust predictive framework for optimizing the thermomechanical performance of advanced porous materials in engineering applications.