A peridynamic framework and simulation of non-Fourier and nonlocal heat conduction

Non-Fourier and nonlocal heat conduction phenomena have been observed in many cases in modern industry. They have been modeled by differential equations with phase lags or by Fourier-type integral formulation. This paper presents a peridynamic non-Fourier heat conduction model to consider the non-Fourier and nonlocal effects simultaneously. The model is formulated in the framework of generalized state-based peridynamics (PD) by introducing the concept of dual phase lags (DPL) into the peridynamic framework, and is thus referred to as the PD-DPL model. The model is not only suitable for transient heat conduction from nano- to macro-scales, but also applicable to phase-lag diffusion in other fields. Numerical procedures are presented for solving the resulted equation, and the results for examples are in good agreement with other solutions and available experimental data. Compared with classical non-Fourier heat conduction models, the PD-DPL model can be easily applied to problems with discontinuities.