This study explores the role that the microstructure plays in determining the macroscopic static response of porous elastic continua and exposes the occurrence of position-dependent nonlocal effects that are strictly correlated to the configuration of the microstructure. Then, a nonlocal continuum theory based on variable-order fractional calculus is developed in order to accurately capture the complex spatially distributed nonlocal response. The remarkable potential of the fractional approach is illustrated by simulating the nonlinear thermoelastic response of porous beams. The performance, evaluated both in terms of accuracy and computational efficiency, is directly contrasted with high-fidelity finite element models that fully resolve the pores’ geometry. Results indicate that the reduced-order representation of the porous microstructure, captured by the synthetic variable-order parameter, offers a robust and accurate representation of the multiscale material architecture that largely outperforms classical approaches based on the concept of average porosity.

本研究探讨了微观结构在确定多孔弹性连续体的宏观静态响应中所起的作用，并揭示了与微观结构的配置密切相关的位置相关非局部效应的发生。然后，发展了一种基于变阶分数阶微积分的非局部连续统理论，以准确捕捉复杂的空间分布非局部响应。通过模拟多孔梁的非线性热弹性响应来说明分数方法的显着潜力。从精度和计算效率两方面评估的性能与完全解析孔隙几何形状的高保真有限元模型直接对比。结果表明，多孔微结构的降阶表示，