Static behavior of power-law coated porous functionally graded metal foam shells

The advancement of theoretical research faces numerous challenges, particularly when it comes to modeling structures, in contrast to the experimental investigation of the mechanical behavior of complex systems. Metal foams are advanced composite materials with high porosity, low weight, and excellent thermal conductivity, making them essential for applications in thermal management, filtration, catalysis, and energy storage. The study addresses the challenges in theoretical research related to modeling complex structures, presenting a more accurate approach by incorporating nonclassical mechanics. It introduces a novel method for modeling tri-directionally coated porous structures with varying microstructures, accounting for intrinsic characteristic lengths and spatial variations in material properties. The study focuses on the static behavior of multidirectionally functionally graded porous metal foam shells, utilizing modified higher-order shear deformation theory and the principle of virtual work. To tackle various boundary conditions, the investigation employs the Galerkin method, providing a comprehensive and refined analysis of the system's behavior. Two types of porous shells, categorized as Softcore (SC) and Hardcore (HC), are analyzed, with five distribution patterns: tri-directional (Type-A), two bidirectional (Type-B and Type-C), transverse unidirectional (Type-D), and axial unidirectional (Type-E).