Granular micromechanics modeling of beams, plates, and shells

We present constitutive laws of structural members, such as beams, plates and shells, using the granular micromechanics approach. These relationships between internal resultants (i.e., internal forces and moments) and kinematic variables (i.e., strains and curvatures) depend solely on the microstructural properties of the constituents and the structure geometry. The macroscopic behavior is derived by investigating the average behavior of grain-pair interactions in all generic directions and, thus, automatically represent complex loading-induced and path-dependent anisotropic responses. We specifically derive closed-form solutions for the constitutive relationship of structural members made of both uniform and functionally graded materials, as functions of grain-scale parameters. Furthermore, we demonstrate the versatility and computational efficiency of the proposed approach, as well as its applicability to nonlinear material systems not amenable to closed-form solutions, by studying structural members made of particle–binder composites that exhibit failure-to-damage deformation mechanisms. These analytical and numerical solutions reveal interesting one-way and two-way coupling behavior between internal forces and moments.