Experimental and multiscale computational static and dynamic study of 3D elements with mesostructure

Numerical and experimental studies were conducted to demonstrate the applicability of the multiscale finite element method (MsFEM) with the higher-order approximation to the prediction of mechanical behavior of 3D printed parts with complex mesostructure. Three scales are considered: the microscale, at which the filament paths are homogenized using an orthotropic material model with experimentally identified properties; the mesoscale with 3D printed structure that is upscaled by MsFEM; and the macroscale, at which the overall problem is effectively solved. To validate the approach that may be useful for designing 3D printed elements, the authors conducted experimental measurements of static bending and free vibrations of beams with four different mesostructures and two print orientations. The measurements were performed using digital image correlation and were compared with numerical modeling performed by the authors. Both results coincide very well for a number of examples. Moreover, the study revealed that the hierarchical higher-order shape functions can accurately represent free vibrations even for the high frequencies.