Experimental and numerical analysis on the buckling behavior of functionally graded cellular media with extension-capable C¹ higher order plate theory

Polymeric cellular materials were primarily developed as means to reduce density of solid polymers and thus saving cost for applications where mechanical strength is not required like the packaging industry. Nevertheless, functionally graded cellular materials showed an attractive mechanical behavior in experimental studies. The fatigue life of porous polycarbonate (PC) with above 90% relative density is reported to be as much as four times that of a solid PC, and greater impact strength with relative density over 60%. The focus of this paper is on fabricating bio-polymeric-based functionally graded porous material with polylactic acid (PLA) and analyze the buckling behavior of their plate-like structures. The analysis includes numerical modeling supported with experimental findings. The modeling is carried out with a higher order shear deformation plate theory (HSDT) accounting for extension in the transverse direction. The proposed HSDT satisfies the constraint on the consistency of transverse shear strain energy a priori in addition to the traction conditions on plate surfaces. Few theories in the area satisfy both conditions. Finite element is used to implement the HSDT with C¹ continuity using conforming elements. The through-thickness varying properties are homogenized at planar-level with the generalized self-consistent scheme. The graded cellular structure is manufactured to vary through the plate thickness while being uniform on-average for the other two planar dimensions. Constrained foaming process is adopted to control the pores' size and structure through the plate thickness.