Remove Homogeneous Layer Assumption from Lamination Theories

Abstract

Composite multilayer structures are often modeled using lamination theories. All lamination theories inherently assume the composite laminate is made of homogeneous layers characterized with lamina constants, which will restrict the lamination theories from capturing the real microstructural details of the composite material, and thus create artificial layer boundaries and result in many phenomena predicted by lamination theories occurred at wrong locations. Another drawback of lamination theories is that the lamina constants can not be rigorously defined. Recently a new theory called Mechanics of Structure Genome (MSG) has been developed without the homogeneous layer assumption. The variational asymptotic method (VAM) has been used to minimize the loss of information between the original 3D heterogeneous structures and the final equivalent plate model without invoking any ad hoc kinematic assumptions. To analyze multilayer plates/shells, MSG decouples the original 3D problem into a plate analysis and a constitutive modeling over a Structure Genome (SG), where SG is the mathematical smallest building block of the multilayer plate/shell structure. Through the analysis of SG, a constitutive relation between the generalized 2D strains and stress resultants is obtained for the plate analysis which can be solved at the same computational cost as Classical Laminate Theory (CLT). Dehomogenization can also be conducted to obtain the displacements, strains and stresses in the original heterogeneous structure. Several examples will be used to disclose the aforementioned flaws of lamination theories and the advantage of MSG. It is numerically demonstrated that while using the same plate elements in ABAQUS, MSG has an excellent accuracy compared to 3D FEA in terms of all the displacements and in-plane stress components, as well as a fair agreement of the transverse normal stress.