Transversely isotropic constitutive properties modeling of tubular sandwich composite structures

Abstract

Sandwich structures have been studied extensively for planar structures; however, the use of composite tubing, manufactured by pultrusion, in a bending situation where a core material can contribute to take shear stresses, can find many applications in modern structures made of composite materials. The objective of this article is to develop analytical solutions for axial effective modulus and major Poisson's ratio of a pultruded unidirectional composite tubing filled with a core material. In this work, the unidirectional composite tubing and its core are considered to have transversely isotropic and isotropic properties, respectively. For the validation of the results, the obtained exact analytical solutions are reduced to a case where both the materials are isotropic and compared to the existing solutions for an isotropic material filling in an isotropic tube. Further validations of our exact analytical solutions for the transversely isotropic tubing and isotropic core are carried out employing a finite element analysis of the same structure, where the results show excellent agreements between the analytical solutions and the numerical results. Finally, a parametric study is conducted to investigate the variations in the effective properties of the two-phase composite cylinder based on the variations in the skin and/or core geometries and their material properties.

Generally cylindrical orthotropic constitutive modeling of matrix-filled carbon nanotubes: Transverse mechanical properties and responses

“…The stiffness matrix,C ij , is the inverse of the compliance matrix, the components of which include engineering material properties, that is,E ii ; ij ; and G ij . For an orthotropic material, the contracted stiffness components (i.e., C ij ) can be calculated from equations (26) and (27), presented below [60 and 61].…”

“…Parameters r i , e j , and C ij in equations (2a) and (2b) are stresses, strains, and cylindrical orthotropic elastic constants, respectively. Due to the axisymmetry of the problem, the reduced form of the strain-displacement relations can be written as [26] e r ¼ @w @r ;…”

“…Parameters σ i , ε j , and C ij in equations (2a) and (2b) are stresses, strains, and cylindrical orthotropic elastic constants, respectively. Due to the axisymmetry of the problem, the reduced form of the strain–displacement relations can be written as [26] where w=w(r) and u represent the radial and axial displacements, respectively. Since this composite cylinder is only subjected to radial uniform external pressure, the axial strain, ε x , does not vary with the radial coordinate r , (i.e., iso-strain condition) and hence, εx (i)=εx(o)=ε=∂u/∂x=a constant for both inner and outer tubes.…”

“…There have been many studies to analytically, numerically, and experimentally investigate the effective properties of traditional composites, nanocomposites, and their constructing unit cells [21–39]. As a result, various micromechanical models are available to predict the macroscopic behaviors of traditional fiber-reinforced composites [e.g., 21–26,37], some of which assume that both fiber and matrix have isotropic or transversely isotropic properties [26]. These assumptions may not be acceptable in many cases, especially for micro- and nanoscale materials and structures that show orthotropic behavior.…”

“…Kalamkarov et al. [26] used linear elastic theory and continuum mechanics to derive exact analytical solutions for the effective axial Young’s modulus, major Poisson’s ratios, displacements, strains, and stress distributions for a two-phase composite cylinder subjected to an axial load. In their work, both constituents were considered to be cylindrically orthotropic (i.e., each with nine independent constants) and perfectly bonded at the interface.…”