Analytical solutions for monoclinic/trigonal structures replicating multi-wall carbon nano-tubes for applications in composites with elastomeric/polymeric matrix

In the last years, due to their exceptional mechanical properties (elastic modulus of about 1 TPa and tensile strength of 130-150 GPa), single and multi-wall carbon nanotubes (CNTs and MWCNTs) have encountered an increasing interest among scientists. More recently, a number of studies have also envisaged the possibility of building up a new generation of composites with elastomeric or polymeric matrix, reinforced with MWCNTs, to gain high mechanical performances and other physical properties. However, independently from problems related to accuracy and costs associated to the processing and the production of MWCNTS and some difficulties in exactly controlling their dimensions, distribution and geometry, a detailed micromechanical description of the overall elastic response of these complex structures-that appear to be constituted by several layers organized as hollow cylindrical phases wrapped around a central core-is still at the center of a vivid debate, because it is expected that their chirality induces an anisotropic (e.g. trigonal/monoclinic) elastic behavior, which is characterized by a coupling between torsion and axial deformations. This is a relevant aspect for the developing of stresses inside the reinforcements and, importantly, for predicting the actual stress regimes at the interfaces and in turn the overall mechanical behavior of these composites, with transferring of spurious shear stresses and size effects. In this framework, due to the difficulties of deriving analytical results for the mechanical response of these multi-wall elastically monoclinic cylinders, the vast majority of the literature efforts have presented numerical results, for example by performing Finite Element (FE) analyses or by estimating the stiffness of these structures, at different scale levels, through molecular dynamics (MD) strategies. The present contribution is therefore aimed to furnish new closed-form elastic solutions for general compound cylinders, made by n hallow monoclinic/trigonal phases and a possible central core, under prescribed boundary conditions of interest for applications, to be implemented in computational FE algorithms for faithfully replicating the actual mechanical response of composites reinforced with MWCNTs.