Abstract
A three-dimensional semi-analytical finite element method (SAFEM-3D) is implemented in this work to calculate the effective properties of periodic elastic-reinforced nanocomposites. Different inclusions are also considered, such as discs, ellipsoidals, spheres, carbon nanotubes (CNT) and carbon nanowires (CNW). The nanocomposites are assumed to have isotropic or transversely isotropic inclusions embedded in an isotropic matrix. The SAFEM-3D approach is developed by combining the two-scale asymptotic homogenization method (AHM) and the finite element method (FEM). Statements regarding the homogenized local problems on the periodic cell and analytical expressions of the effective elastic coefficients are provided. Homogenized local problems are transformed into boundary problems over one-eighth of the cell. The FEM is implemented based on the principle of the minimum potential energy. The three-dimensional region (periodic cell) is divided into a finite number of 10-node tetrahedral elements. In addition, the effect of the inclusion’s geometrical shape, volume fraction and length on the effective elastic properties of the composite with aligned or random distributions is studied. Numerical computations are developed and comparisons with other theoretical results are reported. A comparison with experimental values for CNW nanocomposites is also provided, and good agreement is obtained.
Highlights
Single-walled carbon nanotube (SWNT) composites embedded in a polymer matrix are called nanocomposite materials
Fisher et al [34,35] studied the effect of carbon nanotube (CNT) inclusions on the effective elastic properties of composites by numerical simulation techniques, using finite elements coupled with the Mori–Tanaka model
The SAFEM-3D is implemented over different two-phase fiber-reinforced composites (FRCs), in which the periodic unit cell has 72 similar inclusions embedded in the matrix
Summary
Single-walled carbon nanotube (SWNT) composites embedded in a polymer matrix are called nanocomposite materials. Different techniques have been developed to study the elastic behavior of multi-phase fiber-reinforced composites (FRCs) [15,16]. Fisher et al [34,35] studied the effect of carbon nanotube (CNT) inclusions on the effective elastic properties of composites by numerical simulation techniques, using finite elements coupled with the Mori–Tanaka model. Many research works have reported on the field of nanocomposites reinforced by CNT inclusions; for example, Tarfaoui et al [38] analyzed the effect of CNT additives on the mechanical behavior of three-phase polymer-matrix composites by experimental techniques. The effective coefficients of periodic multi-phase elastic FRCs are calculated by the three-dimensional semi-analytical finite element method (SAFEM-3D).
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