Numerical simulation of composite materials reinforced with carbon nanotubes

The application of carbon nanotubes (CNTs) in innumerable areas of industry is increasing day-to-day. One of their most important applications is in composite materials as the reinforcing phase. Many researchers studied the behavior of composite materials reinforced with short fibers. This paper examines the effect of the position of short fibers on the total stiffness of a composite material reinforced with carbon nanotubes for various volume fractions. Three different situations have been suggested for the position of a CNT fiber with respect to the other fibers in the composite: completely separated fibers, fibers with overlap, and fibers connected through a shared node (long fibers). Three different cases including a case when just overlaps are allowed, a case when just long fibers are allowed and a case when both overlaps and long fibers are allowed have been investigated. It has been shown that the effect of these cases on the Young’s modulus of the composite is significant and that they should be considered for a better understanding of the reinforced composites behavior. In addition, it is shown that the effect of the investigated cases is more remarkable at higher numbers of randomness values

Revisiting Mindlin's theory with regard to a gradient extended phase‐field model for fracture

The application of generalized continuum mechanics is rapidly increasing in different fields of science and engineering. In the literature, there are several theories extending the classical first-order continuum mechanics formulation to include size-effects [1]. One approach is the strain gradient theory with the intrinsic features of regularizing singular stress fields occurring, e.g., near crack tips. It is crucial to realize that using this theory, the strain energy density is still localized around the crack tip, but does not exhibit any signs of a singularity. Therefore, these models seem to be appropriate choices for studying cracks in mechanical problems. Over the past several years, the phase-field method has gathered considerable popularity in the computational mechanics community, in particular in the field of fracture mechanics [2]. Recently, the authors have shown that integrating the strain gradient theory into the phase-field fracture framework is likely to improve the quality of the final results due to the inherent non-singular nature of this theory [3]. In the present work, we will focus on a general formulation of the first strain gradient theory. To this end, the homogenization approach introduced in Ref. [4] is employed. It is based on a series of systematic finite element simulations using different loading cases to determine the equivalent material coefficients on the macro-scale (i.e., for a strain gradient elastic material) by taking the underlying micro-structure into account

A strain gradient enhanced model for the phase‐field approach to fracture

Phase-field modelling has been shown to be a powerful tool for simulating fracture processes and predicting the crack path under complex loading conditions. Note that the total energy of fracture in the classical phase-field formulations includes the strain energy density from the linear elasticity theory resulting in singular stresses at the crack tip. Recently, we have demonstrated that integrating the strain gradient elasticity into the conventional phase-field fracture formulations may improve the final results by alleviating the effects of a singular stress field around the crack tip [1]. The current contribution focuses on a more general formulation of strain gradient elasticity