Modeling the mechanical behavior of reinforced composites remains one of the most difficult challenges in the field of computational mechanics. A meshless method for modeling the nonlinear properties of carbon nanotube (CNT)-reinforced cement-based composites is the primary goal of this thesis.
A computational framework based on the element-free method is developed for the proper evaluation of the elastic properties of CNT-reinforced composites. The geometry of a cylindrical representative volume element (RVE) of composites is considered in which the CNT and matrix are used as elastic continua. The formulas for the evaluation of the effective material constants based on a micromechanics method are analyzed in detail.
The interfaces between CNTs and the matrix are crucial regions in terms of ensuring the load-carrying capacity and other functionalities of nanocomposites. They are also the most difficult regions in which to apply any simulation approaches. To begin, perfect bonding is assumed between the CNTs and the in continuum mechanics models. The components of composites (cement-based material, reinforcement, and interface) are then represented by separate material models. These material models are combined using a model that describes the global effects of the interaction between the reinforcing CNTs and the matrix to simulate the behavior of the composite material.
Among the separate material models, a thermodynamically consistent constitutive model for a cementitious matrix that incorporates plasticity and continuum damage mechanics is presented. An elastoplastic model that accounts for elasticity and the plastic-strain hardening of the reinforcement is also provided. The global effects of bond-slip are incorporated in an attempt to describe this interaction phenomenon in an isotropic perfectly plastic model.
Study of the interface between CNTs and the cementitious matrix at the mesoscale involves the micromorphic theory, which envisions a material body as a continuous collection of deformable particles that each possess a finite size and an inner structure. It is considered to be the most successful top-down formulation of a two-level continuum model to bridge the gap between the micro-level and the macro-level. Therefore, the micromorphic theory is expected to reveal many new classes of physical phenomena that fall outside of classical field theories.
To enlarge the domain of applicability of the micromorphic theory, in our model, any infinitesimal volume is assumed to be occupied by all of the components in their corresponding given volume fractions (i.e., each node represents four degrees of freedom, three directional displacements, and an additional bond-slip displacement, as characterized by the morphological descriptor). The equilibrium equations of conventional Cauchy stress and external body force at the macroscale, as well as generalized microstress and microforce at the mesoscale, are established. A meshless method is then implemented to find numerical solutions to the governing equations derived in the coupled problem. Unlike conventional numerical methods, a meshless method does not require the solution domain to be discretized into meshes, but only requires the information at nodes in the domain, which results in improved computational efficiency while maintaining good computational accuracy.
The numerical implementation and application of a meshless method are important parts of this study. A suitable staggered scheme is adapted for the integration of the incremental constitutive equations. To show the efficiency of the proposed meshless method, Matlab codes for various proposed models are written, and several numerical examples are provided to demonstrate its validity and efficiency.