| Summary: | 博士 === 國立成功大學 === 航空太空工程學系 === 105 === Due to the difficulties of the experimental works on the nanomaterials, many efforts have been recently put on the estimation of their mechanical properties through theoretical and numerical simulations. A semi-analytical method called molecular-continuum (MC) model and a molecular dynamics based (MD-based) nonlinear finite element simulation method are proposed to estimate the stiffness, strength, and fracture toughness of nanomaterials in this thesis.
The MC model is developed by combining the concept of molecular dynamics and continuum mechanics, in which the potential energy describing the interactions of atoms is not restricted to the harmonic potential function, and hence its deriving stress-strain relation is not restricted to be linear. Unlike the usual test performed by applying forces, in this model a displacement field is employed in the representative volume element of a specimen. For predicting the stiffness and strength, the uniform strain field is applied. To estimate fracture toughness, a parameter called the strain intensity factor is introduced, and the near tip solution of linear elastic fracture mechanics rewritten in terms of strain intensity factor is used to locate the atoms of the cracked specimen. Through this model, the Young’s moduli, Poisson’s ratios, and shear modulus of graphene and carbon nanotubes (CNTs) for armchair, zigzag, and chiral types can all be written as simple rational functions in which the dependence of radius, chiral angle, and thickness can be observed clearly from the explicit closed-form expressions by using the harmonic potential functions. Moreover, according to the proposed molecular-continuum model, an integrated symbolic and numerical computational scheme (ISNC) is established to deal with the general nanomaterials. The stiffness defined based upon the initial linear region, and the ultimate strength, yield strength and, mode I/mode II toughness occurring at the later period of the materials can all be predicted. Identical results of the closed-form solutions and ISNC verify the correctness of our derivation. Comparison of the results obtained by other methods or different potential energy functions further justifies the simplicity, validity, and efficiency of the proposed model.
The MD-based nonlinear finite element simulation method to estimate the mechanical properties of nanomaterials is developed by using a frame-like structure to construct the molecular model. The bond stretching energy and bond angle bending energy in molecular dynamics can be simulated by the analogous concept in finite element approach, that is, these strain energies of a beam element caused by tensile stress and bending moment, respectively. The nonlinear modified Morse potential energy is selected and used to calculate the nonlinear stress-strain relation and sectional area of the beam element in our simulation. As the prediction by the MC model, a prescribed-displacement condition is applied in this method. The energy release rate is used to predict the fracture toughness of nanomaterials. Since the value of crack increment must be extremely smaller than the value of crack length for calculating the energy release rate, the continuum model of nanomaterials with nonlinear elastic property is constructed based upon the properties estimated by the beam element model. The mechanical properties for both graphene and CNTs in different types and sizes are presented to illustrate the feasibility of this method.
To verify the correctness of two methods, the existing results provided by the other experimental and numerical methods are compared and discussed in this study. The comparison shows that the results estimated by these models fall in the reasonable range.
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