Numerical Simulation For Finite Deformation Of Low-dimensional Carbon Nanomaterials And Erythrocyte Membrane Based On The Temperature-related Higher Order Cauchy-Born Rule

Nowadays, as one of the most promising fields, nanotechnology is in its rapid development and will have attractive applicability prospects. ID and2D nanostructures, especially graphene sheets, carbon nanotubes and erythrocyte membrane, have been attracting extensive research interest due to their exceptional mechanical properties. In order to have a thorough knowledge of their mechanics, a nanoscale quasi-continuum model is established herein based on the proposed temperature-related higher order Cauchy-Born rule. Furthermore, a meshless numerical framework for the finite deformation of the considered nanomembranes is also constructed in the context of the higher order gradient continuum.In the present thesis, an extended temperature-related higher order Cauchy-Born rule is first developed for the description of the kinematic transformation of nanomembranes at finite temperature. Since the second order deformation gradient tensor is involved in the present approach, the curvature effect of nanomembranes can be related in a convenient way. The elastic energy of an evaluated point in the equivalent continuum can be obtained from homogenizing the deformation energy of a virtual representative cell with use of the temperature-related higher order Cauchy-Born rule as the linkage of the deformation of the segment from microscale to macroscale. Subsequently, the underlying nonlinear constitutive model for nanomembranes can be derived through the second order partial derivative of the continuum elastic energy with respect to deformation gradient tensors.Based on the resulting constitutive model and with use of the Tersoff-Brenner potential as the description of interactions between bonded carbon atoms, the coefficient of thermal expansion, the specific heat and the Young’s modulus of graphene sheet and single-walled carbon nanotubes (SWCNTs) are investigated systematically. The results show that, in the range of lower temperature, the coefficient of thermal expansion of graphene sheet decreases with the increase of temperature. However, the tendency is opposite when temperature is larger than270K. It is also noted that the influence of the radius of SWCNTs on their coefficient of thermal expansions is not significant. Besides, the specific heat of graphene sheet and SWCNTs is almost independent on their chirality. From the numerical results, the trends of the Young’s modulus of SWCNTs predicted through the present method are consistent with those from molecular mechanics simulation when temperature is larger than300K. In order to investigate the finite deformation of graphene sheets and SWCNTs, a meshless numerical scheme is established based on the proposed quasi-continuum model. The numerical results demonstrate that the buckling modes of graphene sheets and SWCNTs under different loading conditions can be reproduced based on the present approach, which agree well with those from molecular dynamic simulations. Since the wall of SWCNTs may be contact with itself under large deformation, the Lennard-Jones potential is resorted to for the non-bonded interactions and a generalized contact model is constructed for the large deformation of SWCNTs. The computations reveal that the local deformation pattern in the contact regime is highly dependent on the non-bonded interactions.Finally, a worm-like-chain based symmetrical hexagonal lattice model for the investigation of mechanics of erythrocyte membrane is proposed. With the parameterized membrane model, a quasi-continuum framework and its meshfree method implementation are presented based on the so-called higher order Cauchy-Born rule. The results reveal that the mechanic properties of erythrocyte membrane can be truly displayed with the present method. In addition, the wrinkle of erythrocyte membrane under shear deformation can be reproduced without any structural imperfections involved in the numerical computations. In order to simulate the optical tweezers experiments for the whole cell of erythrocyte, the deformation behaviors of red blood cell are investigated numerically with use of the proposed meshless computational scheme. Due to the occurrence of buckling during the deformation of erythrocyte under tension, we suggest that numerical simulations should be carried out with use of the whole cell rather than one half or one eight of the object. It also should be pointed out that the computational efforts can be reduced rationally since the discretisation of the continuum membrane can be chosen freely.