Design Sensitivity Analysis of Mechanical Properties of Nanomaterials using Molecular Dynamics

Abstract

A design sensitivity analysis (DSA) methodology of mechanical properties of nanomaterials is developed using the molecular dynamic (MD) simulation considering both non-shape and shape design variables. From a practical and engineering point of view, thermal effects are very important for simulations in atomistic level. For applications to practical nano-scale design problems, the constant temperature MD simulation is considered using the Nose-Hoover thermostat. A huge amount of computation is usually required for the MD simulations since they are transient dynamic problems. Furthermore, for the DSA of MD systems that have many design variables, the computational cost is very expensive. The approximated DSA methods such as the finite difference method (FDM) are impractical from the viewpoint of sensitivity accuracy, because the MD simulations may include highly nonlinear design parameters. For an efficient and accurate DSA, an adjoint variable method (AVM) is employed. Since the adjoint equation of motion for transient dynamic sensitivity is derived in the form of a terminal value problem, the time reversibility of the dynamic system is required to develop the AVM. The time reversibility of both original MD and adjoint systems considering ensemble concept is investigated. Even though the MD systems for NVT ensemble are not reversible systems, the availability of whole time history in the original responses enables to develop the AVM for those path-dependent transient dynamic problems. The required adjoint terminal value problems are successfully solved since the tangent of the original system is exactly reconstructed from the kinematics of atoms which are already kept in the original response analysis. One of the reasons why nanomaterials can have physical properties which differ from those in their bulk counterpart is their extremely small size and morphology. To account for the shape effects in the nanoscale design of materials, the development of the shape DSA method is indispensable. We presented a shape design sensitivity analysis method for lattice structures using a generalized Langevin equation (GLE) to overcome the difficulty of discrete nature in atomic systems. Taking advantage of GLE forces, perturbed atomistic region is treated as the GLE impedance forces and the shape design problem of discrete atomic variations is converted into a non-shape problem with GLE impedance forces. The developed shape DSA method is applied to a dynamic crack propagation problem. There are various nanomaterial structures such as nanowires, nanotubes, nanoparticles. Through some numerical examples the accuracy and efficiency of the developed method are demonstrated for various design problems. We especially concentrated on nanowires and carbon nanotubes due to their remarkable mechanical and thermal properties which differ from the bulk materials. To find out the optimal isotope doping configuration of a single-walled CNT for the lowest thermal conductivity while satisfying the given isotope impurity percentage, the developed DSA method is further applied to the design optimization.