HiDeNN-FEM: A seamless machine learning approach to nonlinear finite element analysis.

The hierarchical deep-learning neural network (HiDeNN) (Zhang et al, Computational Mechanics, 67:207-230) provides a systematic approach to constructing numerical approximations that can be incorporated into a wide variety of Partial differential equations (PDE) and/or Ordinary differential equations (ODE) solvers. This paper presents a framework of the nonlinear finite element based on HiDeNN approximation (nonlinear HiDeNN-FEM). This is enabled by three basic building blocks employing structured deep neural networks: 1) A partial derivative operator block that performs the differentiation of the shape functions with respect to the element coordinates, 2) An r-adaptivity block that improves the local and global convergence properties and 3) A materials derivative block that evaluates the material derivatives of the shape function. While these building blocks can be applied to any element, specific implementations are presented in 1D and 2D to illustrate the application of the deep learning neural network. Two-step optimization schemes are further developed to allow for the capabilities of r-adaptivity and easy integration with any existing FE solver. Numerical examples of 2D and 3D demonstrate that the proposed nonlinear HiDeNN-FEM with r-adaptivity provides much higher accuracy than regular FEM. It also significantly reduces element distortion and suppresses the hourglass mode.

Atomistic investigations on the mechanical properties and fracture mechanisms of indium phosphide nanowires.

The mechanical properties of indium phosphide (InP) nanowires are an emerging issue due to the promising applications of these nanowires in nanoelectromechanical and microelectromechanical devices. In this study, molecular dynamics simulations of zincblende (ZB) and wurtzite (WZ) crystal structured InP nanowires (NWs) are presented under uniaxial tension at varying sizes and temperatures. It is observed that the tensile strengths of both types of NWs show inverse relationships with temperature, but are independent of the size of the nanowires. Moreover, applied load causes brittle fracture by nucleating cleavage on ZB and WZ NWs. When the tensile load is applied along the [001] direction, the direction of the cleavage planes of ZB NWs changes with temperature. It is found that the {111} planes are the cleavage planes at lower temperatures; on the other hand, the {110} cleavage planes are activated at elevated temperatures. In the case of WZ NWs, fracture of the material is observed to occur by cleaving along the (0001) plane irrespective of temperature when the tensile load is applied along the [0001] direction. Furthermore, the WZ NWs of InP show considerably higher strength than their ZB counterparts. Finally, the impact of strain rate on the failure behavior of InP NWs is also studied, and higher fracture strengths and strains at higher strain rates are found. With increasing strain rate, the number of cleavages also increases in the NWs. This paper also provides in-depth understanding of the failure behavior of InP NWs, which will aid the design of efficient InP NWs-based devices.

Tuning the mechanical properties of silicene nanosheet by auxiliary cracks: a molecular dynamics study.

Silicene has become a topic of interest nowadays due to its potential application in various electro-mechanical nanodevices. In our previous work on silicene, fracture stresses of single crystal and polycrystalline silicene have been investigated. Existence of defects in the form of cracks reduces the fracture strength of silicene nanosheets to a great extent. In this study, an engineering way has been proposed for improving the fracture stress of silicene nanosheets with a pre-existing crack by incorporating auxiliary cracks symmetrically in a direction perpendicular to the main crack. We call this mechanism the "Failure shielding mechanism". An extensive molecular dynamics simulation based analysis has been performed to capture the atomic level auxiliary crack-main crack interactions. It is found that the main crack tip stress distribution is significantly changed with the presence of auxiliary cracks for loading along both armchair and zigzag directions. The effects of temperature and the crack propagation speed of silicene have also been studied. Interestingly, in the case of loading along the zigzag direction, SW defect formation is observed at the tip of main crack. This leads to a reduction of the tip stress resulting in a more prominent failure shielding in case of zigzag loading than in armchair loading. Moreover, the position and length of the cracks as well as the loading directions have significant impacts on the tip stress distribution. Finally, this study opens the possibilities of strain engineering for silicene by proposing an engineering way to tailor the fracture strength of silicene.

Atomistic Representation of Anomalies in the Failure Behaviour of Nanocrystalline Silicene.

Silicene, a 2D analogue of graphene, has spurred a tremendous research interest in the scientific community for its unique properties essential for next-generation electronic devices. In this work, for the first time, we present a molecular dynamics (MD) investigation to determine the fracture strength and toughness of nanocrystalline silicene (nc-silicene) sheet of varying grain sizes and pre-existing cracks at room temperature. Our results suggest a transition from an inverse pseudo Hall-Petch to a pseudo Hall-Petch behaviour in nc-silicene at a critical grain size of 17.32 nm. This phenomenon is also prevalent in nanocrystalline graphene. However, nc-silicene with pre-existing cracks exhibits anomalous crack propagation and fracture toughness behaviour. We observed two distinct types of failure mechanisms (crack sensitive and insensitive failure) and devised mechano-physical conditions under which they occur. The most striking outcome is: despite the presence of a pre-existing crack, the crack sensitivity of nc-silicene is found to be dependent on the grain size and their orientations. The calculated Fracture toughness from both Griffith's theory and MD simulations indicate that the former over-predicts the fracture toughness of nc-silicene. Finally, this study is the first direct comparison of atomistic simulations to the continuum theories to predict the anomalous behaviour in deformation and failure mechanisms of nc-silicene.