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A CONSTITUTIVE MODEL FOR NANOSTRUCTURES BASED ON SPATIAL SECANT
| Title: | A CONSTITUTIVE MODEL FOR NANOSTRUCTURES BASED ON SPATIAL SECANT |
| Author: | GONDHALEKAR, ROHIT H |
| Description: | With the rapid advances in the synthesis of nanomaterials, it is becoming increasingly important to investigate their physical properties. Apart from experimental techniques, a variety of modeling and simulation methods are available that can be used to evaluate the physical properties of nanostructures. These methods can be classified in two major categories: atomistic and continuum. The atomistic methods seek to track the information on atom by atom basis. In many of the atomistic methods, interatomic potentials are used to model the system. These methods are robust and yield results which are in accordance with the experimental findings. The other category is the methods that are based on continuum concepts. It is generally believed that continuum theory can be applied successfully at micro length scale. However, at the nanoscale, the atomic bond size effects cannot be neglected and continuum concepts cannot be applied directly. This serves as a motivation to develop a new model. The proposed model borrows concepts such as interatomic potentials from the atomistic models and concepts such as hyperelasticity from the continuum models. Deformation gradient can be thought as a deformation measure in the formulation of hyperelastic model. However, it is shown that using such deformation measure leads to the wrong mapping of atomic bonds in various configurations of the system. The proposed model uses 'spatial secant' as the deformation measure. This deformation measure is based on atomistic variables and is not exactly the same as those used in continuum theory. Using spatial secant as the deformation measure guarantees that atomic bonds are correctly mapped which is essential for the accuracy of the proposed model. It is shown that the proposed model strongly depends on the mechanics of the interatomic bond. This serves as a consistent link to other atomistic simulation methods such as molecular dynamics thereby guarantying the accuracy and reliability of the model. The robustness of the model will be shown through the benchmark problems at the end of the study. |
| Permanent Link: |
http://rave.ohiolink.edu/etdc/view?acc_num=ucin1120144896
http://hdl.handle.net/2374.OX/9936 |
| Date: | 2005 |
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