Deformation gradients for continuum mechanical analysis of atomistic simulations
We present an expression developed for calculating an atomic-scale deformation gradient within atomistic simulations. This expression is used to analyze the deformation fields for a one-dimensional atomic chain, a biaxially stretched thin film containing a surface ledge, and a FCC metal subject to i...
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| Published in | International journal of solids and structures Vol. 46; no. 2; pp. 238 - 253 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier Ltd
15.01.2009
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| Subjects | |
| Online Access | Get full text |
| ISSN | 0020-7683 1879-2146 |
| DOI | 10.1016/j.ijsolstr.2008.08.036 |
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| Abstract | We present an expression developed for calculating an atomic-scale deformation gradient within atomistic simulations. This expression is used to analyze the deformation fields for a one-dimensional atomic chain, a biaxially stretched thin film containing a surface ledge, and a FCC metal subject to indentation loading from a nanometer-scale indenter. The analyses presented show that the metric established here is consistent with the continuum mechanical concept of deformation gradient (which is known to have a zero curl for compatible deformations) in most instances. However, our metric does yield non-zero values of curl for atoms near loaded geometric inhomogeneities, such as those that form the ledges themselves and those beneath or adjacent to the indentation contact region. Also, we present expressions for higher order gradients of the deformation field and discuss the requirements for their calculation. These expressions are necessary for linking atomistic simulation results with advanced continuum mechanics theories such as strain gradient plasticity, thereby enabling fundamental, atomic-scale information to contribute to the formulation and parameterization of such theories. |
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| AbstractList | We present an expression developed for calculating an atomic-scale deformation gradient within atomistic simulations. This expression is used to analyze the deformation fields for a one-dimensional atomic chain, a biaxially stretched thin film containing a surface ledge, and a FCC metal subject to indentation loading from a nanometer-scale indenter. The analyses presented show that the metric established here is consistent with the continuum mechanical concept of deformation gradient (which is known to have a zero curl for compatible deformations) in most instances. However, our metric does yield non-zero values of curl for atoms near loaded geometric inhomogeneities, such as those that form the ledges themselves and those beneath or adjacent to the indentation contact region. Also, we present expressions for higher order gradients of the deformation field and discuss the requirements for their calculation. These expressions are necessary for linking atomistic simulation results with advanced continuum mechanics theories such as strain gradient plasticity, thereby enabling fundamental, atomic-scale information to contribute to the formulation and parameterization of such theories. |
| Author | Zimmerman, Jonathan A. Gao, Huajian Bammann, Douglas J. |
| Author_xml | – sequence: 1 givenname: Jonathan A. surname: Zimmerman fullname: Zimmerman, Jonathan A. email: jzimmer@sandia.gov organization: Mechanics of Materials Department, Sandia National Laboratories, Livermore, CA 94551, USA – sequence: 2 givenname: Douglas J. surname: Bammann fullname: Bammann, Douglas J. organization: Mechanical Engineering Department, Mississippi State University, Mississippi State, MS 39762, USA – sequence: 3 givenname: Huajian surname: Gao fullname: Gao, Huajian organization: Division of Engineering, Brown University, Providence, RI 02912, USA |
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Chem. Phys. doi: 10.1063/1.437577 |
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| Title | Deformation gradients for continuum mechanical analysis of atomistic simulations |
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