On higher gradients in continuum-atomistic modelling

Sunyk, R. and Steinmann, P. (2003) On higher gradients in continuum-atomistic modelling. International Journal of Solids and Structures, 40(24), pp. 6877-6896. (doi: 10.1016/j.ijsolstr.2003.07.001)

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Abstract

Continuum-atomistic modelling denotes a mixed approach combining the usual framework of continuum mechanics with atomistic features like e.g. interaction or rather pair potentials. Thereby, the kinematics are typically characterized by the so-called Cauchy-Born rule representing atomic distance vectors in the spatial configuration as an affine mapping of the atomic distance vectors in the material configuration in terms of the local deformation gradient. The application of the Cauchy-Born rule requires sufficiently homogeneous deformations of the underlying crystal. The model is no more valid if the deformation becomes inhomogeneous. Nevertheless the development of microstructures with inhomogeneous deformation is inevitable. In the present work, the Cauchy-Born rule is thus extended to capture inhomogeneous deformations by the incorporation of the second-order deformation gradient. The higher-order equilibrium equation as well as the appropriate boundary conditions are presented for the case of finite deformations. The constitutive law for the Piola-Kirchhoff stress and the additional higher-order stress are represented for the simplified case of pair potential-based energy density functions. Finally, a deformation inhomogeneity measure is introduced and studied for a particular non-homogeneous simple-shear like deformation.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Steinmann, Professor Paul
Authors: Sunyk, R., and Steinmann, P.
College/School:College of Science and Engineering > School of Engineering > Infrastructure and Environment
Journal Name:International Journal of Solids and Structures
Publisher:Elsevier
ISSN:0020-7683
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