Numerical implementation of static Field Dislocation Mechanics theory for periodic media

• Published in: Philosophical magazine (Abingdon, England) Vol. 94; no. 16; pp. 1764 - 1787
• Main Authors: Brenner, R., Beaudoin, A.J., Suquet, P., Acharya, A.
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis 03.06.2014
• Subjects: Condensed matter: structure, mechanical and thermal properties; Defects and impurities in crystals; microstructure; Dislocations; Distortion; Elasticity, elastic constants; Exact sciences and technology; Field Dislocation Mechanics; Fourier transform; infinite bicrystal; internal stresses; Linear defects: dislocations, disclinations; Mathematical analysis; Mathematical models; Mechanical and acoustical properties; Mechanical and acoustical properties of condensed matter; Mechanical properties of solids; Media; Microstructure; periodic microstructure; Physical properties of thin films, nonelectronic; Physics; Stresses; Structure of solids and liquids; crystallography; Surfaces and interfaces; thin films and whiskers (structure and nonelectronic properties); Tensors; zero-stress dislocation distributions; Elastic modulus; Fourier transformation; Field theories; Mechanical properties; Distortion; Internal field; Elastic deformation; Implementation; Dislocations; Spatial distribution; Internal stresses; Stress distribution; Analytical method; Stress effects; Microstructure; Analytical solution; Inhomogeneous materials; Periodic field
• ISSN: 1478-6435; 1478-6443
• DOI: 10.1080/14786435.2014.896081

This paper investigates the implementation of Field Dislocation Mechanics (FDM) theory for media with a periodic microstructure (i.e. the Nye dislocation tensor and the elastic moduli tensor are considered as spatially periodic continuous fields). In this context, the uniqueness of the stress and elastic distortion fields is established. This allows to propose an efficient numerical scheme based on Fourier transform to compute the internal stress field, for a given spatial distribution of dislocations and applied macroscopic stress. This numerical implementation is assessed by comparison with analytical solutions for homogeneous as well as heterogeneous elastic media. A particular insight is given to the critical case of stress-free dislocation microstructures which represent equilibrium solutions of the FDM theory.