2019/03/26 by Animesh Pandey, Anurag Gupta, Pandey, Animesh +1
Engineering · Materials Science · Mathematics · Physics and Astronomy · #Combinatorics #Condensed matter physics #Context (archaeology) #Dipole #Elasticity and Material Modeling #Engineering #FOS: Physical sciences #Field (mathematics) #Geology #Geometry #Mathematical Physics (math-ph) #Mathematical analysis #Mathematics #Metal Forming Simulation Techniques #Metric (unit) #Nonlocal and gradient elasticity in micro/nano structures #Physics #Piecewise #Pure mathematics #Quantum mechanics #Surface (topology) #Topological defect #Topology (electrical circuits) #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.1903.10813
arxiv created 2019/03/26 · openalex publication_date 2019/03/26 · arxiv updated 2019/03/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The incompatibility of linearized piecewise smooth strain field, arising out\nof volumetric and surface densities of topological defects and metric\nanomalies, is investigated. First, general forms of compatibility equations are\nderived for a piecewise smooth strain field, defined over a simply connected\ndomain, with either a perfectly bonded or an imperfectly bonded interface.\nSeveral special cases are considered and discussed in the context of existing\nresults in the literature. Next, defects, representing dislocations and\ndisclinations, and metric anomalies, representing extra matter, interstitials,\nthermal, and growth strains, etc., are introduced in a unified framework which\nallows for incorporation of their bulk and surface densities, as well as for\nsurface densities of defect dipoles. Finally, strain incompatibility relations\nare derived both on the singular interface, and away from it, with sources in\nterms of defect and metric anomaly densities. With appropriate choice of\nconstitutive equations, the incompatibility relations can be used to determine\nthe state of internal stress within a body in response to the given\nprescription of defects and metric anomalies.\n