Stress channelling in extreme couple-stress materials Part II: Localized folding vs faulting of a continuum in single and cross geometries |
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| Institution: | 1. Institute of Applied Mechanics of Russian Academy of Sciences,125040, Leningradskiy Prospekt 7, Moscow, Russia;2. Moscow State University Moscow State University of Civil Engineering (National Research University), 129337, Yaroslavskoe shosse 26, Moscow, Russia;3. Moscow Aviation Institute (National Research University), 125993, A-80, GSP-3, Volokolamskoie shosse 4, Moscow, Russia;1. Department of Mathematical Information Technology, University of Jyväskylä, P.O. Box 35 (Agora), FI-40014, Finland;2. Institute for Problems in Mechanics RAS, Prospect Vernadskogo 101, Bld. 1, 119526 Moscow, Russian Federation;1. Iowa State University, Departments of Aerospace Engineering, Mechanical Engineering, and Material Science and Engineering, Ames, IA 50011, USA;2. Material Measurement Laboratory, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA;1. Center for Research and Applications of Nonlinear Systems (CRANS), Department of Mathematics, University of Patras, GR-26500, Patras, Greece;2. High Performance Computing Systems and Distance Learning Lab (HPCS-DL Lab), Technological Educational Institute of Western Greece, 263 34 Patras, Greece;1. Department of Structures for Engineering and Architecture, University of Naples Federico II, via Claudio 21, 80125 Naples, Italy;2. Department of Civil Engineering, University of Salerno, 84084, Fisciano, SA, Italy;3. Department of Civil and Mechanical Engineering, University of Cassino and Southern Lazio, via G. Di Biasio 43, 03043, Cassino, FR, Italy |
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| Abstract: | The antiplane strain Green's functions for an applied concentrated force and moment are obtained for Cosserat elastic solids with extreme anisotropy, which can be tailored to bring the material in a state close to an instability threshold such as failure of ellipticity. It is shown that the wave propagation condition (and not ellipticity) governs the behaviour of the antiplane strain Green's functions. These Green's functions are used as perturbing agents to demonstrate in an extreme material the emergence of localized (single and cross) stress channelling and the emergence of antiplane localized folding (or creasing, or weak elastostatic shock) and faulting (or elastostatic shock) of a Cosserat continuum, phenomena which remain excluded for a Cauchy elastic material. During folding some components of the displacement gradient suffer a finite jump, whereas during faulting the displacement itself displays a finite discontinuity. |
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| Keywords: | Cosserat elasticity Strain localization Green's functions Wave propagation Anisotropy |
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