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One-dimensional nonlocal and gradient elasticity: Closed-form solution and size effect
Institution:1. Engineering Department, University of Ferrara, Via Saragat 1, 44122 Ferrara, Italy;2. Faculty of Civil Engineering and Geosciences, Delft University of Technology, P.O. Box 5048, 2600 GA Delft, The Netherlands;1. Department of Architecture and Civil Engineering, City University of Hong Kong, Kowloon, Hong Kong, PR China;2. City University of Hong Kong Shenzhen Research Institute, Shenzhen 518057, PR China;3. Mechanical Engineering Department, Texas A&M University, College Station, TX 77843-3123, USA;1. Department of Structures for Engineering and Architecture, University of Naples Federico II, via Claudio 25, 80121 Naples, Italy;2. Department of Civil and Mechanical Engineering, University of Cassino and Southern Lazio, via G. Di Biasio 43, 03043, Cassino (FR), Italy;3. Department of Structural and Geotechnical Engineering, University “La Sapienza”, Rome, Italy;1. Department of Structures for Engineering and Architecture, University of Naples Federico II, via Claudio 21, 80125, Naples, Italy;2. Department of Mechanical Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran;3. Department of Civil and Mechanical Engineering, University of Cassino and Southern Lazio, via G. Di Biasio 43, 03043, Cassino, FR, Italy;4. Link Campus University, via del Casale di San Pio V 44, 00165, Rome, Italy;5. Department of Civil Engineering, University of Salerno, via Giovanni Paolo II, 132 - 84084, Fisciano, SA, Italy
Abstract:The equivalence between nonlocal and gradient elasticity models is investigated by making reference to one-dimensional boundary value problems equipped with two integral stress–strain laws proposed by Eringen (Nonlocal Continuum Field Theories (2002)). Corresponding closed-form solutions are derived through a procedure for the reduction of integral to differential equations. The reproduction of size effects in micro/nano rods is discussed. The differential formulation associated with the local/nonlocal model is shown to correspond to the strain-gradient formulation proposed by Aifantis (Mech. Mater. 35 (2003) 259–280).
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