Strain-gradient elastic-plastic material models and assessment of the higher order boundary conditions |
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| Institution: | 1. State Key Laboratory for Strength and Vibration of Mechanical Structures, Xi''an Jiaotong University, Xi''an 710049, PR China;2. Department of Civil Engineering & Mechanics, Huazhong University of Science & Technology, 1037 Luoyu Road, Wuhan 430074, PR China;1. School of Aeronautics and Astronautics, Shanghai Jiao Tong University, Shanghai 200240, People׳s Republic of China;2. School of Computing, Engineering and Mathematics, Western Sydney University, Locked Bag 1797, Penrith, NSW 2751, Australia;3. Institute for Infrastructure Engineering, Western Sydney University, Locked Bag 1797, Penrith, NSW 2751, Australia |
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| Abstract: | A gradient elastic material model exhibiting gradient kinematic and isotropic hardening is addressed within a thermodynamic framework suitable to cope with nonlocal-type continua. The Clausius–Duhem inequality is used, in conjunction with the concepts of energy residual, insulation condition and locality recovery condition, to derive all the pertinent restrictions upon the constitutive equations, including the PDEs and the related higher order (HO) boundary conditions that govern the gradient material behaviour. Through a suitable limiting procedure, the HO boundary conditions are shown to interpret the action, upon the body's boundary surface, of idealized extra HO constraints capable to impede the onset of strain as a nonlocality source and to react with a double traction (of dimension moment/area), work-conjugate of the impeded strain. The HO boundary conditions for the internal moving elastic/plastic boundary are also provided. A number of variational principles are proved. A few simple illustrative numerical examples are worked out. |
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