Nonproportional loading effects on elastic-plastic behavior based on stress resultants for thin plates of strain hardening materials |
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| Institution: | 1. Edison Welding Institute Columbus, OH 43212, USA;2. Mechanical Engineering and Applied Mechanics The University of Michigan Ann Arbor, MI 48109, USA;3. Ford Motor Company Dearborn, MI 48121, USA;1. State Key Laboratory of Petroleum Resource and Prospecting, China University of Petroleum (Beijing), Beijing 102249, China;2. Center of Rock Mechanics and Geohazards, Shaoxing University, Shaoxing, 312000, China;3. CNPC Key Laboratory of Geophysical Exploration, China University of Petroleum (Beijing), Beijing 102249, China;1. Department of Civil and Natural Resources Engineering, University of Canterbury, Private Bag 4800, Christchurch, New Zealand;2. Department of Civil and Environmental Engineering, University of Washington, Box 352700, Seattle, WA 98195-2700, United States;1. Shenyang Institute of Automation Chinese Academy of Sciences, 110000 Shenyang, China;2. University of Chinese Academy of Sciences, 100049, Beijing, China |
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| Abstract: | A stress resultant constitutive law in rate form is constructed for power-law hardening materials. The change of plate thickness is considered in the constitutive law. The elastic-plastic behavior of a plate element based on the stress resultant constitutive law under uniaxial combined tension and bending is determined under a limited number of nonproportional and unloading paths. The results based on the stress resultant constitutive law and the through-the-thickness integration method are compared within the context of both the small-strain and finite deformation approaches. The results indicate that the selection of the normalized equivalent stress resultant and the corresponding work-conjugate normalized equivalent generalized strain is appropriate for describing the hardening behavior in the stress resultant space. However, the hardening rule in a power law form must be modified for low hardening materials at large plastic deformation when finite deformation effects are considered. |
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