A theory of thin plates which is physically as well as kinematically nonlinear is developed and used to characterize elastic material behavior for arbitrary stretching and bending deformations. It is developed from a few clearly defined assumptions and uses a unique treatment of strain energy. An effective strain concept is introduced to simplify the theory to a special theory having fewer parameters and being capable of characterizing paper. A procedure is given for matching the special theory to edgewise compressive data of paperboard.
A Nonlinear Theory for Elastic Plates With Application to Characterizing Paper Properties
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Johnson, M. W., Jr., and Urbanik, T. J. (March 1, 1984). "A Nonlinear Theory for Elastic Plates With Application to Characterizing Paper Properties." ASME. J. Appl. Mech. March 1984; 51(1): 146–152. https://doi.org/10.1115/1.3167559
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