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Mandatory Fields
Destrade, M,Murphy, JG,Saccomandi, G
2012
March
International Journal Of Non-Linear Mechanics
Simple shear is not so simple
Published
()
Optional Fields
Shear stress Simple shear Triaxial stretch UNIVERSAL RELATIONS ELASTIC-MATERIALS STRESS LOAD
47
210
214
For homogeneous, isotropic, non-linearly elastic materials, the form of the homogeneous deformation consistent with the application of a Cauchy shear stress is derived here for both compressible and incompressible materials. It is shown that this deformation is not simple shear, in contrast to the situation in linear elasticity. Instead, it consists of a triaxial stretch superposed on a classical simple shear deformation, for which the amount of shear cannot be greater than 1. In other words, the faces of a cubic block cannot be slanted by an angle greater than 45 degrees by the application of a pure shear stress alone. The results are illustrated for those materials for which the strain-energy function does not depend on the principal second invariant of strain. For the case of a block deformed into a parallelepiped, the tractions on the inclined faces necessary to maintain the derived deformation are calculated. (C) 2011 Elsevier Ltd. All rights reserved.
DOI 10.1016/j.ijnonlinmec.2011.05.008
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