CHARACTERISTICS OF TWO TYPES OF FUNDAMENTAL HYPOELASTIC MODELS FROM THE VIEWPOINT OF SHEARING CONSTITUTIVE RELATIONS

Abstract

 By comparing the two physically different shearing constitutive relations of the Timoshenko beam in finite displacement, the characteristics of the Jaumann rate of the Cauchy stress are examined. Numerical calculations by two representative hypoelastic models using the Jaumann rate and the Truesdell stress rate are compared in the fundamental elastic problems of deep beams and short columns. The column buckling loads numerically obtained indicate that the Jaumann rate of the Cauchy stress cannot take the effect of shear deformation into account properly even at the level of relatively small rotations. Also, the critical stress at the incipience of the plastically localized deformation predicted by the model using the Truesdell stress rate becomes smaller than that predicted by the Jaumann rate. Eventually, the characteristics of the hypoelastic model using the Truesdell stress rate are clarified. Also, the co-rotational stress rates seem to be appropriate to describe the material properties with relatively small elastic shear deformation like single crystals.