Study On Finite Deformation Of The Bar Under Tensile-torsion

Natural rubber and synthetic rubber presents many unique physical and chemical properties, such as high elasticity, large deformation, and is of quite excellent softness, abrasion resistance, insulation and barrier properties, which can meet a wide range of application requirements. It is widely used in engineering particularly. The use of its vulcanization and additives that improves the material's mechanical and physical properties makes rubber have more applications and possess more important business sense. People tried to make authentic description of rubber material, but because of its complexity and molecular characteristics of the dual non-linear material and geometry, and its sensitive impact of time, loading rate and strain amount on the temperature, the surrounding medium and strain, it is more difficult to establish a precise mathematical model. In order to design and calculate, rubber users and manufacturers now use complex numerical techniques, but the precision of which also depends on the constitutive model they utilize, so people must take more effort to looking for a new model of rubber materials.Based on the Gent model and Gao Yu-Chen model, considering strain hardening of the incompressible materials, a new strain energy density function that denotes the new constitutive equation is created by means of finite deformation theory in this paper. Then the limitations of the constitutive parameters and significance are examined using the relation that the empirical formula and finite deformation are small deformation generalized and the typical finite deformation (unidirectional extrude, biaxial tensile and membrane deformation of the bar). The results show:when the constitutive parameters satisfy a>0, n>0, Jm>I1n-3n>0, various constraints (e. g., elastic modulus E>0) can be met and the deformation is stable; the constitutive parameters can be regarded as strengthen dimensionless parameters of this type of rubber material; the constitutive parameters Jm can be considered as ultimate elongation limit parameter of incompressible materials, while the other constitutive parameter a is the same dimension as elastic modulus; this strain energy function can be described as the finite deformation properties of rubber-like materials.This paper presents the drawing methods of the finite deformation problem of the incompressible rubber cylinder under tension-torsion, and calculates the stress, axial force and bending moment of the bar in the application of cylindrical geometry equations, balance equations and constitutive equations. Then using partial derivative symbol of the axial force, we study tensile elongation and shortening of the bar in the case of tensile-tortion, and make comparision with the results of the classic constitutive model, and lastly discuss the effect of the changing material parameters of the constitutive equation on the strain hardening, which illustrates the universality and applicability of the new model.