连续介质力学讲解(第七章).pptx

CONSTITUTIVE EQUATIONS Description of material properties Equations that describe material properties are called the constitutive equation of the material This chapter focuses on non-viscous fluid, Newtonian viscous fluid and the ideal elastic solids constitutive There are other constitutive equations such as thermal conductivity, resistance characteristics, electromagnetic properties, mass transfer and so on. Stress - strain relationship describes the mechanical nature of materials, but also a constitutive equation No viscous fluid On all planes that through one point, no shear stress and normal stresses are all equal. Therefore, stress tensor of no viscous fluid is isotropic, which has the form: P is stress State equation of ideal gas Ideal gas or liquid Incompressible fluid CONSTITUTIVE EQUATIONS Newtonian fluid Newtonian fluid is a viscous fluid, the shear stress are linearly proportional to the deformation gradient, Stress - strain relationship: If the fluid is isotropic CONSTITUTIVE EQUATIONS Hooke elastic solid CONSTITUTIVE EQUATIONS Isotropic material CONSTITUTIVE EQUATIONS We expand it in the rectangular Cartesian coordinate system x，y，z ： can be obtained from these equations , but customarily its inverse form can be written as follows ： Other forms of Hookes law: CONSTITUTIVE EQUATIONS In the case of hydrostatic pressure and small deformation ： （Where V and are volume and volume changes respectively, represents the static pressure） Thus, the coefficient K is appropriately called the bulk modulus of the material. CONSTITUTIVE EQUATIONS The relationships between the elastic constants are equations (7.4-16). In general, CONSTITUTIVE EQUATIONS Conversely, in the temperature change proecess, the strain remains zero then Effects of temperature： If the stress of an object remains zero in temperature change process to For an isotropic Hooker solid ： CONSTITUTIVE EQUATIONS Materials with more complex mechanical behavior No real material is known to behave exactly as any one of them, although in limited ranges of temperature ,stress, and strain, some materials may follow one of these laws quite well. Real materials may have more complex behavior. Nevertheless, the vast literature on continuum mechan