Tham khảo tài liệu 'introduction to continuum mechanics 3 episode 10', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 346 The Elastic Solid . Verify the relations between Cịj and the engineering constants given in Eqs. . Obtain Eq. from Eq. . Derive the inequalities expressed in Eq. . Write down all the restrictions for the engineering constants for a monoclinic elastic solid. . Show that if a tensor is objective then its inverse is also objective. 1 T . . . Show that the rate of deformation tensor D Vv Vv is objective . Show that in a change of frame the spin tensor w transforms in accordance with the equation w - QWQT QQ7 . Show that the material derivative of an objective tensor T is in general non-objective . The second Rivlin-Ericksen tensor is defined by A 2 Ấ1 AfyVv Vv 7A1 where Al 2D See Prob. . Show that A2 is objective. . The Jaumann derivative of a second order tensor T is T TW-WT where w is the spin tensor see Prob. . Show that the Jaumann derivative of T is objective. . In a change of frame how does the first Piola-Kirchhoff stress tensor transform . In a change of frame how does the second Piola-Kirchhoff tensor transform . a Starting from the assumption that T H F and T H F show that in order that the constitutive equation be independent of observers we must have QTQr H QF b Choose Q Rr to obtain T RH U Rr where R is the rotation tensor associated with the deformation gradient F and u is the right stretch tensor. c Show that T h U Problems 347 where h UH U LT Since c u2 therefore we may write T f C 6 Newtonian viscous Fluid Substances such as water and air are examples of a fluid. Mechanically speaking they are different from a piece of steel or concrete in that they are unable to sustain shearing stresses without continuously deforming. For example if water or air is placed between two parallel plates with say one of the plates fixed and the other plate applying a shearing stress it will deform indefinitely with time if the shearing stress is not removed. Also in the .
