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2. A unit cube of incompressible isotropic material undergoes the following deformation 1X1, x2 = 1-1X2, X3 = X3. For this material, the Cauchy stress
2. A unit cube of incompressible isotropic material undergoes the following deformation 1X1, x2 = 1-1X2, X3 = X3. For this material, the Cauchy stress is given as X1 = o=-p1 + 2C1B 2C2B-1, where p is a scalar, C1, C2 are positive constants and B is the left Cauchy-Green deformation tensor. Find the stress components and determine the total loads F1, F2, F3 acting on the faces normal to the 21, X2, X3 directions. [4 marks] Show that when C1 > 3C2, there are three values of for which the body is in equilibrium with F1 = F2 = F3 and find these values. [6 marks] 2. A unit cube of incompressible isotropic material undergoes the following deformation 1X1, x2 = 1-1X2, X3 = X3. For this material, the Cauchy stress is given as X1 = o=-p1 + 2C1B 2C2B-1, where p is a scalar, C1, C2 are positive constants and B is the left Cauchy-Green deformation tensor. Find the stress components and determine the total loads F1, F2, F3 acting on the faces normal to the 21, X2, X3 directions. [4 marks] Show that when C1 > 3C2, there are three values of for which the body is in equilibrium with F1 = F2 = F3 and find these values. [6 marks]
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