4. Consider the following tetrahedron X A (1,0,0) C(0,0,1) 0 (0,0,0) B (0,1,0) The tetrahedron undergoes...

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4. Consider the following tetrahedron X A (1,0,0) C(0,0,1) 0 (0,0,0) B (0,1,0) The tetrahedron undergoes the homogeneous deformation x=1.01X1-0.02X2 x2 = 0.98X2 0.01X3 x3 = 1.02X3 (a) Determine the deformation gradient F, displacement , displacement gradient H, right Cauchy- Green strain tensor C, Lagrangian strain tensor L, infinitesimal strain tensor . (10%) (b) Determine the stretch ratio (dl/dL) of the line elements OA, AB and AC. (10%) (c) Consider a undeformed line element in the in the X-X2 can be expressed as follows dx=dL (cose, sine, 0) Determine the angle at which the maximum stretch ratio (dl/dL) occurs. (10%) (d) Determine the angle change of CAB. (10%) (e) Determine the volume change of tetrahedron OABC. (5%) 4. Consider the following tetrahedron X A (1,0,0) C(0,0,1) 0 (0,0,0) B (0,1,0) The tetrahedron undergoes the homogeneous deformation x=1.01X1-0.02X2 x2 = 0.98X2 0.01X3 x3 = 1.02X3 (a) Determine the deformation gradient F, displacement , displacement gradient H, right Cauchy- Green strain tensor C, Lagrangian strain tensor L, infinitesimal strain tensor . (10%) (b) Determine the stretch ratio (dl/dL) of the line elements OA, AB and AC. (10%) (c) Consider a undeformed line element in the in the X-X2 can be expressed as follows dx=dL (cose, sine, 0) Determine the angle at which the maximum stretch ratio (dl/dL) occurs. (10%) (d) Determine the angle change of CAB. (10%) (e) Determine the volume change of tetrahedron OABC. (5%)