2. At a given time the motion of a continuous medium is defined by (A is a constant parameter): x₁ = X₁ - AX3 x2 = X₂ - AX3 x3 = -AX₁ + AX2 + X3 (a) Obtain the material deformation gradient tensor F(X,t) at this specific time. (b) By means of the inverse equation of motion, obtain the spatial deformation gradient tensor F¹(x, t). Verify that F-F¯¹ = 1.
(c) Determine the conditions under which the motion constitutes an infinitesi- mal strain tensor for this case and obtain the infinitesimal strain tensor. (d) Obtain the material and spatial strain tensors. (e) Compare the results from (c) with the strain tensors of (d) by taking into account the infinitesimal hypotheses.
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