Question

2. The displacement vector of a continuous medium is given as follows: \textbf{u} = 0.2\textit{t} \textit{X}\textsubscript{2} \textbf{e}\textsubscript{1} + 0.3\textit{t} \textit{X}\textsubscript{2} \textbf{e}\textsubscript{2} - 0.1\textit{t} \textit{X}\textsubscript{1} \textit{X}\textsubscript{2} \textbf{e}\textsubscript{3} d. For the particle initially located at (1, -1, 2) determine below questions when the particle is at \textit{t} = 2; i. Determine the deformation gradient, Green, Cauchy, Piola, and Finger deformation tensors, as well as the Lagrange and Euler strain tensors. ii. Calculate the direction of the vector \textbf{n} = [1, 1, -1]\before deformation, and the stress and unit strain along this direction.

          2. The displacement vector of a continuous medium is given as follows:
\textbf{u} = 0.2\textit{t} \textit{X}\textsubscript{2} \textbf{e}\textsubscript{1} + 0.3\textit{t} \textit{X}\textsubscript{2} \textbf{e}\textsubscript{2} - 0.1\textit{t} \textit{X}\textsubscript{1} \textit{X}\textsubscript{2} \textbf{e}\textsubscript{3}
d. For the particle initially located at (1, -1, 2) determine below questions when the particle is at \textit{t} = 2;
i. Determine the deformation gradient, Green, Cauchy, Piola, and Finger deformation tensors, as well as
the Lagrange and Euler strain tensors.
ii. Calculate the direction of the vector
\textbf{n} = [1, 1, -1]\before deformation, and the stress and unit strain
along this direction.

2. The displacement vector of a continuous medium is given as follows:
u = 0.2t X2 e1 + 0.3t X2 e2 - 0.1t X1 X2 e3
d. For the particle initially located at (1, -1, 2) determine below questions when the particle is at t = 2;
i. Determine the deformation gradient, Green, Cauchy, Piola, and Finger deformation tensors, as well as
the Lagrange and Euler strain tensors.
ii. Calculate the direction of the vector
n = [1, 1, -1]deformation, and the stress and unit strain
along this direction.

Added by Samuel S.

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