Continuum Mechanics: Short Review
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Quiz
After reviewing the linked material, try to answer these questions.
Try to state the meaning of deformation gradient. Is its formal definition consistent with your understanding?
$$
\mathbf{F} = \frac{d\mathbf{x}}{\mathbf{X}}
$$
Try to state the meaning of stress. How is it related to traction? Why is it a rank 2 symmetric tensor
$$
\mathbf{t} = \boldsymbol{\sigma} \cdot \mathbf{n}.
$$
Write down the mass balance equation in the differential and the integral form in the spatial coordinate system.
Write down the linear momentum balance equation in the differential and the integral form in the spatial coordinate system.
Write down the energy balance equation in the differential and the integral form in the spatial coordinate system.
Write down the constitutive relations for linear elasticity in the spatial coordinate system.