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The journey to tensors begins with scalars and vectors.

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Cauchy Stress Tensor

\begin{bmatrix} \sigma_x & \tau_{xy} & \tau_{xz} \\ \tau_{yx} & \sigma_y & \tau_{yz} \\ \tau_{zx} & \tau_{zy} & \sigma_z \end{bmatrix}

Any force that causes a stress can be broken down into two component forces, a normal force and a shear force.

Notation

 \tau_{xy}

The first symbol, the x, tells you the shear is moving in the x direction; the y tells you it is the plane normal to the y direction, the xz plane.

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