stress tensor3

# stress tensor3 - 12.005 Lecture Notes 3 Tensors Most...

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12.005 Lecture Notes 3 Tensors Most physical quantities that are important in continuum mechanics like temperature, force, and stress can be represented by a tensor. Temperature can be specified by stating a single numerical value called a scalar and is called a zeroth-order tensor. A force, however, must be specified by stating both a magnitude and direction. It is an example of a first-order tensor. Specifying a stress is even more complicated and requires stating a magnitude and two directions—the direction of a force vector and the direction of the normal vector to the plane on which the force acts. Stresses are represented by second- order tensors. Stress Tensor Representing a force in three dimensions requires three numbers, each referenced to a coordinate axis. Representing the state of stress in three dimensions requires nine numbers, each referenced to a coordinate axis and a plane perpendicular to the coordinate axes. Returning to determining traction vectors on arbitrary surfaces. Consider two surfaces S 1 and S 2 at point Q. Figure 3.1 T (1) S 1 Q S 2 T (2) Q n 1 n 1 ramp n 2 n 2 page Example Figure by MIT OCW.

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Tractions at a point depend on the orientation of the surface.
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stress tensor3 - 12.005 Lecture Notes 3 Tensors Most...

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