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Deep within the earth what force is so great that a rock behaves like a stretched rubber band?

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pressure

The amount of stress on a rock may be greater than the rocks strength. In that case, the rock will undergo strain or deformation   Figure below  . Deep within the Earth, the pressure is very great. A rock behaves like a stretched rubber band. When the stress stops, the rock goes back to its original shape. If more stress is applied to the rock, it bends and flows. It does not return to its original shape. Near the surface, if the stress continues, the rock will fracture  rupture  and break.

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