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Residually Stressed Elastic Solids

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Most of elasticity has been built on the assumption that when you remove all load off a solid (free boundary conditions), it will relax to a “natural” configuration, where the stress throughout the body will disappear. Using this we can stipulate the potential energy as a function of the stretch, which works much like in a 3D spring; the more you stretch it the higher potential energy.

Sadly, experiments have shown that biological materials care not for this assumption: they are in a constant state of stress, even when removing all external load the solid retains a residual stress in their interior. How then do we design a coherent potential energy function?

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