Final answer:
Strain energy is the potential energy stored due to deformation of a material. It relates to the internal restoring forces which are represented by stress tensors that resist deformation and lead to energy storage within the material.
Step-by-step explanation:
Strain energy is a type of potential energy that is stored in a system due to the deformation of the system from its equilibrium state. The strains in an elastic material generate internal forces that resist deformation and seek to return the system to its unstrained state. This is analogous to the elastic potential energy stored in a simple harmonic oscillator, as described by Hooke's Law. According to physics principles, when a material is deformed, the internal restoring forces, often explained by stress tensors in the field of material science, work to recover the original shape and in this process store energy internally.
The energy concept is essential when considering the response of materials to mechanical stress and when analyzing phenomena such as shape memory effects or the behavior of polymeric gels. In the study of strain energy, both elastic free energy per unit volume and the related stress tensors are important for understanding how materials can store and release energy upon deforming and returning to their original shapes.