find an expression for the energy density in terms of stress and strain
Answers
Evaluation of strain energy from stress
Evaluation of strain energy from stress - strain graph
“We know that when a material behaves elastically, the work done on straining it is stored as energy in it. We call this “(elastic) strain energy”. We can derive the “strain energy density (ρe)” in a material by “calculating the area under its stress - strain graph”. “The definition of the density of energy is analogous to the definition of the density of mass. It is the energy stored per unit volume (how many joules are stored in 1m3 of the material).”
“Attaching the calculation as a snap”
Where:
“F is the applied force,
E is extension obtained at force F,
A is the area of the cross section of the object and
L is the length of the object
With the knowledge of ρε we can calculate the total energy stored in an object (i.e. that given by the area under the force -extension graph) if we know the volume of the object.”