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Strain Energy | Overview and Formula Derivation

What is Strain energy?


Strain Energy is defined as the internal work done to deform a body by the action of externally applied forces.


Let’s say we have an axially loaded bar on which load is applied gradually which increases from 0 to P and due to this load the length of the bar increases by ΔL. The external work done by the applied load will be given as:

External work, W = Average load x Displacement = P/2 x ΔL


Why are we interested in strain energy?


The elastic body has a property - it can store this energy when some external force is applied and this energy can be recovered when this external force is removed - so this energy becomes usable to us.


Strain Energy Formula Derivation




If we assume that there is no energy loss or in other words, if this is a perfectly elastic body then we can say this external work done is equal to internal work done.


For a perfectly elastic material, External work done = Internal work done


​According to the definition, internal work done is the strain energy stored.


Strain energy = P/2 x ΔL = 𝜎A/2 x 𝜖 x L = 𝜎/2 × 𝜖 × V = 𝜎/2 × 𝜎/E × V = 𝜎2/2E×V


For unit volume, strain energy U = 𝜎2/2E = P2L/2AE


From the above formula, we can see that strain energy/volume is directly proportional to the square of stress applied and inversely proportional to the modulus of elasticity of a material.


The SI unit of strain energy is Joules/m3.


Now watch this video to visually understand the concept of strain energy and other concepts more clearly.



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