DERIVATION OF ELASTIC STRAIN ENERGY

According to quantum physics, it can be stated that strain energy is determined as the stored energy in an object up to its limit of elasticity. In simpler words, derivatives of strain energy can be denoted as the stored energy in a body due to deformation force. Resilience is another term used to determine strain energy. “N-m” or Joules is the SI unit of strain energy. The differentiation formula of “strain energy” is “U = σ2 / 2E × V”. Strain condition of a body occurs when the deforming force results in a change in its size and shape. “ε = Change in dimension/Original dimension = Δx/x.” is the differentiation formula of strain derivatives.

“Elastic strain energy”: Overview

In context to the “derivatives” of strain energy, it can be stated that the energy, which is associated with the extension of an elastic object or the compression state, is devoted as “elastic potential energy”. For example, in the case of spring, which mainly adds a spring force “F = – kx”, when it consists of a free end and has “x” as displacement, then “U(x) = ½ Kx2” will be the “elastic potential energy” of spring. According to the differentiation formula of strain derivatives, the configuration of spring when it is in relaxed length is denoted as “x = 0; U= 0”. 

“Elastic strain energy”: Derivatives

In the year 1660, a specific law of elasticity named Hooke’s law was established by Robert Hooke, one of the famous English scientists. According to Hooke’s law, it can be stated that for relatively smaller objects, which are in their deformation state, the size or displacement of deformation is proportional to the body’s load or deforming force directly. In the context of derivatives of “elastic strain energy”, it can be determined that energy strain is the stirred energy in an object due to deformation or external forces. 

• In an integration process of strain energy, it has been observed that on incorporating an applied force over a beam’s length, a constant expression is mainly obtained. 
• The energy strain/ unit volume is denoted as the density of the energy strain. 
• The area of the body that is covered under strain-stress curving towards the deformation point is also denoted as the energy of tensile strain. 
• In order to bring the entire system of the elastic body into its original size and shape it is important to release the applied force.

Strain energy in respect to limit of elasticity

In context to derivatives of strain energy, it can be stated that when a body’s shape and size change under a pressure of an external force, then that body undergoes a strained condition. The strain of a body is considered when the changes take place in its unit size. For example, in the case of a suspended wire when its original length is increased under pressure of an applied load, then in that situation-ratio of increased length to the original wire’s length is devoted as strain. The ratio of strain generally has no limit. In order to recover the original shape and size of the elastic bodies, deforming forces are applied to the bodies in the form of external forces. The differentiation formula of strain is provided as “Strain = Δ L L = Change in Length Original Length”. The properties of these elastic bodies show a certain value of their deforming force. If the rate of deforming force is gradually increased then the body will reach a state where it can never get back to its original shape or size and its elastic property will be destroyed. 

The differentiation formula of elastic strain energy

In the context of the differentiation formula of strain energy, it can be stated that a deformable structure like stretches and springs generally stores a specific kind of energy, which is known as strain energy. The differentiation formula of strain is provided as “Strain = Δ L L = Change in Length Original Length”. 

Conclusion

In context to derivatives of “elastic strain energy”, it can be stated that the differentiation formula of “strain energy” is “U = σ2 / 2E × V”. A body is denoted as in its strain condition when a body’s shape and size change under pressure of an external force. It has also been understood that the limit of elasticity is the state when a body reaches its maximum elastic state by incorporating deforming force, when that force increases the elasticity of that body is gradually destroyed, and it can never get back to its original size and shape.