Strain Energy Calculation With The Principal Stresses

Strain energy is a very important aspect of classical mechanics. Stored strain energy can be calculated in different methods. One method is the calculation of strain energy with the principal stresses. But you need to calculate the principal stresses first, to use them in the calculation of strain energy of the system. 

Strain Energy Due To The Principal Stresses

Principal stresses on a cubic unit volume(Image Source:D. K. Singh – Strength of Materials-Springer, 2020, pg.418).

For the triaxial system, you will have three different principal stresses. And for biaxial systems, you will have two different principal stresses. According to the system that you are dealing with, you need to use proper calculation. 

Stored Strain Energy For Biaxial Systems

In biaxial systems, the third principal stress value which is also denoted as σ3 is neglected. In this case, you need to be calculated the σ1 and σ2 values. You can use the calculator below to calculate the total stored strain energy for your system; 

Strain Energy Calculator Of Biaxial Principal Stresses

In this calculator, you just need to enter the required values. Then click on the ‘Calculate!’ button to see the result. You can also click on the ‘Reset’ button to perform another calculation. 

In this calculator; ‘σ1’ and ‘σ2’ values are the principal stress values of the biaxial system. Enter the elasticity modulus of the material. The volume that you want to calculate the total strain energy, which undergoes these principal stresses. Enter the Poisson’s ratio of the material. 

You can use the suggested units in parentheses to obtain the result.

Stored Strain Energy Calculation For Triaxial Systems

The difference of this calculator is that there is an additional ‘σ3’ value because of the triaxial system.

Strain Energy Calculator Of Triaxial Principal Stresses


As you see above that calculation of the stored strain energies in bodies is very simple with the calculators above. 

Mechanicalland does not accept any responsibility for calculations made by users in calculators. A good engineer must check calculations again and again.

You can find out much more calculators like this in Mechanicalland! Take a look at the other engineering calculators available in Mechanicalland!

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