According to the given question, the Maximum Shear strain Energy theory was postulated by Von Mises. Below is a detailed explanation of this theory.

Theory of Maximum Shear Strain Energy:
The Maximum Shear Strain Energy theory, also known as the Distortion Energy theory or Von Mises theory, is a criterion used to determine the yielding and failure of ductile materials under complex stress conditions. It is based on the assumption that failure occurs when the elastic strain energy per unit volume reaches a critical value.

Postulation by Von Mises:
The theory was postulated by Richard von Mises, an Austrian-born mathematician and physicist, in 1913. Von Mises proposed this theory as an extension of the Tresca's maximum shear stress theory, which was limited to materials with isotropic behavior.

Basis of the Theory:
The Maximum Shear Strain Energy theory is based on the concept that failure occurs when the distortion energy per unit volume exceeds a certain limit. Distortion energy is the energy required to distort or deform the material, and it is related to the shear strain energy.

Shear Strain Energy:
Shear strain energy is the energy stored in a material due to the application of shear stress. It is given by the equation:
Shear Strain Energy = (1/2) * Shear Modulus * Shear Strain^2

Distortion Energy:
Distortion energy is a measure of the total amount of energy required to distort the material. It is calculated using the principal stresses and is given by the equation:
Distortion Energy = (1/2) * (σ1 - σ2)^2 / Yield Strength

Critical Limit:
According to the Maximum Shear Strain Energy theory, failure occurs when the distortion energy per unit volume exceeds a critical limit. This critical limit is often taken as the yield strength of the material.

Applicability:
The Von Mises theory is applicable to ductile materials that exhibit significant plastic deformation before failure. It is commonly used to analyze the yielding and failure of materials in structural engineering, mechanical engineering, and material science.

In conclusion, the Maximum Shear Strain Energy theory, postulated by Von Mises, is a criterion used to determine the yielding and failure of ductile materials under complex stress conditions. It is based on the concept of distortion energy, which is related to the shear strain energy. According to this theory, failure occurs when the distortion energy per unit volume exceeds a critical limit, often taken as the yield strength of the material.