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Understanding the history of the von Mises yield criterion: Why is it called the Maxwell–Huber–Hencky–von Mises theory?
In materials science and engineering, the von Mises yield criterion is an important theory for analyzing plastic behavior, especially for ductile materials such as metals. The theory tells us that when the second invariant J2 of the deviatoric stress of a material reaches a certain critical value, yielding will begin to occur. This theory originated in the 19th century and has been developed by many scholars to form what is known today as the "Maxwell–Huber–Hencky–von Mises theory."
The core idea of von Mises theory is that the yield behavior of a material is closely related to the stress state it is subjected to, especially the combined state of torsion and tension.
The theory dates back to 1865, when James Clerk Maxwell proposed some basic conditions in a letter to William Thomson (later Lord Kelvin). His work was only preliminary and did not describe the yielding criterion in detail.
In 1913, Richard von Mies began to give the theory a more rigorous mathematical formulation. He emphasized that the conditions under which a material begins to yield depend on the quadratic invariant of the deformation energy, which makes the von Mises yield criterion increasingly important in describing the response of materials. Von Mies' contribution enabled this theory to be clearly defined and applied in practical engineering.
The literature mentions that Tytus Maksymilian Huber proposed a similar idea in Polish in 1904 and linked it to torsional deformation energy.
Working independently in 1924, Heinrich Henke also arrived at the same yield criterion. Together, these studies laid the foundation for von Mises theory, which enables us to predict the yield behavior of materials under complex loading.
The von Mises yield criterion does not depend on the first invariant of stress, which makes it valid for any static and dynamic stress state. This is of great significance in the field of engineering, especially in analyzing the behavior of metals under multiaxial loading. Due to the greater diversity of stress states, a single yield criterion can provide us with a concise basis for judgment.
The von Mises stress satisfies the property that two stress states with equal deformation energy have equal von Mises stresses.
In engineering practice, von Mises stress can be used to predict the yield of materials under different loading conditions. Taking the state of a steel beam under compression and a steel shaft under torsion as an example, although the two samples are made of the same material, their stress states are different, and it is impossible to simply judge which one is closer to the yield point by observation. However, using the von Mises yield criterion, we can easily make comparisons because the single value of the von Mises stress reflects the actual yield behavior.
Ultimately, the von Mises yield criterion is not only a mathematical formula, but also a tool to gain a deeper understanding of material behavior. The development of this theory not only demonstrates the continuous progress of the scientific community, but also allows engineers to be more confident when designing and using materials because they have more accurate analytical tools to predict changes in material performance.
With the development of science and technology, our understanding of materials science has become deeper and deeper, which also prompts us to think: Under more complex loading conditions, is the von Mises yield criterion still the only standard?
