Von mises stress what is it

We hope this article has shed some light onto what it actually is and where it came from, such that next time you look at an FEA output database, you can visualize the image above and how it relates to the stress states within your analysis. And please look forward to more simulation related content here at the Fidelis Blog.

Huber, M. Von Mises, R. Gottingen , pp. Hencky, H. What Is von Mises Stress? Recent Posts See All. And Which Should You Use? Post not marked as liked 1. Post not marked as liked 5. What Is Finite Element Analysis? Using this information an engineer can say his design will fail, if the maximum value of Von Mises stress induced in the material is more than strength of the material.

It works well for most cases, especially when the material is ductile in nature. In the following sections we will have a logical understanding of Von Mises stress and why it is used.

One of the most easy way to check when a material fails is a simple tension test. Here the material is pulled from both ends. When the material reaches the yield point for ductile material the material can be considered as failed. The simple tension test is a unidirectional test, this is shown in the first part of Fig Now consider the situation in second part of Fig. Can we say here also, that the material fails when the maximum normal stress value induced in the material is more than the yield point value?.

We will explore what Von Mises stress is in the coming section. The concept of Von mises stress arises from the distortion energy failure theory. Distortion energy failure theory is comparison between 2 kinds of energies, 1 Distortion energy in the actual case 2 Distortion energy in a simple tension case at the time of failure. According to this theory, failure occurs when the distortion energy in actual case is more than the distortion energy in a simple tension case at the time of failure.

It is the energy required for shape deformation of a material. This is like scaling an object. In contrast, deviatoric strain corresponds to the shearing and distortion effects observed.

Now that we understand the idea of volumetric and deviatoric strains, we can go ahead and define the distortion energy. We should always remember that the mechanical behavior of materials is also governed by the two laws of thermodynamics. As per the first law of thermodynamics, energy is neither created nor destroyed.

It is only converted from one form to another. So, when a mechanical force acts on a body or upon application of a prescribed displacement , some work is being placed on the body. This energy is stored in as strain energy in the body. Strain energy density is defined as:. In other words, this is the total strain energy stored in each differential volume of the body. If this strain energy is summed over all the differential volumes or otherwise called integration over the entire volume , we can obtain the total strain energy stored in the body.

Out of this total energy, a part goes into changing the volume of the material or volumetric strain and is otherwise known as volumetric energy. The rest of the energy is used to distort the shape of the material and is otherwise known as deviatoric energy. The von Mises stress is related to this total stress component going into the distortion energy. Or in mathematical terms:. However, the product of any volumetric and deviatoric tensor is always zero.

Thus, the strain energy density reduces to:. The representative stress here is the von Mises stress. Taking a leaf out of the 1-D stress state, the von Mises stress can be rewritten as:. The next important issue to consider is the idea of principal stresses. In a generic situation, the stress is a full symmetric matrix. In this situation, it is difficult to make design decisions considering data from simple uniaxial experiments.

However, in any situation, there will exist a plane that is subjected to pure volumetric loading. Rotating a general stress tensor leads to a diagonal matrix. The diagonal elements are known as principal stresses.

You can attend our free on-demand FEA Master Class and get a practical grasp of this interesting topic! The three principal stresses can be treated as coordinates and the resulting von Mises stress can be plotted.