## FEA for beginners (Part IV): Material models

Every time you use Finite Element Analysis you need to assign a material model to all the components. Since there are plenty of them, one question arises: which one should you use for your particular case?

To begin with, there might be more than one material model which can provide an accurate solution to your problem. However, it is likely that one of them will present some advantages when compared to the others, such as computational time or the number of parameters which have to be defined. When you have spent time working with a certain kind of material (e.g. metals) you will have gained some experience that will help you choosing between different options whenever you face a similar Finite Element model. But, what happens when you are new and you don’t know where to start?

If you don’t know anything about the topic (and even if you think you know everything), my honest advice is to read the official documentation of the FE package that you are using. It doesn’t matter if it is Abaqus, LS-DYNA or ANSYS. Those documents are there for you to use them! In fact they are quite complex and sometimes extremely hard to understand, but even the best FE analysts use them all the time! And this applies to all the other options that you will need to define for your FE model. For example, the LS-DYNA manuals are available online in PDF format and, from my point of view, they are well organised (i.e. keyword, materials, theory…). On the other hand, Abaqus documentation is a website where you search for an specific topic. Then you can see other useful links which are related to that topic, as well as some theoretical background. I’m not going to lie, they are not easy to read and it takes a while before you get familiar with them. But trust me, they are worth it.

Once you have found a few material models which you think can work, it is the time for you to learn how they work. This is extremely important! Don’t be lazy and try to understand the numerical approach which is behind each material model. Then you will see what parameters are required and if they are trying to simulate a behaviour which is much more complex than the one you are interested in. Hopefully, by doing this you will be able to reduce the number of possible options and, what is more important, you will be able to identify potential errors in your model. In addition, reading the theoretical information will help you to find all the parameters that you need to define and, sometimes, how they should be obtained or the standard that should be followed for obtaining them experimentally. Hence, you will have to run several cases paying attention to some details such as the step time, computational time, complexity of the model compared to the accuracy that you want to achieve…

If you follow this way of proceeding, you will find it “easy” to extrapolate it to other options of your FE model. For instance, if you are studying composite materials you will probably have to define a failure criterion so in order to select the most suitable one, you may find this methodology useful. Another example could be the debonding of two components, since there are different ways for creating that effect.

In order to illustrate these ideas, let me introduce a relatively simple material model which I find particularly useful for simulating metals: the Johnson-Cook model. This numerical model considers three relevant features which affect the material behaviour: strain hardening, strain rate ad thermal softening. Based on the results of the experiments that the two authors conducted on twelve different materials, an efficient equation was developed:

Where: A is a constant equal to the yield stress of the material; B, C, m and n are constants; e is the equivalent plastic strain; e* is the effective normalised strain rate; T* is the homologous temperature.

Johnson and Cook provided enough information about how to extract the parameters mentioned above from the experimental data. This constitutive model is very implemented in every single FE package and, depending on the one you are using, you may find a simplified version where the last term of the equation is omitted (i.e. the temperature effect is neglected or not relevant for the case studied). Nevertheless, as I said before, you should read the whole publication in order to identify a very important feature of this model: after the ultimate tensile strength (UTS), the numerical model diverges from the experimental results. This is explained because the researchers were only interested in the region which is prior to the UTS. According to them, that rage of strain is only relevant when the deformation before the failure occurs is studied.

With that last example, I hope you have understood that not only knowing which material model you will use, but also understanding why that particular model is applicable to your case, are equally important.