The purpose of this blog post is to provide an introduction to the wide array of materials that we can model using Abaqus (and many other FEA solutions). Since materials behave in wildly different ways in the real world, it’s important that we can capture these in our simulations accurately and efficiently.

## Introduction To Material Models In FEA

We encounter a wide variety of materials when carrying out stress analysis problems. For example, metals behave quite differently than rubbers. Composites are a combination of multiple materials and cellular structures respond differently again to applied load. To add to that, material models need to account for the particular range of physics that we’re looking to simulate. If we’re running a static linear analysis of a steel structure, it is reasonable to assume that all we’ll need to represent is the isotropic, linear-elastic aspect of the material behavior. On the other hand, if we’re looking at the thermal behavior of a polymer that is stressed over the course of a long period of time, we’ll need to include temperature and viscoelastic dependence of a highly nonlinear material.

Additionally, we can consider failure of materials and split or remove the elements that represent them in order to model damage. Fatigue behavior can also be assessed by cycling the load in the simulated material multiple times, with differing response occurring during each cycle.

Sufficed to say, the complexity of the material model must match the physics that we are trying to understand.

## Range Of Material Models In Abaqus

When carrying out finite element analysis, we are not really modeling the real material behavior. For instance, the dislocation motion is not actually occurring in a typical metal plasticity model. Rather, we use constitutive models, where a mathematical representation of the expected behavior under load is developed and implemented. From a mathematical perspective, the implementation of a constitutive model involves the integration of the state of the material within an element over a particular time increment, at least in a nonlinear analysis.

Abaqus is capable of simulating many different types of materials and material behavior, some of which are summarized in the list below:

- Linear elasticity
- Nonlinear elasticity, which is common in rubbers and foams – The material has no permanent deformation, but it does not follow linear stress-strain behavior
- Plasticity – Allows us to model permanent deformation under load
- Composite behavior – Where two or more materials are combined in order to provide the ‘best of both worlds’ – think carbon fiber as a great example
- Concrete type behavior – Where strength is different in tension and compression
- Viscous behavior – Where a material either extends or relaxes over long periods of time under load or stress, respectively
- Thermal response – In terms of both heat flux and mechanical behavior based upon temperature
- Electrical response
- Gasket behavior – Where nonlinear compression is important

Many of these behaviors can be combined within a single material model, and all of these models/features can be either isotropic, meaning independent of direction, or anisotropic, meaning direction dependent.

Below are a few examples of stress-strain behavior for some of the more commonly utilized material models with Abaqus:

## Advanced Material Modeling Methodologies

Sophisticated Abaqus users can take advantage of the unrivalled versatility of the software to push the boundaries of material modeling. Below are a couple of examples of how we might do this.

### User Subroutines

Although the library of material models built into Abaqus is vast, highly complex simulations may need to utilize material models that are not available – the library is far from comprehensive. An example might be the phase change behavior of a steel during fast cooling, where volume change between austenite and martensite is important. In those cases, we can actually develop our own material models by way of user subroutine.

So called UMATs allow the user to code material models to essentially do whatever they want, where the level of complexity possible is essentially endless. In Abaqus, user subroutines are implemented using Fortran code.

### Unit Cell Modeling

Let’s imagine that you have a complex material like a particle reinforced composite, or you’re trying to model the anisotropic behavior of a metal based on the crystal plasticity structure, you might not know what the constitutive behavior looks like beforehand without robust physical test data. You may, however, know exactly how each individual component/cell of the material (resin, reinforcement, grain etc.) behaves on its own.

Of course, it would be impossible to build a complete FEA model of a structure with accurately represented individual grains of metal; it would simply be too large (at least with today’s computing power). In this case, it may be valuable to model a ‘unit cell’ of the overall makeup of the material. This way, it is possible to extract the overall constitutive behavior – based on measuring various responses of the unit cell under loading. We can then develop a mathematical model and implement it in a user subroutine such that the true behavior of the material in our structure can be simulated efficiently with a reasonable number of nodes and elements.

## How To Choose A Material Model

Choosing a material model for your FEA analysis is not necessarily an easy task. Sure, if you’re dealing with an isotropic metal, there’s probably an easy solution for that. But if the material that you’re simulating is unusual in any way, then it takes some more thought.

This is where the analyst earns their salt. It really comes down to understanding the behavior that you’re looking to replicate and selecting a model that represents that the best. It’s not always necessary to go ‘by the book’. For example, a fibrous mat that has much higher strength in compression than tension might be well represented by a model that was originally developed for concrete, such as the Drucker-Prager plasticity model.

And if all else fails, the advanced methodologies outlined above allow you to generate your own bespoke models with an almost limitless degree of complexity. That is one of the things that makes Abaqus such a robust solver for all manners of engineering challenge.

## Final Thoughts

This article has laid out the basic gist of material models available in Abaqus and many other FEA solvers. Hopefully it provides at least a cursory roadmap to selecting the correct model for the physics at hand.

If you’d like to learn more from the experts at Fidelis, or have any other engineering simulation related questions, don’t hesitate to ,**reach out to the team** and we’ll be sure to point you in the right direction!