It´s been a while since the last time I wrote about Finite Element Analysis. For that reason, this week I would like to express some of my concerns about two material models which are available in LS-DYNA for crushable foams.
Crushable foams are widely used in the aerospace and automotive industries due to their energy absorption capabilities and their low weight. This means that companies can take advantage of those properties in order to produce lightweight vehicles, improving the efficiency in terms of fuel consumption while making the structures safer for the occupants.
In these terms, original equipment manufacturers (OEMs) normally use foams as the core of sandwich structures, in order to combine the properties of different materials. Nevertheless, both the manufacturing process and the experimental tests are usually expensive and time consuming, and this can lead to non-profitable results. Because of that, FEA has become an extremely powerful tool for analysing and predicting the behaviour of structures. The fact that the set up of the FE models usually requires simple tests reduces the cost of the process, even more if we take into account that once the models are validated, they can be used for predicting other type of scenarios which would be extremely expensive to test in reality.
However, as I already stated in previous posts, we have to be aware of the capabilities of the material model that we are planning to use. Why am I repeating this again? Well, basically because I have found some dangerous assumptions in two foam material models within the commercial FE package LS-DYNA. In particular:
- *MAT_CRUSHABLE_FOAM (*MAT_063)
- *MAT_MODIFIED_CRUSHABLE_FOAM (*MAT_163)
The main difference between those two material models is that the second one allows the users to define strain rate dependency. This is crucial, since this means that if we wanted to simulate quasi-static loading cases, we would be able to use *MAT_063, reducing the computational time of the simulation. However, if we wanted to analyse a dynamic case, the results from the FE model (using *MAT_063) would be completely wrong. So, once again, we should always understand what we are trying to analyse before choosing a material model.
Apart from that, despite the fact that both models assume a perfectly elastic behaviour of the material when the component is unloaded, in reality most foams presents a certain level of degradation in terms of the stiffness. Nonetheless, this degradation is usually observed in cyclic loading cases (fatigue) and the variation can be small enough to be neglected.
Furthermore, the feature that I have found to be a potential source of dramatic errors is the way these two material models predict the tensile behaviour. According to the LS-DYNA documentation: “tension is treated as elastic-perfectly-plastic at the tension cut-off value”. That statement is not always true. As a matter of fact, foams which are loaded in tension usually exhibit a brittle behaviour (i.e. they fail after reaching their tensile stress, without a plastic region). Therefore, these models are basically considering an isotropic hardening of the foam, removing the densification region from the tensile behaviour. Other FE packages, such as Abaqus, allow the users to choose between this isotropic hardening or a more realistic volumetric hardening.
My advice is that we should always look at the theory behind these wonderful numerical models. Otherwise, we could be obtaining results which are completely wrong, wasting time and resources and, what is more dangerous, increasing the risk of serious accidents in real life due to engineers’ negligence.