New Horizons

In this entry, I'll briefly speak about computing robustly the deformation on a given object represented by a Finite Element mesh. There are a handful of methods to do that more or less robustly, and I'll just discuss them, with a speaking a little bit about their distinctive aspects. Classic lagrangian formulation The most used one in industrial commercial packages (like abaqus, ansys, etc). This is simply a linearization of Green-Lagrange strain tensor and deriving it to get the proper residual and stiffness matrix from one single Newton step. This method is absolutely rigourous, meaning that as long your mechanical behavior is well captured by the strain model  you'll get reliable results. However it has two main drawbacks: first you have to be careful when applying new forces or constraints and do it incrementally otherwise you may really blow up your model. For instance applying too much force will cause some elements to invert which won't be re-inverted thanks