During my masters I have develop two finite element analysis (FEA) software’s in python. Commercially available solutions render acceptable results, and are much less time consuming that designing your own platform. However, doing so provides you a deeper insight into finite elements analysis. Additionally, for some situations not contemplated by the commercial software, developing your own solutions can come in handy.
A heat conduction problem on a square domain with a circular exclusion is considered. The temperature field of the system under a heat source is computed via FEA. The software generates a 2D mesh with either linear or quadratic elements. The mesh can be refined, decreasing the element size.
Various phenomena occurring at the macroscopic engineering scale originate from the physics and material mechanics of the underlying micro-structure. The overall behavior of macro-heterogeneous materials strongly depends on the properties of the micro-structure.
A computational homogenization algorithm links the micro-structure to the macro-scale. The micro-structure is modeled in sufficient detail in a so-called representative volume element (RVE). In this way, the complete complex behavior of the micro-structure is taken into account in the structural behavior of the specimen.
In this model the plastic behavior of an "L" shaped specimen under an imposed displacement is analyzed (both isotropic and kinematic hardening). This behavior is non-linear. To solve the problem, incremental displacements are taken, and the stiffness matrix is updated in every iteration (non-linear solver).
The meshes are generated with external software.
Macroscopic scale
Microscopic scale
Results for microscopic scale.
Results for several materials in the macroscopic scale.