Image-based finite element mesh construction for material microstructures

One way of computing the macroscopic behavior of a material sample with complex microstructure is to construct a finite element model based on a micrograph of a representative slice of the material. The quality of the results produced with such a model obviously depends on the quality of the constructed mesh. In this article, we describe a set of routines that modify and improve the quality of a 2D mesh. Most of the routines are guided by an effective element “energy” functional, which takes into account the shape quality of the elements and the homogeneity of the elements as determined from an underlying segmented image. The interfaces and boundaries in the image arise naturally from the segmentation process. From these routines, we construct a close-to-automatic mesh generator that requires only a few inputs, such as the linear sizes of the largest and smallest features in the micrograph.