In this post, we compute numeric values of the apparent stiffness introduced in this post. Our goal is to find the solution to the general problem depicted below.
We use a numeric approach that is akin to the finite element method. More precisely, we minimize the total potential energy of …
In this post, we compute symbolic expressions of the apparent stiffness introduced in this post. Our goal is to find the solution to the general problem depicted below.
We consider a simplified case, where the mesh is square and vertical and horizontal springs have equal stiffnesses …
In the previous instalment of this series on homogenization, we derived the homogenized properties of a rectangular spring mesh. Our goal in this post is to analyse the “convergence” towards the homogenized stiffness; meanwhile, we will discuss the size of the so-called representative volume element (RVE).
In the previous instalment of this series on homogenization, we discussed volume and ensemble averages for random heterogeneous materials. In view of introducing statistical and representative volume elements, we will introduce in this post our first homogenization example, namely a two-dimensional, rectangular mesh of springs that is loaded in its …
In the previous instalment of this series on homogenization, we discussed homogenization of a distribution of black dots on a white background to a uniform shade of gray. In that example, homogenization boils down to evaluating the fraction of the total area occupied by the dots: this is the so-called …
In the previous instalment of this series, we introduced homogenization and the separation of scales. In the present post, we will discuss two strategies to carry out homogenization: the experimental and the theoretical approaches. To do so, we will again use the analogy with the halftoning technique.
Remember that we …
Most of my research activities deal with upscaling the mechanical properties of heterogeneous materials. This is also known as homogenization. So what is homogenization? This series explores this question; it is largely based on the introduction to my Habilitation defense.
In order to introduce homogenization, we will draw inspiration from …