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You’ve reached the blog of Sébastien Brisard. My most recent posts are listed below. A full list of posts can be found in the “Archives” section. If you are wondering why this blog is relatively “low-tech”, read the “About this blog” section.

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I hope you will enjoy reading this blog!

13 May 2021 — Numerical analysis of a spring mesh

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.

The problem considered here

We use a numeric approach that is akin to the finite element method. More precisely, we minimize the total potential energy of …

12 May 2021 — Symbolic analysis of a spring mesh

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.

The problem considered here

Outline of the derivation

We consider a simplified case, where the mesh is square and vertical and horizontal springs have equal stiffnesses …

26 April 2017 — New paper on Discrete Digital Projections Correlation

Our paper “Discrete Digital Projections Correlation: a reconstruction-free method to quantify local kinematics in granular media by X-ray tomography” has recently been published in Experimental Mechanics. The abstract is reproduced below

We propose a new method to measure the translations and rotations of each individual grain in a granular material …

23 February 2017 — New paper out!

My paper “Towards improved Hashin--Shtrikman bounds on the effective moduli of random composites” has recently been published in Mechanics & Industry. The abstract is reproduced below

The celebrated bounds of Hashin and Shtrikman on the effective properties of composites are valid for a very wide class of materials. However, they incorporate …

13 June 2016 — New paper

My paper “Reconstructing displacements from the solution to the periodic Lippmann--Schwinger equation discretized on a uniform grid” has recently been published in International Journal of Numerical Methods in Engineering. The abstract is reproduced below

Uniform grid solvers of the periodic Lippmann--Schwinger equation have been introduced by Moulinec and Suquet for …

08 December 2015 — New paper published

My student Vinh Phuc Tran has recently had one of his papers published in Mechanics of Materials. The paper is called Stochastic modeling of mesoscopic elasticity random field. The abstract is reproduced below

In the homogenization setting, the effective properties of a heterogeneous material can be retrieved from the solution …

19 February 2014 — On the double dot product

The double dot product of two tensors is the contraction of these tensors with respect to the last two indices of the first one, and the first two indices of the second one. Whether or not this contraction is performed on the closest indices is a matter of convention. In …

31 January 2014 — The elastic acoustic tensor and its inverse

In this post, I will introduce the acoustic tensor of linearly elastic materials. Closed-form expressions of the inverse of this tensor can be derived in the case of isotropic materials. This will later come in handy to derive closed-form expressions of the periodic Green operator for strains.

We consider a …

02 January 2014 — Extract images from PDF files

I recently scanned a document as a PDF file, and I wanted to retrieve the embedded images. I really mean extract the images, and not convert the pages of the document to images (which would entail loss of data). There is a nice command-line tool to do that: pdfimages, which …

05 November 2013 — New accepted manuscript

One of my manuscripts has just been accepted for publication in the International Journal of Solids and Structures. It is called A variational form of the equivalent inclusion method for numerical homogenization. The abstract is reproduced below

Due to its relatively low computational cost, the equivalent inclusion method is an …

31 August 2013 — New accepted manuscript

It is my pleasure to announce that one of my papers has recently been accepted for publication in the Journal of the Mechanics and Physics of Solids. It's called New boundary conditions for the computation of the apparent stiffness of statistical volume elements.

It introduces a new set of boundary …