Denis Caillerie

3D analysis of paper microstructures at the scale of fibres and bonds

The evolution of paper microstructure parameters, such as porosity and fibre orientation, as a function of papermaking conditions is most often studied at a macroscopic scale. However, modelling the physical and mechanical properties of papers using upscaling approaches requires understanding the deformation micro-mechanisms that are induced by papermaking operations within the structure of paper fibrous networks for individual fibres and fibre-to-fibre bonds. We addressed this issue by analysing three-dimensional images of model papers. These images were obtained using X-ray microtomography. The model papers were fabricated by varying forming, pressing, and drying conditions. For each image, this analysis enabled an unprecedented large set of geometrical parameters to be measured for individual fibres (centreline, shape and inclination of the fibre cross sections) and fibre-to-fibre bonds (inter-bond distance, number of bonds per unit length of fibre, bond surface area) within the fibrous networks. The evolution of the as-obtained microstructure parameters was analysed as a function of papermaking conditions. All results were in accordance with the data available in the literature. A key result was obtained for the evolution of the number of fibre-to-fibre contacts per fibre as a function of the network density. A representative number of contacts was obtained using relatively small imaged volumes. These volumes must only contain enough fibre segments the cumulated length of which is of the same order as the mean fibre length. These results were also used to validate microstructure models for the prediction of the number of fibre-to-fibre contacts within fibrous networks.

Geometrical Modelling of the Fibre Organization in the Human Left Ventricle

The aim of the present study is to check, by means of elementary mathematical tools, a conjecture according to which myocardial fibres are geodesic curves running on some surfaces. This conjecture was first stated and experimentally checked by Streeter (1979) for the equatorial part of the left ventricle free wall. Quantitative polarized light microscopy provides measurements on fibre orientation that could lead to evidence that the conjecture remains true for the whole of the left ventricle. Study of the right ventricle is under progress.

FEM × DEM Multi-scale Analysis of Boundary Value Problems Involving Strain Localization

The paper presents a FEM × DEM multiscale modeling analysis of boundary value problems involving strain localization in cohesive granular materials. At the microscopic level, a discrete element method (DEM) is used to model the granular structure. At the macroscopic level, the numerical solution of the boundary value problem (BVP) is obtained via a finite element method (FEM) formulation. In order to bridge the gap between micro- and macro-scale, the concept of representative volume element (REV) is applied: the average REV stress and the consistent tangent operators are obtained in each macroscopic integration point as the results of DEM simulation. The numerical constitutive law is determined through the DEM modeling of the microstructure to take into account the discrete nature of granular materials. The computational homogenization method is described and illustrated in the case of a hollow cylinder made of cohesive-frictional granular material, submitted to different internal and external pressures. Strain localization is observed to occur at the macro scale in this simulation.

Nonlinear elasticity of cross-linked networks

Cross-linked semiflexible polymer networks are omnipresent in living cells. Typical examples are actin networks in the cytoplasm of eukaryotic cells, which play an essential role in cell motility, and the spectrin network, a key element in maintaining the integrity of erythrocytes in the blood circulatory system. We introduce a simple mechanical network model at the length scale of the typical mesh size and derive a continuous constitutive law relating the stress to deformation. The continuous constitutive law is found to be generically nonlinear even if the microscopic law at the scale of the mesh size is linear. The nonlinear bulk mechanical properties are in good agreement with the experimental data for semiflexible polymer networks, i.e., the network stiffens and exhibits a negative normal stress in response to a volume-conserving shear deformation, whereby the normal stress is of the same order as the shear stress. Furthermore, it shows a strain localization behavior in response to an uniaxial compression. Within the same model we find a hierarchy of constitutive laws depending on the degree of nonlinearities retained in the final equation. The presented theory provides a basis for the continuum description of polymer networks such as actin or spectrin in complex geometries and it can be easily coupled to growth problems, as they occur, for example, in modeling actin-driven motility.

Spontaneous polarization in an interfacial growth model for actin filament networks with a rigorous mechanochemical coupling.

Many processes in eukaryotic cells, including cell motility, rely on the growth of branched actin networks from surfaces. Despite its central role the mechanochemical coupling mechanisms that guide the growth process are poorly understood, and a general continuum description combining growth and mechanics is lacking. We develop a theory that bridges the gap between mesoscale and continuum limit and propose a general framework providing the evolution law of actin networks growing under stress. This formulation opens an area for the systematic study of actin dynamics in arbitrary geometries. Our framework predicts a morphological instability of actin growth on a rigid sphere, leading to a spontaneous polarization of the network with a mode selection corresponding to a comet, as reported experimentally. We show that the mechanics of the contact between the network and the surface plays a crucial role, in that it determines directly the existence of the instability. We extract scaling laws relating growth dynamics and network properties offering basic perspectives for new experiments on growing actin networks.