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Rangées de graines.. © INRA, Elena Schweitzer © Fotolia

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Multi-scale mechanical modelling: from the nanometric scale to the macroscopic properties of bread crumb

Cereal products are the basis of our diet. Their texture is a relevant indicator of sensory perception. Mechanics of Materials allows us to extract objective data about mechanical behaviour of such products including ultimate properties and their breakdown. Using Finite Element simulation, scientists study relationships between the structure of a given product and its mechanical properties at different scales. The Finite Elements Method predicts these properties for “virtual” structures that match “real” structures. It was applied to the case of cellular products such as bread crumb. Numerical results revealed a non-negligible role of cell architecture on the elasticity of bread crumb structures in addition to the major role of the void content. Mechanical modelling will be applied to the mastication of cereal products. This approach will relate the process to the functional properties in order to more effectively predict the breakdown of these products for improved digestion.

Updated on 06/17/2013
Published on 06/10/2013

Material sciences applied to cereal products

Cereal products are the basis of our diet. Their texture is a relevant indicator of sensory perception. Material mechanics cannot be separated from structural information that is closely linked to the mechanical behaviour of products, which is why it is important to study mechanical property-structure relationships.  As a result of the variability of the size of structural heterogeneities, these relationships must be broken down at different scales.
Digital techniques are absolutely necessary for the construction of robust mechanical models capable of making realistic predictions, given the impossibility of measuring the effect of certain heterogeneities (for example, the in situ measurement of a cell wall property in a cellular material).
The Finite Element Method (FEM), known for its deterministic description, increasingly integrates the complexity of structures. Application of the FEM is highlighted in the following examples within the framework of the study of starch-based cereal products.
Digital simulation using Finite Element Analysis, coupled with an adequate deterministic model, allows a prediction of the mechanical behaviour of these products in relation to their structure. Better still, this type of approach anticipates these same properties for "virtual structures" comparable to "real" structures. Virtual generation designates structural possibilities for improving products by standard food transformation processes. The results obtained are illustrated below in the case of cellular products such as bread crumb through the application of a deterministic multi-scale approach.


Simulation at different scales reveals the mechanical behaviours of a bread crumb  

Starting with the composite that forms the cell wall, simulation of the nanoindentation test reveals the major role of the starch-zein interface (Fig. 1) .  This effect is flagrant when we look at the behaviour at the microstructure scale.  In order to better understand the role of the interface, it is possible to extrapolate on the basis of an average interface effect, thanks to the notion of interphase properties. Behaviour modelling thus becomes more coherent with mechanical tests. Nevertheless, the validity of this coherence is relative to the observation scale and requires a homogenisation approach to make the necessary transition from the microstructure scale to the macroscopic scale. As long as this transition does not take place, the variability of mechanical properties measured at the macroscopic scale cannot be explained.

Figure 1 : (a) Simulation d’un essai de nano-indentation : échelle de l’interface. (b) Modèle à trois phases: échelle de la microstructure. (c) Simulation d’un essai de flexion: échelle macroscopique. (d) Modèle élastique associé à une structure cellulaire à base d’amidon (mie de pain): échelle du produit transformé.. © INRA
Figure 1 : (a) Simulation d’un essai de nano-indentation : échelle de l’interface. (b) Modèle à trois phases: échelle de la microstructure. (c) Simulation d’un essai de flexion: échelle macroscopique. (d) Modèle élastique associé à une structure cellulaire à base d’amidon (mie de pain): échelle du produit transformé. © INRA

Figure 1: (a) Simulation of a nanoindentation test: interface scale. (b) Three-phase model: microstructure scale. (c) Simulation of a bending test: macroscopic scale. (d) Elastic model linked to a starch-based cell structure (bread crumb): transformed product scale.

Applying mastication models

While waiting for the implementation of such an approach, we were able to identify the mechanical behaviour of starch-zein composites at the macroscopic level using an inverse approach.
In this case, the material is said to be homogeneous in that the microstructure is implicitly involved in its behaviour.  Given the cell wall properties, it was possible to describe the simulation of the behaviour of a processed product. Numeric results reveal a non-negligible role of the cellular architecture on the elasticity of bread crumb-type structures in relation to the dominant role of the vacuum.
The application of mechanical models of mastication of cereal products is in progress.  This approach will make it possible to link the process to utilisation properties in order to more effectively predict the degradation of these products to improve their digestion.


  • UMR Centre des Sciences du Goût et de l'alimentation (CSGA) CNRS, INRA, Université de Bourgogne et AgroSup Dijon
  • Laboratoire de Mécanique de Lille est une Unité Mixte de Recherche (UMR 8107) entre le CNRS et l'Université des Sciences et Technologies de Lille
  • Laboratoire de Science et Ingénierie des Matériaux et Procédés, CNRS-INP Grenoble-Université Joseph Fournier 
  • GéM : Institut de Recherche en Génie Civil et Mécanique, CNRS-Université de Nantes-Ecole Centrale de Nantes 
  • FEMTO-ST : Franche-Comté Electronique, Mécanique, Thermique et Optique – Sciences et Technologies CNRS-Université de Besançon 

See also