Numerical modeling of wheat fractionation role of starch volume fraction

Wheat endosperm is a cemented granular material composed of a binary-sized mixture ofalmost spherical starch granules bounded to one another with an amorphous proteinmatrix. The milling properties of wheat grains depend on this typical microstructure, largelycontrolled by the genetic background and the growing conditions. An original Atomic ForceMicroscopy nano-scratch methodology has been developed [1] to assess the localrheological properties of the protein matrix, the starch granules and their interface. Thedetermined relative stiffness and failure strength, together with information on the phasedistribution, were then used to construct 2D numerical samples of wheat endosperm. Thegranular structure of the sample with different granular packing was computed using aMolecular Dynamics approach. The protein matrix was added in the form of bridgesconnecting neighboring particles. The samples were then meshed using a triangular latticeof one-dimensional spring elements that were characterized by stiffness and yield force.The rheological properties of each element were set according to the location of its twonodes leading to five different elements: starch, matrix, starch-matrix, starch-starch andvoids. The samples were then subjected to an increasing uniaxial tensile stress until failureusing an iterative procedure based on conjugate gradient minimization. The LatticeElement Method, developed by Topin [2,3], was used for the simulations and a parametricstudy was performed where the protein content, the starch granular packing and thestarch-protein adhesion, suggested to be responsible of the wheat fragmentation, werevaried. The results showed that, depending on the sample porosity, the bulk elasticproperties do not follow the mixing law of diluted composites, highlighting the granularbackbone effect of percolating particles. A non-linear evolution of the bulk elastic modulusas a function of the sample porosity was also noted, with little effect of the granule solidfraction. Concerning the failure properties, the results showed that the particle volumefraction has a greater influence on the yield stress at high starch-protein adhesion and thatfor the same porosity, increasing particles volume fraction leads to higher yield stress.Finally, we noted that the yield stress strongly depends on the sample porosity at highstarch-protein adhesion and is weakly affected by the porosity at low adhesion, whateverthe particle volume fractions.