Some Mathematical Aspects of Mastication and Its Simulation by Machines

If the deformation process of a specimen satisfies the condition: H(t) = g(H o ) · f (t) (Eq. l), where H(t) is the deformed specimen length at time (t), g(H o ) is a function of the initial length (H o ) only and f(t) a function of time only, then the true strain e(t) and the strain rate e(t) are: e(t) = In f(t) (Eq. 2), and e(t) = [d In f(t)] /dt (Eq. 3). These imply that the stress‐strain (or force‐time) relationship of a homogeneous material is independent of the specimen length and is only determined by the rheological properties of the material and the selected function f(t). If the deformation histories produced in mastication satisfy the condition set by Eq (1) it would provide a partial mathematical explanation to why sensory textural‐rheological properties are not affected by the specimen dimensions in contrast to instrumental parameters obtained by existing testing machines. The construction of machines that provide such straining histories is physically possible (they would not, however, be operated at a constant deformation rate), and there‐ fore it is theoretically possible to obtain instrumental parameters that are dimension independent. The concept is demonstrated with some simplified rheological models and its possible application to food testing evaluated.