Stress-strain solid foods

The stress-strain data can be generated from either tension or from compression tests. For soft solids, compression tests are preferred since it avoids the need to clamp the sample ends. Consequently, compression tests are widely used in testing foods. However, the friction between the loading plates can be significant, as noted by several investigators (58-61). 

Some materials break at high strain rates but yield at small rates. Several soft-solid foods yield under the conditions normally applied, as during spreading on bread. The magnitude of the yield stress then correlates... 

Peleg, M. (1977). Operational conditions and the stress strain relationship of solid foods— theoretical evaluation. J. Text Stud. 8, 283-295. 

A uniaxial stress is usually designated by the symbol o, and a shearing stress by X. For certain lipids that behave like solid food systems, the relationship between stress and strain is represented by a straight line through the origin, up to the so-called limit of elasticity. The proportionality factor E for uniaxial stress is called Young s modulus, or the modulus of elasticity. For a shear stress, the modulus is called Coulomb modulus, or the tensile modulus G. 

Rheological properties of food materials over a wide range of phase behavior can be expressed in terms of viscous (viscometric), elastic and viscoelastic functions which relate some components of flie stress tensor to specific components of the strain or shear rate response. In terms of fluid and solid phases, viscometric... 

If the solid does not shows time-dependent behavior, that is, it deforms instantaneously, one has an ideal elastic body or a Hookean solid. The symbol E for the modulus is used when the applied strain is extension or compression, while the symbol G is used when the modulus is determined using shear strain. The conduct of experiment such that a linear relationship is obtained between stress and strain should be noted. In addition, for an ideal Hookean solid, the deformation is instantaneous. In contrast, all real materials are either viscoplastic or viscoelastic in nature and, in particular, the latter exhibit time-dependent deformations. The rheological behavior of many foods may be described as viscoplastic and the applicable equations are discussed in Chapter 2. 

In real food polymers, a distinction can be made between a viscoelastic solid, which contains some cross-links that are permanent, and a viscoelastic liquid, where, under the influence of stress, the relative movement of whole molecules will be observed. As shown in Figure 8.9, in the case of a viscoelastic solid, after application of the stress, the strain will eventually reach a constant value, and upon removal of the stress, the strain will finally return to the remaining value of food primary energy, which was not entirely dissipated. For a viscoelastic liquid, a permanent deformation will remain after removal of the stress. In the stress relaxation area, the deformation value will decay to zero for a viscoelastic liquid, whereas for a solid, it will reach a constant, nonzero value. It can also be seen as either a decreased value to the zero or a constant, nonzero value, as pointed out by the dashed line. Both values characterize the rheology parameters of foods under certain conditions. One of the reasons for this is that the factors of time-dependent foods are not necessarily related to their elastic modulus. This can be explained by the series of small deformations without rupture, which are dependent in different ways and are based on the primary molecular microstructure of foods. The time required for the stress to relax to a definite fraction of its initial value is the relaxation time. 

In the rheological structure of most food systems there is a viscous element present, and the deformation curves are often highly influenced by the rate of the imposed strain. This is due to the fact that the material relaxes (or flows) while tested under compression and the resultant deformation of this flow is dependent on the nature of the viscous element (Szczesniak, 1963 Peleg and Bagley, 1983). In the viscoelastic food systems, where during processing it is caused to oscillate sinusoidally, the strain curve may or may not be a sine wave. In cases when a periodic oscillatory strain is applied on a food system like fluid material, oscillating stress can be observed. The ideal elastic solid produces a shear stress wave in phase with... 

Large Deformations. For most soft solids, the direct proportionality between stress and strain only holds up to a very small strain, rarely over 0.01. One may, of course, calculate an apparent modulus Ea = a(e) / e, which is for most foods smaller than the true modulus (cf. 

Rheology is the study of flow of matter and deformation and these techniques are based on their stress and strain relationship and show behavior intermediate between that of solids and liquids. The rheological measurements of foodstuffs can be based on either empirical or fundamental methods. In the empirical test, the properties of a material are related to a simple system such as Newtonian fluids or Hookian solids. The Warner-Bratzler technique is an empirical test for evaluating the texture of food materials. Empirical tests are easy to perform as any convenient geometry of the sample can be used. The relationship measures the way in which rheological properties (viscosity, elastic modulus) vary under a... 

A plastic material is one that shows little or no deformation up to a certain level of stress. Above this yield stress the material flows readily. Plasticity is conunon to widely different materials. Many metals yield at strains less than 1%. Concentrated suspensions of solid particles in Newtonian liquids often show a yield stress followed by nearly Newtonian flow. These materials are called viscoplastic or Bingham plastics after E. C. Bingham, who first described paint in this way in 1916. House paint and food substances like margarine, mayonnaise, and ketchup are good examples of viscoplastic materials. 

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