Summary Advanced Food Physics (FPH-30306)

Summary Advanced Food Physics

Soft solid: A material with a predominantly elastic response to an applied force  material can store
energy and does not immediate yield  tan δ < 1  modulus E,G < 108 Pa

 Gels
o Polymer gel (gelatin, polysaccharide gel)  triple helix structures
o Particle gel (whey protein, casein micels)  network of clusters
 Closely Packed System (CPS)  mayonnaise
o High density of soft deformable particles, low MC
o Mechanical strength is determined by stiffness of the particles
 Cellular materials  apple
o Closely packed relatively soft cells are surrounded by a stiff matrix
o Mechanical strength is determined by the stiffness of the matrix

There are four modes of deformation of soft solids

1. Uni-axial compression of compressible materials
𝜎
 𝐸𝑢 = 𝑥𝑥 (σ = stress in x-direction, ϒ = deformation in x-direction)
𝛾𝑥𝑥
2. All-sides compression of compressible materials
𝜎 𝛥𝑉 𝛥𝑥 𝛥𝑦 𝛥𝑧
 𝐾= (ΔV = V – V0) ( = + + )
𝛥𝑉∕𝑉0 𝑉0 𝑥 𝛾 𝑧
3. Uni-axial compression of (partially) incompressible materials
 Deformation in the x-direction causes deformations in the y- and z-directions.
 The extend of the deformations is determined by the Poisson ratio.
𝑦
 𝜇 = − 𝑦𝑦𝑦
𝑥𝑥
 µ = 0  compressible materials (no deformation in perpendicular directions)
 µ = 0.5  for incompressible materials (ΔV = 0)
4. Bi-axial loading of (partially) incompressible materials
𝐸𝑢
 𝐸𝑏 = (1−𝜇)
5. Shear
𝜎𝑥𝑦
 𝐺= 2𝑦𝑥𝑦

G and Eu are relatively easy to measure, K is more difficult  measure G and Eu and calculate K

 Linear behaviour (calculate Eu over <1% deformation of linear part)
 Plastic or strain thinning behaviour
 Fracture

Eu  represents the stiffness of the material
σfr (fracture stress)  represents the strength of the material
εfr (fracture strain)  represents the longness of the material
1/ εfr  is a measure for the brittleness of the material
Wfr (work of fracture)  represents the toughness of the material

For plastic or strain thinning phase  apparent modulus  two formulas

When slope goes to zero or even negative values  fracture or rearrangement of the structure 
feta cheese

Ketchup is a weak solid at rest and a liquid after a little (yield) stress

, The response of a material (viscous or elastic) to a deformation strongly depends on the speed of
deformation  relaxation time  relaxation occurs through disentanglement or breaking of bonds
 stored elastic energy is released and dissipated into heat

For large deformations the Hencky strain is a better measure for the deformation than the Cauchy
strain

Fracture: the breaking in one or more macroscopic planes of all bonds between structural elements
of the solid

 Linear elastic fracture
o As a result of applied stress elastic energy is stored in the material (Wel)
o Fracture plane  all bonds have to be broken, and new surface is created  Wfr =
Wbond
o Fracture occurs when Wel > Wbond
o Wel = ½ VEµϒ2xx = ½ Vσ2xx/Eu
o The experiment fracture stress is often lower than the theoretical prediction
 Reason  defects in the structure leads to stress concentrations  local
stresses can be much higher than the macroscopic stress
 σloc can be calculated from the overall stress
 the local stress > fracture stress  sufficient for fracture initiation, not for
spontaneous propagation
 The Lcr can be calculated  beyond the Lcr more elastic energy is released
from the system than required for the breaking of bonds  spontaneous
propagation.
 Elastic-plastic fracture
o Local plastic deformation in the region around the notch leads to
 Decrease in local stress concentration as a result of relaxation processes
(breaking of bonds or disentanglement)
 Local elastic energy is dissipated into heat
 As a result larger overall stress is needed for fracture of the material
o The actual fracture stress is also increased by
 Non-smooth fracture plane
 Additional side-crack may develop during fracture
o Slow deformation rate  local stress concentrations relax  material will yield
rather than fracture abruptly
o If material has a relaxation time  slow deformation leads to relaxation  low
values of Ψ will resulting in yielding rather than fracture.

Texture: All structural and mechanical properties of food conceived by humans by their touch, eyes
and ears

Deformation mode should mimic processes in the mouth

1. Uni- or biaxial deformation to mimic behaviour of soft materials between tongue and palate
2. Cuttings tests to mimic biting behaviour for hard materials