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
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
