1. Roles of Models in Study of Agricultural Material
Jiri Blahovec Czech University of Agriculture, Prague, Czech Republic

2. What could be Termed as a Model?
Everything understandable has number without which nothing can be understood or sensed.
Kroton’s Philosopher in 5th century BC
the artificial logic system, usually expressed by mathematical means, having external parameters as close as possible to the external parameters of a real system that is analysed Models make possible to overcome some theory gaps and/or simplify some complicated theories or systems

3. Model Types Based on original descriptive properties
Very important for AM modelling
Substance oriented
Structural oriented
Functional oriented
Mixed

4. Model Types Materialistic modelling
Physical
Mathematical:
Stochastic
Deterministic
Dynamic
Static

5. Model Types Under model forming
Inductive
Deductive – more frequent in AM

6. Model Types Under model use
Descriptive
Explanatory

7. Physical Quantity Type
scalars, vectors, tensors …

8. Physical Quantity Unit
Q = {Q}[Q]
SI - homogeneous system of Units

9. Physical Quantity Equations
Dimensional Analysis
Checking the sides of equations that the both sides have the same dimension
Model parameters are Physical quantities
Example:
[a] = [y]
[b] = [y] / [x]
[c] = [y] / [x]2

10. Structural Model of Precision Farming
Agronomist’s view
Engineer’s view

11. Plant Modelling
Functional: growth, production, sensitivity to influence of environment, reproduction, position in agricultural systems, etc.
Structural: role of parts, tissues, cells including relations
Composition: composition of the individual parts in relation to the production quality
Properties: technological, engineering, sensory
Tissue Properties: cell role

12. Cells of Biological Origin
sponge
bone
leaf
plant stalk

13. Cells
Part & Property Plants Animals Fibres carbohydrates: cellulose, proteins: myosin, actin, collagen hemicellulose Fibres location cell wall inside cell Storage substances starch (oil) fat (glycogen) their location inside cell plastides in special cells Cell wall thickening cellulose, hemicellulose, collagen on external side of cell lignin wall Filling of apoplast pectin later lignifications fat, molecular setting Pigments - location chlorophyll in chloroplasts myoglobin in cell

14. Simple Elastic Model of Cell Tissue (SEMCT) (structural, mathematical, deductive, descriptive)
With thin membrane-like cell walls (cells filled by liquid - parenchyma)
With thick cell walls (cells filled by liquid - sclerenchyma)
With thick cell walls (cells filled by gas – wood)

15. SEMCT for Parenchyma 1
Raw Potato (cell wall elasticity, Nilsson et al, 1958)
p - turgor pressure
tw - cell wall with thickness r0 - cell radius
Ew - cell wall modulus of elasticity
. - Poisson ratio function, B - function of .

16. SEMCT for Parenchyma 2
Blahovec, 1985 continuation of the idea of Nilsson et al, 1958 squeezing out of cellular liquid cell characteristics: crude fiber content cf or cell dimension
For potatoes and several other flesh products:
C1 = MPa C2 = 0.95 MPa/(%)2 R = 0.927
C3 = MPa C4 = MPa/% R = 0.911

17. SEMCT for Sclerenchyma
Gibson & Ashby, 1988
ρs – cell wall density
Es – cell wall modulus
K1 – constant describing details of cell wall arrangements, range [0,1] K2 – constant (~ 0.03) p – internal pressure patm - external (atmospheric) pressure σel - stress at elastic limit

18. SEMCT for Wood Gibson & Ashby, 1988 - cell wall buckling elastic
plastic
Gibson & Ashby, cell wall buckling
ρs = 1500 kg.m-3
Es = 35 GPa
E – modulus of elasticity G – shear modulus τs – shear strength C
Parameter T R L E G
τs C C n E G τs

19. Successful Modelling!
Thank you for your attention!