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

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

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

Model Types Materialistic modelling Physical Mathematical: Stochastic Deterministic Dynamic Static

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

Model Types Under model use Descriptive Explanatory

Physical Quantity Type scalars, vectors, tensors …

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

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

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

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

Cells of Biological Origin sponge bone leaf plant stalk

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

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)

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 .

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 = 0.0518 MPa C2 = 0.95 MPa/(%)2 R = 0.927 C3 = 0.435 MPa C4 = 1.398 MPa/% R = 0.911

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

SEMCT for Wood Gibson & Ashby, 1988 - cell wall buckling elastic plastic Gibson & Ashby, 1988 - 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 0.54 0.8 1 G 0.074 0.074 0.074 τs C7 C7 0.086 n E 3 3 1 G 3 3 1 τs 2 2 1

Successful Modelling! Thank you for your attention!