a 3-d finite element analysis of the sunflower helianthus ...€¦ · a 3-d finite element analysis...

A 3-D finite element analysis of the sunflower (Helianthus annuus L.) fruit under impact: a useful approach for the understanding and improvement of its hullability

L. F. Hernández1,3 & P. M. Bellés2,3

1Plant Morphology Lab., Dept. of Agronomy 2Dept. of Engineering – IMA, Universidad Nacional del Sur. Bahía Blanca, Argentina 3Comisión de Investigaciones Científicas (CIC-PBA), La Plata, Argentina

Abstract Before oil extraction sunflower seeds are hulled, i.e. the pericarp (hull) is separated from the seed by mechanical impact. Hullability (H), defines how easily the hull can break and set apart from the seed and has a direct effect on the industrial oil extraction performance. H mainly depends on the fruit’s morphology and hull’s biomechanical properties. The study of hulls showing histological differences could be useful to infer its best distribution of tissues and to define, for breeding purposes, the best hull architecture for industrial processing. Using a numerical approach we have been able to calculate and visualize the pattern of stresses produced in the hull after the fruit impact. A 3-D model of an entire fruit was designed in terms of strain incompatibilities between two different tissues, parenchyma and sclerenchyma. Using a non-linear FE commercial code, It was seen that the points of contact between those tissues, with different mechanical properties, and the hull’s longitudinal parenchymatous rays were more likely to mechanically fail. The simulated patterns of failure closely agree with those observed after subjecting fruits to compressive loads. The procedure described here can be considered the first step of a protocol of analysis leading to a genetic improvement of H and could be useful to quantify and qualify, under different hull structural parameters, the distribution and magnitude of the stresses generated in the pericarp during the mechanical hulling. Keywords: finite element, hullability, hull, modeling, pericarp, sunflower.

Design and Nature II, M. W. Collins & C. A. Brebbia (Editors)© 2004 WIT Press, www.witpress.com, ISBN 1-85312-721-3

1 Introduction

Sunflower grains are botanically defined as fruits. They are composed by a thin outer shell, the pericarp, also known as “hull”, that surrounds and contains the seed, usually named “kernel”. The pericarp accounts for 20-26% (dry basis) of the total fruit weight. The seed contains the largest proportion of oil that is found in a fruit (Seiler [22]). The pericarp is a brittle structure composed by different tissues which have different physical and biochemical properties. The two main ones found in a mature fruit are parenchyma and sclerenchyma (Esau [9]). The later one has a high proportion of lignin (20-25% d.b.) (VanSoest et al [24]). These tissues are transversally and longitudinally arranged forming compact bundles known as rays (Lindström et al [15], Seiler [22]). Sunflower fruits are hulled before they enter in the process of oil extraction. Hulling consists in the separation of the pericarp from the seed. The hulling machinery frequently used in the oil industry is based on the principle of impact. Large propellers centrifugally throw the fruits at high speed (15 to 30 m.s-1) against a hard surface where their pericarps totally or partially break apart. The ability of the pericarp to break and to separate from the seed can be quantitatively defined with a hullability index (H) (Denis et al [6, 7]), calculated as (MHW/THW) x 100, Where: MHW = weight of the pericarp obtained using laboratory hulling machines that simulate the industrial process and THW = total weight of the pericarp obtained by manual hulling.

1.1 Morphological properties of the fruit that modifies H

The magnitude of H mainly relies on various pericarp structural properties such as its thickness (Dedio [4], Denis et al [5, 6]), number of parenchymatic rays, cell lignification and moisture content (Beauguillaume and Cadeac [2], Gupta and Das [11], Leprince-Bernard [14]). Some of these properties can be genetically modified (Fick and Miller [10]) or changed with environmental growth conditions (Dorrell et al [8]) and crop management (Baldini and Vannozzi [1], Dedio and Dorrell [3]). Fruit and seed size play also a very important role in the magnitude of H (Tranchino et al [23]). Large fruits are easily hulled. Small fruits on the other hand, usually have a thin and flexible pericarp which is tightly attached to the seed (Beauguillaume and Cadeac [2], Leprince-Bernard [14], Lindström et al [15]) and more difficult to break (Denis et al [7], Morrison et al [17]). It is generally assumed that fruits with a high H usually have a comparative large size and relatively thick pericarp (Beauguillaume and Cadeac [2]). Due to the late genetic improvement, sunflower fruits have increased its oil content and at the same time decreased the thickness and relative proportion of the pericarp (Fick and Miller [10]). So in the modern genotypes it is found that high seed oil content is negatively correlated with H (Baldini and Vannozzi [1], Denis et al [5, 6]).


254 Design and Nature II

The site of the impact of the fruit inside the hulling machine also affects the magnitude of the pericarp breakage during the process. If the fruit impacts longitudinally or transversally H is higher than if it impacts on its convex sides (Leprince-Bernard [14]).

1.2 Possibilities to improve H

Hullability is closely related to the morphological, histological and biomechanical properties of the pericarp. So if the optimization of the “architecture” of the pericarp for improving H is pretended, the accurate definition of its constitutive tissues, how they are arranged in fruits with different H and its biomechanical properties are important variables to be defined. Using biotechnological techniques it is now possible to genetically change the mechanical properties of plant tissues, particularly modifying the metabolism for lignin synthesis (Hepworth and Vincent [12, 13], Pilate et al [19], Ralph et al [21], Whetten et al [26]). In the view of this promising scenario, defining the best distribution and quality of the sunflower pericarp tissues, predicting the localization of the breakage sites and quantifying the magnitude of stresses produced when the fruit impacts during mechanical hulling, may help to define the best tissue composition and arrangement involved in the “ideal pericarp architecture”. This information then could allow us to efficiently use the available biotechnological tools to improve H.

2 Theoretical approach to the study of the pericarp breakage: modelling and stress simulation

The objective of the present work was to develop a 3-D model of the sunflower fruit pericarp and identify, using a numerical approach, the magnitudes of tensions and stresses at the site of fruit’s impact, validating the calculated results with those obtained with mechanical tests performed in the laboratory. Morphological studies on sunflower fruits with contrasting morphology were made. Load-displacement test on whole fruits were also carried out. A finite element model of the hull was developed and analysed simulating its impact against a rigid surface with different fruit's orientations.

2.1 Histology of the fruit’s pericarp

The anatomy of the pericarp was defined by studying transverse and tangential sections of whole fruits from two sunflower genotypes with highly contrasting morphology, i.e. small fruits with thin pericarp and larger fruits with thick pericarp. Sections were appropriately stained to obtain a detailed location of the main tissues within the pericarp and to determine their distribution according to their lignification level. This information was used to elaborate a model of tissue distribution.


Design and Nature II 255

Figure 1: Uniaxial compression tests of full-grown fruits using an Instron UTM.

a. A sunflower fruit mounted at the beginning of the test. b. Average load-deformation curve. byp: bio-yield point (Gupta and Das [11]). c. Fruits showing a characteristic hull’s breakage pattern at the byp when mounted longitudinally (c1), transversally (c2) o laterally (c3). For different fruit morphology and orientations, 25 fruits were analysed.

2.2 Pericarp breakage tests under uniaxial compression

Uniaxial compression tests were made using an Instron (mod. 1122) universal testing machine (UTM) with a 0-100 Kg load cell and an integrator at a cell’s speed of 1,0 mm.min-1. The load magnitudes necessary to reach the structure breakage and to empirically define the breakage pattern were obtained (Fig. 1).

2.3 Biomechanical properties of the tissues

The more relevant mechanical properties (density and elastic modulus) of the main tissues to be considered in the model [rays of parenchyma (Rp) and sclerenchyma (Te)], were adopted from the literature (Niklas [18], Preston [20], Whetten et al [26]). Some of these parameters were further adjusted from tensile and compressive tests made on longitudinal pericarp’s segments of known dimensions, using a testing machine for small plant samples designed in our laboratory. It is based in a high precision electronic balance, mounted on a cantilever system that firmly holds an automated small displacement screw driven by an actuator. The samples were gripped in simple-side acting grips and pressed or pulled at approximately 5 mm.min-1. Data was collected and downloaded to a PC. Pericarp segments of 7,0 mm length and 2,0 mm width and thickness between 100 and 300 µm were tested. From the force-deformation relationships obtained, the transformed stress/strain relationships were used to calculate the structural elastic modulus (Est) (Niklas [18], Whetten et al [26]) for a whole fruit with 11,0 % relative humidity and the rupture modulus (RM) (Niklas [18]) for each fruit’s orientation.

Deformation (mm)

b

Forc

e (N

)

��

��

��

��

��

��

��

��

��

��

��

��

��

0

10

20

30

40

50

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

a c1

c3

c2 byp



2.4 Model of the fruit’s pericarp: morphology and histological architecture

A 3D model of the hull was built based on randomly selected fruits of different genotypes. They were digitised on two orthogonal planes, perpendicular to the longitudinal axis. Using adequate CAD software contour coordinates of these profiles were obtained and integrated. The 3D model was properly meshed (Fig. 2a-b) using the shell element. Three-nodal triangles and 4-nodal squares were used, giving the model a configuration of 2131 elements with 2080 nodes (Logan [16]). The elementary histological distribution of the pericarp in the model was mainly based in two types of tissues according to their cell arrangement, Te and Rp (Fig. 2c), its mechanical properties and thicknesses. Another three element groups were defined in order to give the model more realistic structural properties. They where the fruit ends, basal and apical, and the pericarp border (Fig. 2).

Figure 2: Meshed model of a sunflower fruit, obtained by a digitalisation of the coordinates in different planes of images taken from full-grown fruits. A: orthogonal isometric view B: lateral view. be: basal end; ae: apical end; pb: pericarp’s border. C: Simplified model of the histological components of the pericarp. Rp: ray of parenchyma; Te: ray of sclerenchyma. Strata a, b and c are the external epidermis, inner tissue and internal epidermis respectively (See also Fig. 3).

2.5 Calculation and localization of stresses in the model under simulated impact

The analysis was performed using ACCUPACK/VE from ALGOR (vers. 12, Algor Inc., Pittsburgh, PA) (Logan [16]), a software processor for non-linear calculation to conduct a Mechanical Event Simulation (MES) simulating an impact speed of 30 m.s-1. Impact simulation was registered at a capture rate of 100 steps per second.

b e

R p T e

T e R p

a

b

c

ae

b e B A C

pb pb



Figure 3: Histology of the pericarp (after Lindström et al [15]). A. Portion of a

transversal cut showing the distribution of tissues. (a: epidermis + hipodermis; b: sclerified cells; c: compressed lower parenchyma cells. B. tangential longitudinal portion of the pericarp where the distribution of the parenchyma rays (Rp) and the sclerified tissue (Te) are observed. Bar = 200 µm.

3 Results

The pericarp of the sunflower fruit is a biological structure with an orderly arrangement of tissues (Seiler [22]) distributed in layers. From the outside there is an epidermis of rectangular cells (A, Fig. 3a) protected by a cuticle; the hypodermis, composed of cells with thin walls and an amorphous layer of phytomelanin (B, Fig. 3a); a layer of numerous rows of elongated polygonal sclerenchymatic cells, which strengthens the structure towards the longitudinal axis of the fruit and with a stiffness gradient of radial direction that increases from the outside to the inside of the fruit (B, Fig. 3a, Te, Fig. 3a). This layer is interrupted at regular intervals by parenchymatic rays (Rp, Fig. 3a), numerous parenchymatic cells with thin walls loosely arranged and an inner epidermis (C, Fig. 3a) (Lindström et al [15]). The average load-deformation curve obtained in the laboratory tests for different fruits and orientations showed a linear response (Fig. 2b) with a similar pattern expected for a brittle organic structure (Wainwright et al [25]). This trend was maintained up to the structural collapse (Fig. 1c). In the three positions tested, the breakage pattern show debris of pericarp oriented in a parallel direction towards the major axis of the fruit (Fig. 1c). Mechanical properties of the histological components in the model of Fig. 2c, for three impact orientations are described in Table 1. The graphical representation from the numeric simulation for three impact orientations are shown in Fig. 4. Sequential images were captured at a speed of 100 steps per sec. The magnitudes of the stresses generated at the site of impact are shown in Table 2. The highest values were produced at the area of impact (Fig. 4a, d and g), suggesting that immediately after the impact the structure can

Te Rp Te Rp

a

b

c

A B



sustain an irreversible damage that leads to its instability and rupture. Stresses are propagated basipetally and radiated as a consequence of the alternance of rays with quite different mechanical properties and of its longitudinal distribution in the pericarp matrix (Fig. 4b-c, e-f and h-i). Table 1: Mechanical properties of the histological components of the FE model

of Fig. 2 for three impact orientations. The first column describes the orientation of the fruit for impact. Rp: Ray of parenchyma. Te: Ray of sclerenchyma, E = elastic modulus (MN.m-2); δ = density (Kg. m-3); ν = Poisson coefficient; thick: tissue thickness (µm). The magnitudes were calculated from values described for each tissue [18] and from laboratory load tests on whole fruits and pericarp longitudinal segments from fruits of thin pericarp (100 µm) or thick pericarp (300 µm). These magnitudes were adjusted taking in account the orientation of impact. Each value is the mean of 25 samples.

Tissue thickness

(µm)

Mechanical properties of the model’s

components

Fruit orientation

Re

Rp

Re

Rp

Apical

end

Basal end

Dorsal border

100

300

100

300

E: 57,0

δ: 800 ν: 0,25

E: 30,0 δ: 300 ν: 0,45

100

300

100

300

E: 70,0

δ: 800 ν: 0,25

E: 40,0 δ: 300 ν: 0,45

100

300

100

300

E: 230,0

δ: 800 ν: 0,25

E: 40,0 δ: 300 ν: 0,45

E: 30,0 δ: 600 ν: 0,40 thick: 300

E: 30,0 δ: 700 ν: 0,25 thick: 350

E: 10,0 δ: 600 ν: 0,25 thick: 300

The comparison between the stress magnitudes, particularly the rupture modulus, (Niklas [18]) obtained from laboratory tests and those calculated from FE model (Table 2) show that the regions of the hull able to collapse are longitudinally distributed, parallel to the parenchymatic rays. The stress patterns calculated in the simulation agree with the breakage pattern observed in laboratory tests (Fig. 1c1-c3). The alternate distribution or Rp and Te (Fig. 3b), is the main reason to give the model its structural response (Fig. 4).



Figure 4: Simulation of impact at a speed of 30 m.s-1. The stress magnitudes are

shown for three orientations: longitudinal (a-c), transversal (d-f ) and lateral (g-i) , in a sequence of three images, from the beginning of the simulations (t0; a,d y g) and two consecutive moments (b-c, e-f y h-i). The site of impact is indicated with an arrow. The stress pattern is distributed following the alternate arrangement of the tissues that conform the model, from the site of impact (arrow). This pattern resembles the pericarp breakage pattern obtained in laboratory compression tests (Fig. 1c).

4 Conclusions

The model described in this paper is a theoretical representation of the sunflower fruit’s pericarp geometry, its constitutive tissues and their biomechanical properties. In any case, it is able to predict stress distribution patterns resembling the breakage pattern experimentally observed in whole fruits tested under uniaxial compression (Fig. 1c, Fig. 4). It is the arrangement of the pericarp tissues, with complex biomechanical properties and different yielding strains (rays and sclerified parenchyma) which determines its response to the applied loads. It is seen that the closest values between the CFT, calculated from laboratory tests in whole fruits and in the simulation where present at the site of impact (Table 2; Fig. 4b,e,h). It suggest that in this place the structure will suffer an irreversible damage that will drive the complete structure to collapse.

A D G

B E H

C F I



Table 2: Calculated tensions and simulated tensions at three orientations of impact. Rp: Ray of parenchyma, Te: Ray of schlerenquima, Est: structural elastic modulus (Niklas [18]), calculated for the whole fruit from laboratory tests). CFT = critical fracture tension. It was estimated following Niklas [18], where CFT = Es . 0,0092; RM = Rupture modulus; VM = VonMises (Logan [16]) obtained from the FE model after MES. These values were captured at the moment of the simulated impact from two pericarp thicknesses: Rp = 100 y 300 µm and Te = 100 y 300 µm.

Tissue

thickness

(µm)

Fruit orientation

Re

Rp

Est

Calculated (Lab. test)

RH% =

7,0

( N.m-2 )

CFT

Theoretical fracture stress

(Lab test)

HR% = 7,0 (N.m-2 = Est . 0,0092) [18]

RM Experimentally

calculated (Lab. test)

RH% = 7,0

(at byp)

( N.m-2 )

VM

Calculated in the

simulation

( N.m-2 )

100 300

100 300

9,11.106

35,10.106

0,84 . 105 3,22. 105

1,53 . 105

7,10. 105

0,88 . 105 4,02 . 105

100 300

100 300

22,33.106 48,27.106

2,05 . 105 4,44. 105

3,30 . 105 9,20 . 105

1,83 . 105 5,20. 105

100 300

100 300

37,48.106

66,25.106

3,44 . 105 6,09. 105

3,34 . 105

11,81 . 105

3,51 . 105 5,89 . 105

The fruit model presented here is based only in the hull, assuming that a very soft seed, that usually does not fill its interior, will not interfere in the stress patterns developed immediately after impact. This situation is frequently found in the real sunflower fruit. Even though the FE model described here is a simplified version of the fruit, the results obtained can confirm the validity of the simulation. It was able to detect the effects of the impact during the hulling process. In this sense the model allows to evaluate combined effects of material properties and geometry of the sunflower fruits. As far as we know, this is the first simulated demonstration of a sunflower pericarp breakage pattern based on the mechanical properties and the distribution of its tissues. The development of this model may be considered a starting point to define in an accurate way, the morphological characteristics of the pericarp that determine its hulling ability, something that may be very difficult to solve with an empirical approach.



Acknowledgements

This work is supported by the Secretaría Gral. de Ciencia y Tecnología (SeGCyT-)UNS, the Argentine Sunflower Association (ASAGIR) and Dow AgroSciences of Argentina. Authors want to thank Dr. C.N. Pellegrini (CIC) for histological processing, Mrs. L. I. Lindström for her valuable comments, and Engs. D. Ercoli and Mr. G. Massimiliani, (Polymers Lab., PLAPIQUI -CONICET) for their kind help with the INSTRON UTM.

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