Thermal And Dynamic Mechanical Properties Of Tomato Peel Biology Essay

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Tomato Lycopersicon esculentum Mill. is one of the most popular fruit among the world because of its nutrient components such as vitamin C and lycopin. As the largest tomato producer in the US, California produces 13.3 million tons tomatoes in 2009 which worth 1200 million dollars in total (California tomato grower association). Most of the tomatoes are processed into value-added food products, such as ketchup, paste, tomato sauce, diced tomatoes and so on (). Peeling operation is one of the water consuming and energy intensive steps among tomato processing, which causes environmental concerns due to the large amount usages of chemicals and thus producing waste water. Hot water and lye (Sodium hydroxide) are commonly used in the peeling process, which thus introduce waste water and chemicals to be processed before drained away to avoid ().

Infrared dry-peeling technology has been successfully used to peel tomato (xuan). This dry peeling method treats the tomato surface directly without any heating medium and chemicals thus to save water and energy. However, the mechanism behind infrared peeling is not well understood (?). Two possible reasons could be assumed. One is the peel structure was modified or partly destroyed to cause the peel fracture. The other one is the loosening of the connection between the peel and the out layer flesh.

The mechanical properties of tomato peel have been studied for both agronomic and processing purposes. The grower may want the peel to be firm enough, since the thick peel with high stiffness could resist the mechanical affects from surface crack during harvesting or transportation, while the consumer need the peel to be thin and soft for better taste (Hetzroni et al., 2011). The food industries may also prefer the firm tomato skin to be easily peeled and collected. The tensile measurement was proofed to be sufficient for the analysis biomechanical characteristics of tomato peel (Hetzroni et al., 2011). It was found that the mechanical properties showed large variation between different varieties, and the tensile measurement was independent from the punch measurement. The tomato skin consists of an external epidermal layer and two to four layers of thick-walled hypodermal cells with collenchymalike thickening (Ho & Hewitt, 1986). The epidermis has been suggested to be the fruit component controlling mechanical strength, which is related to cracking and puncture resistance. The mechanical properties of ripe tomato skin under uniaxial tension have been characterized by strength, strain at failure, overall stiffness and degree of stiffening. It was found that ripe tomato skin was stronger in the transverse than the longitudinal direction (Hershko et al., 1994), which meant that the longitudinal direction should be paid more attention when analyzed the tomato peeling since it would crack first during heating or mechanical force.

Ho, L.C., Hewitt, J.D., 1986. Fruit development. In: Atherton, J.G., Rudich, J. (Eds.), The

Tomato Crop: A Scientific Basis for Improvement. Chapman and Hall, London,

New York.

Hershko, V., Rabinowitch, H. D., Nussinovitch, A., 1994. Tensile characteristics of ripe

tomato skin. Lebensm. Wiss. Technol. 27, 86-389.

Dynamic mechanical analysis (DMA), which would provide the dynamic response information of the sample to the change of temperature or frequency, has been widely used in the determination of the material properties (Zhou et al. 2009). It could supply useful information about the mechanical nature of the material, such as storage modulus, loss modulus, and the glass transition temperature (Li et al., 2010). The mechanical response of the tomato peel tested by DMA during heating could well illustrate the actual changing status of the tomato peel in infrared heating process. The frequency sweep could help to understand the tomato peel response to different mechanical condition like peeling or the following transportation. DMA???2-3

Jackman has utilized dynamic oscillation techniques to evaluate the oscillatory strain and viscoelastic parameters of excised tomato discs in order to determine the effects of turgor pressure and chilling on structure and failure mechanisms (Jackman et al., 1992; Jackman and Stanley, 1992; Jackman et al., in press).

The dynamic mechanical pa

Tomato peels have also been found to exhibited pronounced viscoelastic properties and strain-hardening behavior (Matas et al., 2004). A simple rheological model for the tomato fruit wall has been proposed, and the results indicated that the outer fruit wall and the CM of Inbred 10 and Sweet 100 cherry tomatoes are isotropic, viscoelastic, and, to different degrees, strain-hardening structures .

Matas, A. J., Cobb, E. D., Bartsch, J. A., Paolillo, D. J., & Niklas, K. J. 2004. Biomechanics and Anotomy of Lycopersicon Esculentum Fruit Peels and Enzyme-treated Samples. American Journal of Botany, 91(3), 352-360.

Zhou, Y.-g., Wang, L.-j., Li, D., Yan, P.-y., Li, Y., Shi, J., Chen, X. D., & Mao, Z.-h. (2009). Effect of sucrose on dynamic mechanical characteristics of maize and potato starch films. Carbohydrate Polymers, 76 (2), 239-243.

Li, X.-Y., Wang, Y., & Li, D. (2009). Effects of flaxseed gum addition and drying conditions on creep-recovery properties and water vapour transmission rate of starch-based films. International Journal of Food Engineering, 5 (4), article No. 10.

To the best of our knowledge, there is no study on the dynamic mechanical properties of tomato as affected by infrared heating. Thus this study would focus on the mechanical properties of tomato in different infrared heating time. Four testing modes (static force, creep, temperature ramp, and frequency sweep) were used to approach to investigate the changes of tomato skin during infrared peeling. This study would provide useful information for the understanding of the mechanism of tomato infrared peeling. Besides, it could also help to numerically evaluate the infrared peel performance thus to optimize the process.

2. Materials and methods

2.1 Materials

The XXXX variety Roma tomato was collected in the local farm (Woodland, California, US). The tomatoes used in this study were chosen as the medium size, which have weight of 83±16, volume of 88±17 mL, and soluble content of 4.9±0.2. Sodium hydroxide at analytical grade was purchased from Sigma (St. Louis, US). Deionized water was used in the entire study.

2.2 IR heating

The IR heating equipment was described in detail in previous study (). The tomato was heated between two natural gas-powered IR radiator plates at constant power rate for 30s, 45s, 60s or 75s, respectively. And then the tomato peel was carefully removed from the sample using blade. The flesh was removed as much as possible from the peel. Fresh tomato without IR heating was used as reference.

2.3 Dynamic Mechanical Analysis

Two groups of samples were analyzed for dynamic mechanical properties using a DMA 8000 (PerkinElmer, Waltham, Massachusetts, US). First group was the IR treated one as described in section 2.2. The second group was peel cut longitudinally from fresh tomato to be used as control sample.

The tomato peel sample was prepared with four rectangular razor blades mounted on a wood block to get approximate dimension of 9mm*5mm*0.1mm. The accurate dimension of each sample was measured using an electric caliper and input the DMA software to minimize the affect of dimension difference on the result. Tests were conducted immediately after the skin samples were cut from the fruit. If failure developed at or near the clamping grips of the flat strip or the circular disk samples, the test was aborted and its data were discarded.

The film tension geometry was used for both groups of samples. Four testing modes were chosen for the test: static force, creep-recovery, frequency sweep, and temperature ramp. In the static force test, an increasing static force was applied to the sample with rate of 0.2 N/min. The maximum force applied was 3 N. The applied force and corresponding displacement of the sample were recorded during the experiment. In the creep-recovery test, the sample was equilibrated for 1 minute. Then a static force of 0.3 N was applied to the sample and held for 2 min, after which the force was removed and the sample was allowed to recover for another 2 min. In the frequency sweep, the sample was tested in the frequency range of 0.01-10 Hz with constant preload displacement of 0.05 mm. Ten data points were recorded for every frequency decade. In the temperature ramp, the sample was heated from room temperature to 120 â-¦C at heating rate of 5 â-¦C/min with constant preload displacement of 0.05 mm. The frequency was kept at 1 Hz during the temperature ramp tests.

Plastic preservation film was used to cover the sample surface to prohibit the water evaporation in the static force, the creep-recovery, and the frequency sweep tests, while Aluminum foil was used in the temperature ramp test. The static force, the creep-recovery, and the frequency sweep tests were all conducted at 25 â-¦C

2.4 Statistical analysis

All the mechanical measurements were carried out at least in triplicate. The experimental data were obtained directly from the PerkinElmer software V 5.4.7 软件名ç°ç‰ˆæœ¬ (PerkinElmer, Waltham, Massachusetts, US). The average of the three runs was reported as the measured value with standard deviation.

Duncan's multiple comparison tests were conducted to determine the significant effect of IR heating on the mechanical properties of tomato peel samples at p < 0.05 using the SAS software (SAS Institute Inc., Cary, NC, USA). The creep data was modeled according to Berger's model, using the non-linear regression feature in SPSS 13.0 (SPSS Inc., Chicago, USA).

3. Results and discussion

3.1 Static force test

Static force





et al., 1994).

Hershko, V., Rabinowitch, H.D., Nussinovitch, A., 1994. Tensile characteristics of ripe

tomato skin. Lebensm. Wiss. Technol. 27, 86-389.

这篇æ-‡ç« è¯´æ¨ªå‘的力å¤äºŽçºµå‘çš„¼Œè·Ÿè‚察的结果¼ˆè£‚ç-•æ€»æ˜¯çºµå‘¼‰ä¸€è‡´ã€‚推论错了吼Ÿåº”该是裂纹多为横向才能å¾-到此结果。

应力应变曲线的power lawæ-¹ç¨‹¼ŒK表示高度¼Œè¿˜æ˜¯longitudinal小¼Œn代表æ-œçŽ‡¼Œå˜åŒ-趋势反过来


考虑一下模仿这个做power lawæ-¹ç¨‹¼Ÿ¼Ÿ¼Ÿ¼Ÿ¼Ÿ



Fig. 1 一个碱液浓度的图¼Œ

Fig. 2 一个浸泡æ-¶é-´çš„图


This initial, linear region of the curve, up to the inflection, is known as Hooke's region, and it represents

non-destructive elastic deformation that reflects the elastic

modulus; it is often used by materials engineers as an index of stiffness

of the sample. The slope, k, of Hooke's region represents the

stiffness of the tissue. With the Y-axis representing load and the

X-axis representing extension, the steeper the slope, the stiffer the


The slope of the linear portion of the curve, up to the inflection

point (greatest slope in Fig. 2), represents non-destructive elastic

deformation that reflects the elastic modulus, and is often used by

materials engineers as an index of stiffness of the sample.


Biomechanical characteristics of tomato fruit peels


The offset value is used for automatic offset

yield calculation; it is also known as the proof strength point, and

is specified as a fraction of the sample gauge length that is used to

locate the 1% proof-stress point.

这个offset怎么确定¼Ÿä¸Žæ ‡å‡†ç›´çº¿åç¦»5%¼Ÿé‚£è¿™æ¡æ ‡å‡†ç›´çº¿å¦‚何确定¼Ÿ

3.2 Creep test

Fig. 4 一个creep recovery的原å‹å›¾¼Œåˆ†ä¸¤ä¸ªå½±å“¼šIR peeling æ-¶é-´ä»¥åŠæ¸©åº¦

Creep test and creep curve modeling have been used to the tomato cuticle and epidermis in previous studies (Petracek & Bukovac, 1995; Thompson, 2001). The creep test results of the IR heated tomato peels were shown in Fig. 4. When the static force was applied at the beginning of the test, there was an enormous in the displacement during the first ten seconds. After that, the displacement of the tomato peel would continue to increase at a relatively low speed till the end of the experiment. But the IR treated samples with different heating time didn't show significant difference comparing with the control sample.

Petracek, P. D. & Bukovac, M. J., (1995). Rheological Properties of Enzymatically lsolated Tomato Fruit Cuticle, Plant Physiology, 109, 675-679.

Thompson, D. S., (2001). Extensiometric determination of the rheological properties of the epidermis of growing tomato fruit. Journal of Experimental Botany, 52(359), 1291-1301.

Creep behavior of tomato peel can be described using Burger's model (Chuang & Yeh, 2006)¼Œwhich is a four element model consisting of springs and dashpots in the form of Maxwell and Kelvin components. The total strain ε is given by the following expression:


Where E1 (Pa) is the instantaneous elastic modulus; E2 (Pa) is the retarded elastic modulus; η1 (Pa s) is the coefficient of viscosity associated with viscosity flow; t2 (s) is the relaxation time and σ (Pa) is the constantly applied compressive stress. The parameters Е1, Е2, η1, and t2 can be obtained from fitting the experimental data to the equation with SPSS software.

Chuang, G. C. C., & Yeh, A. I. (2006). Rheological characteristics and texture attributes of glutinous rice cakes (mochi). Journal of Food Engineering, 74, 314-323.

Table 1 Burger's model parameters of the creep curves of IR heated tomato peels.


E2 (Pa)

t2 (s)

η1 (kPa•s)




























Parameters for the Berger's model of tomato peels in the creep test are listed in Table 1. The experimental data fitted Berger's model well (R2 > 0.99).The E1 value was not shown in the table because the instant elastic deformation was hardly detected in the creep curves of tomato peel. The E2 value is the symbol of retarded elastic deformation, reflecting the resistance caused by the 3D structure change of the tomato peels (Wang et al., 2009). All the IR heated samples have higher E2 value than the control sample, indicating that the IR heating could increase the sample's resistance to long-term deformation. The E2 value of the tomato peels have been found to be increasing with the temperature increase in previous study (Lopez-Casado et al., 2010). The relaxation time, t2, is the time required for the applied stress to decrease to 1/e (approximately 36.8%) of its initial value under constant deformation (Jiménez-Avalos et al., 2005). All the IR heated samples have slightly higher t2 value than the control, but have no significant difference between each other (p > 0.05). The η1 value is the reflection of the viscosity of the samples, which didn't show significant difference between the IR treated samples and the control, as shown in Table 1. The modeling of the creep curves has been used on the tomato cuticle in previous study, in which comparable but lower E2 values and higher t2 values have been reported (Lopez-Casado et al., 2010).

Jiménez-Avalos, H. A., Ramos-Ramírez, E. G., & Salazar-Montoya, J. A. (2005). Viscoelastic characterization of gum arabic and maize starch mixture using the Maxwell model. Carbohydrate Polymers, 62, 11-18.

Wang, Y., Wang, L. J., Li, D., Xue, J., & Mao, Z. H. (2009). Effects of drying methods on rheological properties of flaxseed gum. Carbohydrate Polymers, 78(2), 213-219.






把creep数据å-对数,之后做线æ€æ-¹ç¨‹,æ-œçŽ‡å³ä¸ºrate of creep.

这些人发现,从rate of creep来看,peel å’ŒCM之é-´æ²¡æœ‰å¤ªå¤ä¸åŒ.但是力从小到å¤ä¸Žä»Žå¤åˆ°å°ä¹‹é-´åŒºåˆ«æ˜Žæ˜¾.

这篇æ-‡ç« ä¸­creep循环用了逐渐增加的力,并计ç®-young's modulus随着力增加而增加,这说明西红柿皮的材æ-™ç‰¹æ€æ˜¯å-"应力历史"影响的。但是此æ-‡åŒæ-¶è€ƒè™‘了两个因素¼Œä¸€ä¸ªæ˜¯"应力历史"、一个是力的增夼Œè€Œæˆ‘的实验可以证明¼Œåº”力历史肯定有影响。对于一个材æ-™æ¥è¯´¼Œæ¨¡é‡E不应该变åŒ-¼Œå¦‚果实验够精确。

完整皮的young's modulus在5-25MPa, CM的在10-60MPa之é-´,与本æ-‡ç›¸ç¬¦åˆ

è¿™çæ¨¡åž‹çš„æ-¹æ³•åœ¨ä¸‹è¾¹è¿™ç¯‡æ-‡ç« é‡Œè¾¹ä¹Ÿæœ‰ç”¨åˆ°,ä»-们用

LTE和KE1表示short-term creep, 用KE2和VFE表示medium to long-term behaviour

Log-time function element, Kelvin element, viscous flow element

都是Rheological model的一獼Œæ‹¿æ¥å‡‘çš„¼Œè·Ÿæˆ‘用的模型有点像


这个图说明主要承å-力的部分是cuticle,å…¶ä»-的细胞多点少点æ- æ‰€è°“

3.3 Temperature ramp of the tomato peels

Fig. 4. Effects of infrared treatment on the storage modulus (E') and loss modulus (E'') with response to the increasing temperature (the labels with number shows the treatment time).

The mechanical response of tomato peels to the increasing temperature as affected by infrared heating was shown in Fig. 4. The storage modulus values of all the samples firstly decreased with the increase of temperature (see Fig. 4A), then started to increase after reached their lowest point (named as "transition point" in this study) around 60-80 â-¦C depending on the treatment time. This trend was consistent with previous study in which the storage modulus of tomato peels was found to start decreasing around 20 â-¦C (Matas et al., 2005; Lopez-Casado et al., 2007). However, no transition point was reported in the above study due to the temperature limit (up to 45 â-¦C) and lack of data (only 5 data for the whole temperature range) (Lopez-Casado et al., 2010). As shown in Fig. 4, all the IR treated samples have both higher storage modulus value and higher loss modulus value than the control sample. The loss modulus was found to have similar trend with the storage modulus (see Fig. 4B), in which the loss modulus firstly decreasing then started to increase when the temperature was increasing. Transition point was also found in the temperature curve of loss modulus. But it was not discussed in detail because of it was highly coefficient with the transition temperature of loss modulus.

Matas, A. J., López-Casado, G., Cuartero, J., & Heredia, A. 2005. Relative Humidity and Temperature Modify the Mechanical Properties of Isolated Tomato Fruit Cuticles. American Journal of Botany, 92(3), 462-468.

Lopez-Casado, G., Salamanca, A., & Heredia, A. 2010. Viscoelastic nature of isolated tomato (Solanum lycopersicum) fruit cuticles: a mathematical model. Physiologia Plantarum, 140, 79-88.

Lopez-Casado, G., Matas, A. J., Dominguez, E., Cuartero, J., & Heredia, A. 2007. Biomechanics of Isolated Tomato (Solanum lycopersicum L.) Fruit Cuticles: the Role of the Cutin Matrix and Polysaccharides. Journal of Experimental Botany, 58(14), 3875-3883.

Fig. 5. Effects of infrared treatment on the transition point of the tomato peels during temperature ramp (a. Transition temperature; b. Modulus value at transition point; c. Tan delta value at transition point) 1.

1 Values of each bar with different labels were significantly different (p < 0.05).

The mechanical information of the tomato peels treated by infrared heating at the transition point was analyzed and illustrated in Fig. 3. The transition temperature of all the treated samples are significantly lower than the control sample, which indicating that the tomato peels are going to get their mechanical failure at lower temperature. This could be a symbol for easy peeling during the tomato processing in food industry, where the tomato was firstly heated before peeling. All the IR treated samples shown similar transition temperatures between each other as indicated by Duncan test (shown in Fig. 5a). It reflects that even a short time IR treatment could achieve low transition temperature of the tomato peel.

All the samples have comparable but lower modulus value with previous studies on tomato cuticular membrane. It make sense because cuticular membrane is a thin layer but supply the main mechanical support for the peel, thus making it has higher modulus values based on the calculation (Allende et al., 2004; Matas et al., 2005). Both of the storage modulus and loss modulus values of infrared treated samples are significantly higher than that of the control samples, as shown in Fig. 5b. This difference in modulus indicated that IR treated tomato would likely to remain larger peels and less cracks during the peeling process. It is because the high mechanical strength of the IR treated sample could help to hold the peel from cracking. 这个地æ-¹è¿˜å·®ä¸€å¥delta的描述

Allende, A., Desmet, M., Vanstreels, E., Verlinden, B. E. & Nicolaï, B. M. 2004. Micromechanical and geometrical properties of tomato skin related to differences in puncture injury susceptibility. Postharvest Biology and Technology, 34, 131-141.

3.4 Frequency sweep of the tomato peels

Fig. 6. Frequency spectra for the storage modulus and loss modulus of tomato peels treated by IR heating (a for storage modulus; b for loss modulus; c for tan delta). The solid lines in the figure a and b are the trend lines of the Power Law model.

The frequency response of the modulus of tomato peels as affected by the IR treatment was shown in Fig. 6. All the modulus values of the samples were increased with the increase of frequency, indicating the viscoelastic nature of tomato peels. And the modulus values of IR treated samples were all higher than the control sample. This kind of modulus difference was also similar with that in the temperature ramp tests. A possible reason is that the IR treatment could reduce the moisture content of the tomato peels, especially the surface cuticular parts. And the cuticular membranes, which was mainly made up of pectin, was the part contribute most to the mechanical strength of the tomato peel. And then the modulus values were increased, because the moisture content was found to be negative for the mechanical strength of tomato peels (Lopez-Casado et al., 2007).

Lopez-Casado, G., Matas, A. J., Dominguez, E., Cuartero, J., & Heredia, A. 2007. Biomechanics of Isolated Tomato (Solanum lycopersicum L.) Fruit Cuticles: the Role of the Cutin Matrix and Polysaccharides. Journal of Experimental Botany, 58(14), 3875-3883.

The frequency dependence of storage modulus (also called elastic modulus) E' and loss modulus (also called viscous modulus) E'' for tomato peels can be approximately described, for the frequency range studied, by the Power Law model (Ikeda & Nishinari, 2001):



where K' and K'' are constants and n' and n'' may be referred to as the frequency exponents, and ω is the frequency. The value of n' and n'' can provide useful information regarding the viscoelastic nature of food materials (Ã-zkan et al., 2002).

Ikeda, S., & Nishinari, K. 2001. On solid-like rheological behaviors of globular protein solutions. Food Hydrocolloids, 15, 401-406.

Ã-zkan, N., Xin, H., & Chen, X. D. 2002. Application of a depth sensing indentation hardness test to evaluate the mechanical properties of food materials. Journal of Food Science, 65, 1814-1820.

The Power Law parameters of the frequency spectra of tomato peels treated by infrared heating were shown in Table 1. These results could be used to accurately describe the effects of IR or lye treatment on the frequency response of the modulus. The K' and K" values could be used as standard values for the overall modulus range. And the n' and n" values could reflect the level that how much the modulus of tomato peels would be affected by the increase of frequency. Because of the complexity of the tomato peel structure, there is usually a considerably big variation in the mechanical analysis of tomato peel (Hetzroni et al., 2011). But the Power Law modeling could enable the expression of the changes caused by IR treatment in terms of basic mechanical parameters, which are least affected by the type of instrument method (Hershko et al., 1994). As shown in Table 1, the K' and K" values are steadily increased along with the increase of heating time. The 30s samples are slightly higher than the control in K' and K" values. But the 45s, 60s, and 75s samples are significantly higher than the control and have no significant difference between each other in K' and K" values (p < 0.05). It means that the 45s infrared heating was enough to dry the cuticular membranes to certain distance so that the storage and loss modulus would be higher than the control. The K' and K" values of the treated sample are more than two times as the control ones. No significant difference is found between the control and treated samples in n' and n" values.

Since the mechanical characteristics of the tomato peels were strengthened by the infrared heating as indicated by the temperature ramp and frequency sweep results, the mechanism of the infrared peeling would less likely to be because of the structure destroy of the peel caused by heating. In general, the applying of IR heating could increase the mechanical parameters of the tomato peel so that the peel would remain in large piece to help the peel collection process following heating and peeling. The larger piece of peel has also been observed in the practical usage when comparing the infrared heating and the common lye peeling methods (data not shown). Thus the mechanism behind IR peeling would more likely be the loosening of the connection between the cuticular membrane and the out layer of flesh, which still need future confirmation.

Hetzroni, A., Vana, A., & Mizrach, A. 2011. Biomechanical characteristics of tomato fruit peels. Postharvest Biology and Technology, 59, 80-84.

Hershko, V., Rabinowitch, H. D., & Nussinovitch, A. 1994. Tensil Characteristics of Ripe Tomato Skin. LWT- Food Science and Technology. 27, 386-389.

Table 1. Power Law parameters for the frequency spectra of tomato peels treated by IR heating.

Heating time

K1 (MPa)



K2 (MPa)







































Postharvest Biology and Technology 59 (2011) 80-84

Biomechanical characteristics of tomato fruit peels

Amots Hetzroni, Arie Vana, Amos Mizrach

Matas, A. J., Cobb, E. D., Bartsch, J. A., Paolillo, D. J., & Niklas, K. J. 2004. Biomechanics and Anotomy of Lycopersicon Esculentum Fruit Peels and Enzyme-treated Samples. American Journal of Botany, 91(3), 352-360.

Cuticular membranes比peel更强å¤çš„另一个证据¼ŒåŒæ ·ç”¨æ¥è£é‡Šlye减小

Pectin的作用。这篇就是酶处理的æ-‡ç« ¼Œ

这个特æ€è·Ÿè¥¿çº¢æŸ¿æ˜¯å¦æ•æ„Ÿæ€ susceptibility to cracking when ripe

表皮主要有两部分组成¼ŒCPå’ŒCL¼Œç»„成CM¼Œå…¶ä¸­CL主要成分是pectin-rich region




所谓的strain harden现象,有个图片示意,就是细胞被拉长了

We believe that strain-hardening and strain-softening reflects

the response of microfibrils in the CM to tensile forces.

Prior work indicates that fibrillar components in cell walls can

progressively align in the direction of applied tensile forces

such that the effective Young's modulus increases (see Ko¨hler

and Spatz, 2002).

However, when excessively extended, the

fibrils may slip past one another (as their matrix deforms) and

the Young's modulus decreases.

KO¨ HLER, L., AND H.-C. SPATZ. 2002. Micromechanics of plant tissues beyond

the linear-elastic range. Planta 215: 33-40.

According to this model, a tensile force causes cell wall fibrils to increasingly align parallel to the direction of the applied force, thereby increasing the CM Young's modulus

(strain-hardening). When excessively extended, fibrils begin to

slip past one another decreasing the CM Young's modulus

(strain-softening). The magnitude of the ''critical'' force will

depend on the original net orientation and abundance of CM

fibrils, which will correlate to some degree with the thickness

of the CM.

Lopez-Casado, G., Matas, A. J., Dominguez, E., Cuartero, J., & Heredia, A. 2007. Biomechanics of Isolated Tomato (Solanum lycopersicum L.) Fruit Cuticles: the Role of the Cutin Matrix and Polysaccharides. Journal of Experimental Botany, 58(14), 3875-3883.

Mechanical behaviour of isolated tomato fruit cuticles and their cutin matrices

这两个词貌似代表不同的 东西,西红柿皮的è’质层,讨论的æ-¶å€™å¯ç”¨