Determination of the Viscoelastic Properties of Agar/Agar-Gelatin Gels Based on Finite. Element Method Optimization

Transcription

1 Food Sc. Technol. Res., 14 (6), , 2008 Determnaton of the Vscoelastc Propertes of Agar/Agar-Gelatn Gels Based on Fnte Element Method Optmzaton Gyeong-Won Km 1*, Gab-Soo Do 2, Yeonghwan Bae 3 and Yasuyuk Sagara 4 1 Natonal Insttute of Agrcultural Engneerng, Rural Development Admnstraton, 249 Seodun-dong, Gwonson-gu, Suwon, , Korea 2 Department of Boenvronmental and Agrcultural Engneerng, College of Boresource Scences, Nhon Unversty, 1866 Kameno, Fujsawa-sh, Kanagawa, , Japan 3 Department of Industral Machnery Engneerng, Sunchon Natonal Unversty, 315 Maegok-dong, Sunchon, , Korea 4 Department of Global Agrcultural Scences, Graduate School of Agrcultural and Lfe Scences, Unversty of Tokyo, Yayo, Bunkyo-ku, Tokyo, , Japan Receved December 3, 2007; Accepted July 1, 2008 An FEM algorthm was developed to determne the vscoelastc propertes of soft tssues of agar/agargelatn gels based on the curve-averaged data from stress relaxaton experment of parallel plate compresson and FEM optmzaton technque. Ths approach enabled more realstc and pertnent expresson of the mechancal behavor of the gels than conventonal methods, and allowed smultaneous and logcal characterzaton of all vscoelastc parameters, based on geometry, relatng to both Prony seres and Maxwell model such as elastc modulus, Posson s rato, relatve modulus, relaxaton tme, and dynamc vscosty, etc. Several assumptons were made n the FEM model such that the soft tssue materals were homogeneous n phase and sotropc, gravty effect was neglgble, and the response was transent and controlled by dsplacement. To demonstrate the valdty of the FEM model, the results of FEM optmzaton were compared wth those of conventonal method of nonlnear regresson for agar/agar-gelatn gels, and also the predcted mechancal behavor of FEM on compressve creep as an nterrelaton wth stress relaxaton by the FEM model was compared wth the expermental creep of 1% agar gel. The relablty of the FEM optmzaton method was confrmed by small stress devaton wthn 4.7% between expermental data and the FEM smulaton usng optmzed parameters for stress-relaxaton evaluaton for agar/agargelatn gels and by stran devaton wthn 3.4% for creep predcton of 1% agar gel. Keywords: agar, gelatn, gel, homogeneous structure, stress relaxaton, creep, FEM optmzaton, vscoelastc propertes *To whom correspondence should be addressed. Emal: km8415@rda.go.kr Introducton Mechancal propertes of sold/gel food materals are consdered as one of the most mportant factors n the desgn, manufacturng, and sensory evaluaton of food. Agar/ agar-gelatn s wdely used base materal for food as well as bomedcal and ndustral applcatons (Watase and Arakawa,1968; Ishhara et al., 2000; Anand and Scanlon, 2002). As food materal, the agar/agar-gelatn gels possess the characterstcs of vscoelastc rheology propertes (Kobayash and Nakahama, 1986) whch are expressed by elastc modulus, Posson s rato, and relaxaton tme (Anand and Scanlon, 2002). To determne the vscoelastc propertes of soft food materals, ndentaton tests usng flat-, cone-, and balltype ndentor (Anand and Scanlon, 2002; Lu et al., 2006), or compresson tests usng parallel plates (Km et al., 1992) were conducted, and then nonlnear regresson analyses were performed on vscoelastc models such as generalzed Maxwell model for stress relaxaton (Chen, 2000; Wang, 2003; Tels et al., 2003), or Burgers model for compresson creep (Wang et al., 1992, Park, 1993). However, the vscoelastc parameters obtaned by these statstcs-based analyss models n general are nsuffcent to express the mechancal behavor of orgnal materal snce they do not reflect the geometry of

2 526 specmen (ANSYS, 2004; Km et al., 2008). Furthermore, separate specmens are needed to determne the mechancal parameters such as elastc modulus, Posson s rato, etc, and thus the lack of unformty among the specmens mght reduce the relablty of the parameters especally for soft food materals. FEM analyss for food, fruts, and bologcal organsms has been appled to predct or compare the mechancal behavor of the materal of nterest by utlzng the vscoelastc parameters obtaned from mechancal tests (Chen and De Baerdemaeker, 1993; Wu and Ptts, 1999; Rong et al., 2004; Lu et al., 2006). Km et al. (2008) suggested a two-stage FEM algorthm to determne the vscoelastc propertes of apple flesh based on homogeneous structure model. In the frst stage, they determned the elastc modulus and Posson s rato of apple flesh specmen by usng Prony seres model (Chen, 2000; Wang, 2003; ANSYS, 2004) and FEM optmzaton method. In the second stage, they obtaned elastc modulus, relatve elastc modulus, and relaxaton tme based on stress-relaxaton model. However, the dfference n textural propertes between surface and core of apple flesh makes the assumpton of homogeneous phase questonable, and also the process of determnng vscoelastc propertes was a bt too complcated. It s consdered to be very practcal to develop a method of determnng all pertnent vscoelastc propertes of soft and homogeneous food materals smultaneously wthout performng multple and ndependent tests. The objectve of ths research s to develop an FEM algorthm of smultaneously determnng vscoelastc propertes of agar/agar-gelatn gels based on the results of stress-relaxaton tests. Ths methodology s expected to allow more realstc expresson of the mechancal behavor of soft textures followng generalzed Maxwell model based on the results of penetraton, ndentaton, as well as parallel plate unaxal compresson tests. Materals and Methods Specmens for compresson tests Agar gel of 1% concentraton (weght per volume) was used as a food model havng homogeneous and sotropc structure. Pure agar reagent (Lot No. Mta6118, Nacala Tesque, Inc., Tokyo, Japan) was dssolved n dstlled water solvent of 90 to 95 and G-W. Km et al. the obtaned solutons were held at the same temperature for 5 mnutes wth magnetc hot strrer. And then the solutons were cooled down to 50 n room temperature condton wth contnuous strrng. Fnally, the solutons were poured nto acrylc cylndrcal molds of 26 mm nner dameter and 40 mm heght before they were transferred nto an ncubator to make gels and to get stablzed at 25 for 20 h. Also, 1.0% agar-0.5% gelatn, 1.0% agar-0.75% gelatn, and 1.0% agar-1.0% gelatn gel specmens were prepared as addtonal food models. To make agar-gelatn gels, the gelatn solutons of pertnent concentratons were prepared by dssolvng gelatn reagent (Tayokagaku Co., Ltd., Shnmatch, Yokkach, Me, Japan) n dstlled water at room temperature wth magnetc strrng for fve mnutes, and they were heated to 70. The two solutons of agar and gelatn were mxed at 70 and cooled down to 50. The agar/agar-gelatn gel specmens were cut nto peces of 25 mm heght at one end of the cylndrcal molds. The average heghts of the agar/agargelatn gel specmens are lsted n Table 1. To avod spontaneous dehydraton, all specmens were kept covered wth PARAFILM (ALCAN Packng Inc. Chcago, USA) untl they were tested. Experments and stress-relaxaton model Three dfferent types of compresson experments were conducted wth RHEONER Ⅱ texture analyzer (Yamaden Co., Tokyo, Japan). The pre-contact force and trgger force were 0.04 N and 0.01 N, respectvely, and a constant cross-head speed of 0.1 mm/s was used. Pror to each compresson experment, a pece of frcton paper (Kmtowel wper, KURESYA Inc., Tokyo, Japan) of 0.03 mm thckness was put on the lower compresson plate and the sectoned plane of each specmen was placed on the frcton paper. To determne the amount of ntal deformaton n stress relaxaton, compresson rupture experments were performed wth three agar gel specmens. The force-deformaton (F-D) curves of the compresson rupture experments ndcated that elastc regon of ntal deformaton was up to 8% stran. Therefore, 5% stran was selected as the ntal stran of agar/agar-gelatn gel specmens for stress-relaxaton experments. The agar/agar-gelatn specmens were deformed at a constant rate of 0.1 mm/s up to the ntal stran (ε 0 = 0.05) and allowed to relax for 240 s. Three nomnal stress-tme curves obtaned from the stressrelaxaton experments for each type of agar/agar-gelatn Table 1. Average heght of agar/agar-gelatn specmens (mm). 1% agar a1.0-g 0.5 a1.0-g 0.75 a1.0-g a1.0-g 0.5 = 1.0% agar-0.5% gelatn, a1.0-g 0.75 = 1.0% agar-0.75% gelatn, a1.0-g 1.0 = 1.0% agar-1.0% gelatn.

3 Vscoelastc Propertes of Agar/Agar-Gelatn Gels by FEM gels were averaged n tme (curve-average) by usng Mcrocal Orgn (Verson 6, Mcrocal Software Inc., Northampton, MA, USA) and ths was utlzed as the representng stresstme curve for each agar/agar-gelatn gel type. The results of nomnal stress obtaned by curve-average and FEM analyss were compared at fve ponts n tme, t 0 /1.5, t 0, 30 s, 60 s and fnal relaxaton tme. By utlzng Maxwell model, the vscoelastc parameters for each agar/agargelatn gel type were obtaned as the ntal values of vscoelastc parameters of FEM optmzaton and the results were compared wth those of conventonal method based on nonlnear regresson analyss. The parameters were estmated by Marquardt-Levenberg nonlnear regresson method (Chen, 2000) of Mcrocal Orgn. The generalzed Maxwell model for each agar/agar-gelatn gel wth two parallel Maxwell elements can be expressed as Eq. 1 usng equlbrum and decay modul and relaxaton tmes of Prony seres,.e., a seres of the form n t / τ α e where α = 1 s the exponental coeffcents wth two terms (Chen, 2000; Wang, 2003; ANSYS, 2004; Km et al., 2008). σ ( t) = ε 0[ Ee + E1 exp( ( t t0) / τ1) + E2 exp( ( t t0) / τ 2)] E = Ee + ( E + 2 ) 0 1 E η = τ E ( =1, 2 ) where σ(t) and ε 0 are nomnal relaxaton stress and nomnal ntal stran, respectvely. E 0 and E e are the nstantaneous and equlbrum elastc modul, respectvely. E 1 and E 2 are the frst and second decay elastc modul, and τ 1 and τ 2 are the frst and second relaxaton tmes of the Prony seres, respectvely. η s the specfc vscosty (dynamc vscosty) of -th term. t ( t t 0 ) and t 0 are current tme and the past tme untl the begnnng of the relaxaton, respectvely. FEM model and optmzaton algorthm A hexahedral FEM element model was created by usng ANSYS 8.1 (1) 527 (ANSYS Co., Canonsburg, PA, USA), a commercal FEM program, to express the homogeneous and sotropc structure for agar/agar-gelatn gel specmens. The elements used for homogeneous model had three degrees of freedom at each node: translatons n the nodal x, y, and z drectons. The geometry of ths model was a three-dmensonal cylnder and made symmetrcal to the three axes to save computer run tme. Every element n ths model was meshed to a length of about 1.0 mm wth the excepton of the heght beng about 2.0mm by a quadrlateral meshng key n ANSYS, 2004 (Fg. 1). The procedure of FEM optmzaton s llustrated n Fg. 2. The FEM optmzaton technques appled n ths research were to smulate the same expermental condtons as the compresson experments (Km et al., 2008), and to obtan optmum vscoelastc parameters such as elastc modulus (E), Posson s rato (ν), relatve modul (β 1 E, β 2 E ) and relaxaton tme (τ 1, τ 2 ) n the Prony seres whch mnmzed the sum of nomnal stress errors at the fve ponts n tme by Sequental Unconstraned Mnmzaton Technque (SUMT) algorthm whch s used to solve an unconstraned problem usng penalty functons (Km et al., 2008; ANSYS, 2004). The vscoelastc parameters obtaned from the Maxwell model were utlzed as ntal estmates for FEM smulaton, and Posson s rato of 0.4 was adapted from lterature (Anand and Scanlon, 2002). The dfference n nomnal stress between the experments and FEM was used as a state varable and ts value was mantaned below 1% at ntal stran (ε 0 ) and below 3% at the other four ponts n tme to enforce convergence durng FEM optmzaton. The bounds for the desgn varables are: E 0 ± 50% for elastc modulus, 0.3 to 0.5 for ν, 0.01 to 1.0 for β 1 E and β 2 E, and 0.1s to 1000 s for τ 1 and τ 2. And all FEM optmzaton analyses were transent wthout gravty effect and controlled by dsplacement. In the kernel functon of FEM analyss, t was assumed Fg. 1. Orgnal experment geometry (left) and the smplfed symmetrc FEM geometry model of agar/agar-gelatn gel.

4 528 G-W. Km et al. Fg. 2. Flow dagram of FEM optmzaton procedure to determne the vscoelastc propertes of agar/agar-gelatn gels. that the quotent of decay modulus and nstantaneous modulus for each term of Prony seres was held constant for elastc, shear, and bulk modulus components as follows: E E G G K K E G K β = = β = = β = ( =1, ) (2) where β 1 E, β 1 G, and β 1 K ndcate relatve decay modul for Young s, shear, and bulk n relaxaton, respectvely, for the -th term of the Prony seres. Also, G and K are the -th term of decay shear modulus and decay bulk modulus, respectvely. Eq. 3 s the consttutonal equaton of stress whch s composed of shear and bulk kernel functons (ANSYS, 2004; Km et al., 2008) based on heredtary ntegraton for FEM Cauchy stress or true stress. t de t dδ σ = 2G ( t τ ) dτ + I K ( t τ ) dτ (3) 0 dτ 0 dτ where G(t) s the kernel functon for shear relaxaton and K(t) s for bulk relaxaton. Also, σ and I are the Cauchy stress and unt tensor, respectvely; τ s past tme; and e and Δ ndcate devatory stran and volumetrc stran, respectvely. Objectve functon for the FEM optmzaton algorthm s gven by the followng equaton: 5 Stress_dff. = wσ Re g ( or wσ Exper ) wσ FEM (4) = 1 where σ Reg and σ FEM are nomnal stresses of nonlnear regresson model and FEM, respectvely. Evaluaton of FEM optmzaton Intal valdatons were made on the FEM smulaton results of stress relaxaton for agar/agar-gelatn gel specmens wth reference to the expermental data. Two sets of vscoelastc parameters, one by FEM optmzaton (FEM usng optmzaton) and the other by nonlnear regresson (FEM usng regresson), were fed nto each FEM model for the smulaton of valdaton, and the nomnal stress values at the ntaton and end of relaxaton for each case were compared wth those of expermental averages. The second valdatons were made wth the set of vscoelastc parameters obtaned by FEM optmzaton on the compressve creep behavor of 1% agar specmens. Therefore, separate creep experments of three specmens (average heght of mm) for the valdaton 5 = 1

5 Vscoelastc Propertes of Agar/Agar-Gelatn Gels by FEM of the parameters were carred out wth 1% agar gels usng a constant load speed of N/s up to 11.9 s and holdng the load of 0.86 N untl t beng removed at s. It was assumed that the generalzed Maxwell model and heredtary ntegraton for FEM Cauchy stress (Eq. 3) were not suffcent to predct the compressve creep behavor of vscoelastc materals snce there are two dfferent deformaton natures on Newtonan dash pots n Burgers model whch conssts of a Maxwell element joned n seres wth a Vogt (or Kelvn) element (Park, 1993). Therefore, recovery behavor was gnored and only undrectonal loadng was consdered n the predcton of creep behavor n the FEM creep analyss. Two smulaton tests were performed on the analyss of creep behavor: quas-statc loadng as n the case of stress-relaxaton analyss and dynamc loadng consderng gravty effect n transent analyss. The strans at the tmes of creep ntaton and unloadng were evaluated by the two smulaton tests and compared wth expermental data. Results and Dscusson Nomnal stress The stress-relaxaton experments for 1% agar gel specmen provded nomnal stress values of ± kpa,1.626 ± kpa, ± kpa, ± kpa, and ± kpa at 8.1 s (t 0 /1.5), 12.4 s (t 0 ), 30 s, 60 s, and 240 s, respectvely. The representng curve through curve averagng n tme provded nomnal stress values of kpa, kpa, kpa, kpa, and kpa at the fve tme ponts as above, whch were wthn ± 0.84% of the average value at each tme pont. Smlar curves were obtaned by curve averagng for the three types of agargelatn gels and they were utlzed for non-lnear regresson 529 analyss and to compare drectly wth the results of FEM optmzaton. Table 2 shows the values of the objectve functon (Eq. 4, sum of stress errors) rangng from to kpa for the four types of agar/agar-gelatn gel specmens as a result of FEM optmzaton. Also the fnal values of the state varables (nomnal stresses at t 0 /1.5, t 0, t 1, t 2, and t 3 ) resulted n to kpa for 1% agar gel. At t 0, whch determnes nstantaneous elastc modulus, FEM nomnal stress decreased to kpa as the gelatn contents ncreased to 1.0% n 1.0 % agar specmen. The dfference n nomnal stress values between FEM analyss and expermental data remaned wthn 5.1% for the four types of agar/agar-gelatn gels. Especally at the ntal stage of stress-relaxaton, t 0, the dfference n stress values ranged from -2.4 to -1.0%. Vscoelastc propertes The vscoelastc parameters of 1% agar soluton obtaned by FEM optmzaton were: E = kpa, ν = 0.437, β E 1 = 0.128, β E 2 = 0.45, τ 1 = s, and τ 2 = s. As n the case of the elastc modulus by nonlnear regresson analyss, the modulus obtaned by FEM analyss decreased as the gelatn contents ncreased, and the dfferences n the values obtaned by the two methods were wthn 2.7%. As shown n Fg. 3(a), the FEM elastc modulus of 1% agar-1% gelatn was reduced by 6.6% than that of 1% agar gel. In Fg. 3(b) the FEM Posson s rato for all gels converged well wthn the boundary condton values of 0.3 to 0.5 whch were adapted from lterature (Anand and Scanlon, 2002). Addng 0.5% gelatn to 1% agar gel reduced Posson s rato to (-17%), whle addng 0.75% gelatn and 1% gelatn ncreased Posson s rato to and to 0.403, Table 2. FEM optmzaton results of state varables (nomnal stresses (kpa)) at fve ponts n tme and the objectve functon values n stress-relaxaton for agar/agargelatn gel specmens. Samples t 0 /1.5 t0 t = Relaxed tme ( t t0 ) Objectve t = t 1 t2 t = t = t3 t (s) kpa t (s) kpa kpa kpa kpa functon (kpa) Eq. (4) 1.0 % agar (0.3) (-1.0) (3.0) (4.0) (-0.6) a1.0-g (5.1) (-2.4) (1.1) (1.2) (-4.2) a1.0-g (4.4) (-1.6) (-0.1) (-1.4 ) (-4.7) a1.0-g (4.2) (-2.3) (-0.6) (0.4) (0.0)

6 530 G-W. Km et al. (a) Elastc modulus (b) Posson s rato (c) Relatve modul (d) Relaxaton tme Fg. 3. Effect of added gelatn contents (wt.%) on the vscoelastc parameters of 1.0 wt.% agar-gelatn gel soluton usng FEM optmzaton. respectvely. The maxmum dfference n the relatve modul ( β 1 E, β 2 E ) between the two methods, FEM and nonlnear regresson, was recognzed as up to 42.8%. The varaton n FEM β 1 E among the agar/agar-gelatn gels was relatvely small as compared wth FEM β 2 E, whch was reduced markedly by 45.1% ( β 2 E of nonlnear regresson was 37.9%) when 1% gelatn was added to 1% agar gel. The results dscussed above llustrated that the relatve modul were related to the reducton n the equlbrum modulus (Eq. 1) and the fnal reducton n the magntude of stress-relaxaton. The maxmum dfferences n relaxaton tme (τ 1, τ 2 ) obtaned by the two methods were 22.5% for τ 1 and 6.1% for τ 2. As ndcated n Table 3, Maxwell model (Eq.1) analyss of 1% agar gel for vscoelastc parameters obtaned by FEM optmzaton produced E e = kpa ( E 0 = kpa), E 1 =4.069 kpa, E 2 = kpa, η 1 =58.63 kpa s, and η 2 =2, kpa s. The values of E e ncreased greatly wth the ncrease n the contents of gelatn, addton of 1% gelatn to 1% agar of gel mxtures resulted n E e of kpa, an ncrease by 40.1%. The E e values by FEM optmzaton were lower than those by nonlnear regresson by 6.2 to 14.0%. The values of dynamc vscosty for the four types of agar/ agar-gelatn gels by FEM optmzaton were n the range of to kpa s for η 1 and to kpa s for η 2, the maxmum dfferences were 77.3% for η 1 and 14.8% for η 2 when comparng the results obtaned by the two methods. Each of the vscoelastc propertes (Prony seres parameters and Maxwell parameters) of agar/agar-gelatn gels obtaned by FEM optmzaton at an ntal stran of 5% exhbted smlar trend to the nonlnear regresson parameters n varaton accordng to the contents of gelatn n the gels. However, the maxmum dfferences n the vscoelastc parameters between FEM optmzaton and nonlnear regresson for agar/agar-gelatn gels were as small as 2.7% for nstantaneous elastc modulus, 14% for equlbrum elastc modulus, 42.8% for relatve elastc modulus, and as large as

7 Vscoelastc Propertes of Agar/Agar-Gelatn Gels by FEM 531 Table 3. Comparson of Maxwell model parameters of FEM optmzaton wth those of nonlnear regresson for stress relaxaton of agar/agar-gelatn gel specmens ( ε 0 = 0.05). σ ( t) = ε 0[ Ee + E1 exp( ( t t0) / τ1) + E2 exp( ( t t0) / τ 2)] Items E e (kpa) E 1 (kpa) τ 1 (s) η 1 (kpa s) E 2 (kpa) τ 2 (s) η 2 (kpa s) 1.0% agar a1.0-g 0.5 a1.0-g 0.75 a1.0-g 1.0 FEM Reg FEM Reg FEM Reg FEM Reg % for specfc vscosty. These dscrepances mght have been nduced by the facts that the nonlnear regresson, unlke FEM optmzaton, has no provson for geometry, Posson s rato, and the ncpent-mechancal behavor up to the ntal stran of stress relaxaton (Km et al., 1992; Cheng, 2000); and s based only on statstcal manpulaton of the coeffcents of the exponental decay functon. Evaluaton of stress relaxaton FEM stress-relaxaton smulaton for the four types of agar/agar-gelatn gel specmens was carred out by usng two sets of vscoelastc parameters to compare the performance of FEM optmzaton method (FEM usng optmzaton) and conventonal method of nonlnear regresson (FEM usng regresson), and the resultng nomnal stresses at t 0 and t 3 were evaluated wth reference to expermental values. For four types of gels, the errors n the resultng nomnal stress values for FEM usng optmzaton ranged from -1.6 to -2.4% (1% agar- 0.5% gelatn) of expermental value at t 0 and from -4.7 (1% agar- 0.75% gelatn) to 0.0% at t 3. However, at t 0 and t 3 the errors n the nomnal stress values for FEM usng regresson ranged from -7.5 (1% agar- 0.75% gelatn) to 1.0% and from 6.2 to 7.0%, respectvely (Fg. 4). Ths ndcated that the results of FEM optmzaton method explaned the stress-relaxaton behavor of agar/agar-gelatn gels better than those of nonlnear regresson method. Predcton evaluaton of FEM optmzaton Pror to the evaluaton of FEM smulaton for compressve creep behavor, the appled force was determned by dynamc FEM smulaton based on the expermental reacton force. The appled force thus obtaned was 0.99 N, and the reacton force mantaned the expermental value of 0.86 N. There were Fg. 4. Comparson of nomnal stress of two FEM smulatons usng FEM optmzaton vscoelastc parameters and usng parameters obtaned from nonlnear regresson wth that of experment of 1%-agar gel at ntal stran of 0.05 relaxed for 240 seconds. -3.5% and -6.4% dscrepances from expermental values at creep begnnng tme (11.9 s, 5.2% stran by experment) and at unloadng tme (311.9 s, 9.1% stran by experment), respectvely, when quas-statc FEM smulaton (FEM Opt.) was appled for creep analyss. On the other hand, FEM usng dynamc (wth gravty effect) resulted n 3.4% and 0.0% errors at creep begnnng tme and unloadng tme, respectvely (Fg. 5). Therefore, the effect of dynamc mechancal behavor was not neglgble n the creep behavor of 1% agar gel under constant compresson loadng. The creep behavor of

8 532 Fg. 5. Comparson of stran (%)-tme values of two FEM creep smulatons (dynamc behavor wth gravty (FEM Opt. usng dynamc) and quas-statc wthout gravty (FEM Opt.)), usng the same FEM optmzaton parameters-values, to those of experment of 1%- agar gel. 1% agar gel could be well predcted by the parameters from stressrelaxaton analyss once gravty effect was taken nto account. Consderng the valdty of FEM optmzaton method n analyzng stress-relaxaton and creep behavor, t was expected that ths approach could be appled to determne mechancal propertes of varous vscoelastc materals wth relatvely hgh accuracy. Also, the geometry based FEM optmzaton method s expected to be appled for frozen-thawed and other bomaterals whch are often dffcult to analyze by conventonal methods. Acknowledgement Ths work was supported n part by the Japan Socety for the Promoton of Scence (JSPS). The JSPS RON- PAKU Program s gratefully acknowledged by Gyeong-Won Km (KOSEF-10603). References Anand, A. and Scanlon, M.G. (2002). Dmensonal effects on the predcton of texturerelated mechancal propertes of foods by ndentaton. Trans. of the ASAE, 45, ANSYS. (2004). Elements, theory, and optmzaton. User s Manual, Verson 8.1, Canonsburg, PA. Chen, H. and De Baerdemaeker, J. (1993). Fnte-elementbased model analyss of frut frmness. Trans. of the ASAE, 36, G-W. Km et al. Chen, T. (2000). Determnng a Prony seres for a vscoelastc materal from tme varyng stran data. NASA TM , Hampton, VA. Ishhara, M., Mortaka, H., Nato, S. and Fukuba, H. (2000). Effect of soybean detary fber on the thermal and rheologcal propertes of gellan gum gels. Japan Socety of Home Economcs, 51, (n Japanese). Km, G.W., Km, M.S., Sagara, Y., Bae, Y. H., Lee, I-B., Do, G.S., Lee, S.H. and Kang, S.W. (2008). Determnaton of the vscoelastc propertes of apple flesh under quas-statc compresson based on fnte element method optmzaton. Food Sc. Technol. Res. 14(3), Km, M.S., Park, J.M. and Cho, D.S. (1992). Force-deformaton characterstcs of the frut fleshvscoelastc propertes of frut flesh. J. Kor. Soc. Agrc. Mach, 17, (n Korean). Kobayash, M. and Nakahama, N. Ishhara, M., (1986). Rheologcal propertes of mxedgels. Journal of Texture Studes, 17, Lu R., Srvastava A. K. and Ababneh. (2006). Fnte element analyss and experment evaluaton of boyeld probes for measurng apple frut frmness. Trans. of the ASAE, 49, Park, J.M. (1993). Vscoelastc propertes of fruts and ther applcatons. Ph.D. Dssertaton, Chungnam Natonal Unversty, Daejeon, Korea (n Korean). Rong, W., Qunyng J. and Deqang, W. (2004). On the mechancal damage of grape usng fnte element analyss. ASAE Paper , St. Joseph, MI. Tels-Remero, J. Guzzo-slva L. and Tels V. R. N. (2003). Rheologcal propertes of rehydrated papaya. Brazlan Journal of Food Techonology, 6, Walter, D (1994). Formulars for stress, stran, and structural matrces. John Wley & Sons, Inc., pp Wang, J. (2003). Ansotropc relaxaton propertes of pear. Bosystems Engneerng, 85, Wang, Y., Morshma, H., Seo, Y., Sagara, Y. and IMOU, K. (1992). Study on rheology of whte bread. Journal of Japan Socety for Agrcultural Machnery, 54, (n Japanese). Watase, M. and Arakawa K. (1968). Rheologcal propertes of hydrogels of agar-agar- Stress relaxaton of agarose gels. Bulletn of the Chemcal Socety of Japan, 41, Wu, N. and Ptts, M.J. (1999). Development and valdaton of a fnte element model of an apple frut cell. Postharvest Bology and Technology, 16, 1-8.