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Continuum Mechanics Modelling of Corrugated Board

Nyman, Ulf LU (2004) In Report TVSM
Abstract (Swedish)
Popular Abstract in Swedish

Wellpapp är ett populärt material i förpackningar för transport och lagring av konsumentvaror. Den viktigaste anledningen till dess popularitet är materialets höga styvhet och styrka, i förhållande till vikt och kostnad. Ingenjörsmässig användning av wellpapp kompliceras av många faktorer. En väsentlig nackdel är materialets känslighet för fuktpåverkan, vilken dessutom förvärras vid varierande luftfuktigheter jämfört med en konstant luftfuktighet. Vid lagring av wellpapplådor i miljöer med varierande luftfuktighet, till exempel i ouppvärmda lagerlokaler, är livslängden stokastiskt betingad. Dessutom kan rådande mekanisk belastning vid transport och lagring vara svår att definiera, som resultat av... (More)
Popular Abstract in Swedish

Wellpapp är ett populärt material i förpackningar för transport och lagring av konsumentvaror. Den viktigaste anledningen till dess popularitet är materialets höga styvhet och styrka, i förhållande till vikt och kostnad. Ingenjörsmässig användning av wellpapp kompliceras av många faktorer. En väsentlig nackdel är materialets känslighet för fuktpåverkan, vilken dessutom förvärras vid varierande luftfuktigheter jämfört med en konstant luftfuktighet. Vid lagring av wellpapplådor i miljöer med varierande luftfuktighet, till exempel i ouppvärmda lagerlokaler, är livslängden stokastiskt betingad. Dessutom kan rådande mekanisk belastning vid transport och lagring vara svår att definiera, som resultat av till exempel ovarsam hantering vid lastning, assymetriska staplingsmönster, ojämnt underlag mm.



Traditionellt sett, för att en låda skall klara en given lastnivå, fastställs dimensioner och materialkvaliteter med hjälp av enkla så kallade design formler. Dessa bygger på regression av ett stort antal mätdata av bärförmågan hos lådor, där wellpappens böjstyvhet, tjocklek och lådans omkrets utgör variabler. Dessa modeller ger ingen möjlighet att undersöka det enskilda papperets egenskaper eller förändrade belastningar, ej heller att ta hänsyn till fuktens påverkan av livslängden. Dessa så kallade dolda faktorer är brukligt att införliva med hjälp av reduktionsfaktorer, vilka ofta reducerar tillåten last till en bråkdel av korttidsbärförmågan hos en låda.



Till skillnad mot traditionella designmetoder syftar denna avhandling till att utveckla numeriska modeller för undersökning av belastningar som varar under lång tid. Tillvägagångsättet är att använda principer som härstammar från kontinuummekaniken och hållfasthetsläran. Dessa kan med fördel omformas till generella modeller med hjälp av finita elementmetoden. Tidsberoende variabler som till exempel fukthalt, töjnings- och spänningsfält och materialets styrka kan då simuleras för varierande klimat- och lastbetingelser. I ett första beräkningssteg utnyttjas en blandningsmodell för simulering av fukthalten i materialet. I nästa steg används olinjär hygroelasticitet för att bestämma materialets deformationer. I ett slutligt steg utvärderas materialets ansträngning och risk för kollaps. Metoden öppnar dessutom vägen för att göra en numerisk bedömning av sannolikheten för att en viss låda ej har kollapsat vid en given tidpunkt och rådande klimat. Möjligheten för känslighetsanalys av ingående parametrar finns också. (Less)
Abstract
The storage of compressive loaded boxes in an environment with naturally varying humidity is a practical issue in corrugated board employment. Time dependent variables such as moisture content, strain fields, stress fields and material strength play important roles for the time to failure. Supplementary, the stochastic nature of material and moisture load is obstructing the prediction of a reliable measure of lifetime. This work is composed of a number of portion proposals, each aiming on a method for a specific subproblem of the numerical modelling of time to failure.



Firstly, the focus is the problem of finite deformation hygro-elasticity. The assumption of kinematics is based on an additive split of the stretch in an... (More)
The storage of compressive loaded boxes in an environment with naturally varying humidity is a practical issue in corrugated board employment. Time dependent variables such as moisture content, strain fields, stress fields and material strength play important roles for the time to failure. Supplementary, the stochastic nature of material and moisture load is obstructing the prediction of a reliable measure of lifetime. This work is composed of a number of portion proposals, each aiming on a method for a specific subproblem of the numerical modelling of time to failure.



Firstly, the focus is the problem of finite deformation hygro-elasticity. The assumption of kinematics is based on an additive split of the stretch in an elastic part and a non-elastic part. In time stepping sequences the elastic stretch is updated by the use of the total stretch from the polar decomposed deformation gradient. As a consequence, in the linearized virtual work equation appears a hygroscopic contribution to the stiffness matrix as well as a hygroscopic load vector. Particularly, a numerical procedure for analyzing layered shells is developed.



Further, a numerical method for the transient moisture flow in porous cellulosic materials like paper and wood is examined. The derivation of the model is based on mass conservation for a mixture containing a vapour phase and an adsorbed water phase embedded in a porous solid material. A model for the development of higher order sorption hysteresis is also developed. The model is capable of describing cyclic hardening as well as cyclic softening of the equilibrium water concentration. The model is verified by comparison with the measured response to natural variations in temperature and humidity. A close agreement of the simulated results to measured data is found.



The reliability of geometrically non-linear composite shells is studied by use of the First Order Reliability Method (FORM). A finite difference method is employed in order to find the gradients of the limit state function. A failure stress criterion for corrugated board facings is also proposed. The failure criterion is based on material failure and structural local buckling failure. The structural failure stress is evaluated using a novel analytical solution for the buckling of long orthotropic plates under combined in-plane loading. The failure stress is compared with collapse experiments on corrugated board cylinders and the failure stress presented herein is seen to be in significantly better agreement with the measured stresses than the Tsai-Wu failure criterion alone.



Alongside with the numerical predictive methods, a number of testing procedures on individual paper materials and corrugated board boxes are performed. Firstly, mechanical second order stochastic field parameters of liner and fluting materials are estimated for a variety of materials used for commercial boards. Secondly, reliability testing of corrugated board boxes in a natural dynamic humidity environment is performed. A large number of boxes are loaded with a constant compressive force in an untempered airy indoor climate. Contemporary with the record of time to failures, the moisture transport in individual paper sheets and a sealed corrugated board box is measured. (Less)
Please use this url to cite or link to this publication:
author
opponent
  • Professor Onate, Eugenio, CIMNE, Spanien
organization
publishing date
type
Thesis
publication status
published
subject
keywords
Material technology, assumed natural strain shell, failure criterion, lifetime, reliability, moisture transport, sorption hysteresis, corrugated board, hygro-elasticity, Materiallära, materialteknik
in
Report TVSM
pages
215 pages
publisher
Ulf Nyman, Structural Mechanics, Box 118, SE-221 00 Lund, Sweden,
defense location
V-building, John Ericssons v. 1, Lund Institute of Technology
defense date
2004-05-27 09:15
external identifiers
  • other:ISRN:LUTVDG/TVSM--04/1017--SE
ISSN
0281-6679
ISBN
91-628-6111-5
language
English
LU publication?
yes
id
62f0ad66-7c4d-42fc-bd2a-2a948d13f058 (old id 467123)
date added to LUP
2007-09-10 13:26:40
date last changed
2016-09-19 08:44:53
@phdthesis{62f0ad66-7c4d-42fc-bd2a-2a948d13f058,
  abstract     = {The storage of compressive loaded boxes in an environment with naturally varying humidity is a practical issue in corrugated board employment. Time dependent variables such as moisture content, strain fields, stress fields and material strength play important roles for the time to failure. Supplementary, the stochastic nature of material and moisture load is obstructing the prediction of a reliable measure of lifetime. This work is composed of a number of portion proposals, each aiming on a method for a specific subproblem of the numerical modelling of time to failure.<br/><br>
<br/><br>
Firstly, the focus is the problem of finite deformation hygro-elasticity. The assumption of kinematics is based on an additive split of the stretch in an elastic part and a non-elastic part. In time stepping sequences the elastic stretch is updated by the use of the total stretch from the polar decomposed deformation gradient. As a consequence, in the linearized virtual work equation appears a hygroscopic contribution to the stiffness matrix as well as a hygroscopic load vector. Particularly, a numerical procedure for analyzing layered shells is developed.<br/><br>
<br/><br>
Further, a numerical method for the transient moisture flow in porous cellulosic materials like paper and wood is examined. The derivation of the model is based on mass conservation for a mixture containing a vapour phase and an adsorbed water phase embedded in a porous solid material. A model for the development of higher order sorption hysteresis is also developed. The model is capable of describing cyclic hardening as well as cyclic softening of the equilibrium water concentration. The model is verified by comparison with the measured response to natural variations in temperature and humidity. A close agreement of the simulated results to measured data is found.<br/><br>
<br/><br>
The reliability of geometrically non-linear composite shells is studied by use of the First Order Reliability Method (FORM). A finite difference method is employed in order to find the gradients of the limit state function. A failure stress criterion for corrugated board facings is also proposed. The failure criterion is based on material failure and structural local buckling failure. The structural failure stress is evaluated using a novel analytical solution for the buckling of long orthotropic plates under combined in-plane loading. The failure stress is compared with collapse experiments on corrugated board cylinders and the failure stress presented herein is seen to be in significantly better agreement with the measured stresses than the Tsai-Wu failure criterion alone.<br/><br>
<br/><br>
Alongside with the numerical predictive methods, a number of testing procedures on individual paper materials and corrugated board boxes are performed. Firstly, mechanical second order stochastic field parameters of liner and fluting materials are estimated for a variety of materials used for commercial boards. Secondly, reliability testing of corrugated board boxes in a natural dynamic humidity environment is performed. A large number of boxes are loaded with a constant compressive force in an untempered airy indoor climate. Contemporary with the record of time to failures, the moisture transport in individual paper sheets and a sealed corrugated board box is measured.},
  author       = {Nyman, Ulf},
  isbn         = {91-628-6111-5},
  issn         = {0281-6679},
  keyword      = {Material technology,assumed natural strain shell,failure criterion,lifetime,reliability,moisture transport,sorption hysteresis,corrugated board,hygro-elasticity,Materiallära,materialteknik},
  language     = {eng},
  pages        = {215},
  publisher    = {Ulf Nyman, Structural Mechanics, Box 118, SE-221 00 Lund, Sweden,},
  school       = {Lund University},
  series       = {Report TVSM},
  title        = {Continuum Mechanics Modelling of Corrugated Board},
  year         = {2004},
}