A Micromechanical Approach to the Nonlinear Poroelastic Behavior of Wood in a Multi-scale Frawework

Transcription

1 A Micomechanical Appoach to the Nonlinea Pooelastic Behavio of Wood in a Multi-scale Fawewok Ahmad Rafsanjani, Dominique Deome, Jan Cameliet EMPA Wood Laboatoy, Multiscale Modeling Goup Octobe 21 Wokshop Wood Stuctue/Function Relationships Octobe 5-8, 21, Hambug, Gemany

2 Objective To investigate the elation between macoscopic mechanical and moistue popeties of wood and its nano- and micoscopic stuctue using a multiscale appoach, thus to pedict the coupled moistue and mechanical behavio of wood

3 M1 Mico-mechanical modeling of ievesible mechano-soptive mechanisms in wood Fançois Gagnie ETHZ Pof. Hans Hemann D. Falk Wittel

4 M2 Multiscale poo-elastic model: bidging the gap fom cellula to macoscopic scale Ahmad Rafsanjani EMPA Deome Pof. Jan Cameliet

5 M3 Macoscopic model fo wood including nonlinea elasticity, moistue effects, hysteesis, damage and time dependent effects Matin Dessle EMPA Pof Jan Cameliet Deome

6 E1 4D expeimental investigation of hygo-mechanical behavio of wood on cellula scale Alessanda Patea EMPA D. Michele Giffa Cameliet Deome

7 E2 Multiscale expeimental detemination and desciption of wood unde vaying moistue and mechanical loading Chistian Lanvemann ETHZ Pof Pete Niemz

8 5 PhD students woking in sinegy

9

10 Multiscale model hieachy of submodels desciption of coupled mechanical and moistue behavio diffeent spatial scales inteconnection of submodels up-scaling - homogeneization

11 Themodynamical appoach Enegy state in isothemal case (, u) Legende tansfom (, p) (, u) pu J. Cameliet, R. Guye, D. Deome, 6th Plant Biomechanics Confeence, 29 11

12 (, p) (, u) pu d C d Bdp du Mdp B d

13 modulus of elasticity [MPa] pooelastic modelling of wood - COST meeting Octobe 21 esults 14 data fom Neuhaus calculated values E L E TL E LR 4 2 E R E T moistue content [1] moistue content [1] E TR F.-H. Neuhaus, Elastizitätszahlen von Fichtenholz in Abhängigkeit von de Holzfeuchtigkeit (elasticity numbes of spuce as a function of wood moistue content), PhD thesis (in Geman), Institut fü konstuktiven Ingenieubau Ruh-Univesität Bochum (1981) Empa,, 13 5/16

14 Poisson's atio [1] pooelastic modelling of wood - COST meeting Octobe 21 esults TL TR.8 RL RT LT LR moistue content [1] moistue content [1] moistue content [1] F.-H. Neuhaus, Elastizitätszahlen von Fichtenholz in Abhängigkeit von de Holzfeuchtigkeit (elasticity numbes of spuce as a function of wood moistue content), PhD thesis (in Geman), Institut fü konstuktiven Ingenieubau Ruh-Univesität Bochum (1981) Empa,, 14 6/16

15 (, p) (, u) pu d C d Bdp du Mdp Bd

16 Themodynamical appoach Isothemal state of enegy Mateial Popeties J. Cameliet, R. Guye, D. Deome, 6th Plant Biomechanics Confeence, ) ( ) ( ),, ( ) ) 2(1 ( 2 1 ), ( I B I B p g p f I I I N I I E p s ), (, ), (, ), ( p p M p p B p C ij ij kl ij ijkl Linea Elasticity Nonlinea Elasticity Fluid Fluid-Solid Inteactions

17 Incemental state equation Isothemal Pooelasticity d du Cd Bd Bdp Mdp C B ijkl ij [ E M s ( p)( B B 1 u ( p)] B I 1 1 ) ij ij kl 1 E s ik jl 2 N ij kl M M ( p) M ( p)( B I 1 B1I ) J. Cameliet, R. Guye, D. Deome, 6th Plant Biomechanics Confeence, 29 17

18 Wood micostuctue Effective Medium R T d du C d B d B dp M dp de du C B hom hom d B d M hom dp hom dp U u 18

19 Micomechanics Stain and stess concentation tenso, A E B Eshelby s solution fo ellipsoidal inclusion A [ I S Esh : ( K -1 : K I)] 1 : [ I S Esh : ( K -1 : K I)] 1 1 hom K K A f K : : Moi-Tanaka and Self-Consistent Scheme K matix hom K, K K A A. Zaoui, Continuum Micomechanics: suvey, J. Engineeing Mechanics ASCE, 128 (22) 19

20 Nonlinea micomechanics Elastic Behavio K( ) : C( ) : Linea Compaison Composites (LCC) K( ) K ( E) K hom K( ), hom : E K( ) : A( ) C( ) C E ( ) hom C C( ), hom : C( ) : B( ) P. Ponte Castaneda, Linea Compaison Methods fo Nonlinea Composites, 24 2

21 Lumen: elliptic cylinde inclusion Lumen dimensions Radial L R Tangential L T 21

22 Spuce coss section W. Zillig, Moistue tanspot in wood using a multiscale appoach, PhD Thesis, 29 22

23 Assumptions Elliptic Cylinde(a3 ) C ijkl C ijkl Esh Esh ( p) S ( C) S ( p) Linea Elasticity (N(I1,I2,I3)=) Equilibium moistue content Isotopic Matix Moi Tanaka Scheme J. Qu, M. Chekaoui, Fundamental of Micomechanics of Solids, 26 23

24 Geomety and popeties Ealywood Cell wall mateial popeties L L R T 5m 3m.8 E s 7MPa,.4 Latewood L L R T 15m 3m.4 24

25 moistue content (%) Soption Soption Isothem ,2,4,6,8 1 elative humidity 25

26 Elastic Modulus MPa Fee swelling test Evolution of elastic popeties with moistue 3 25 latewood E T 2 15 latewood E R 1 5 ealywood E T ealywood E R Moistue Content 26

27 moistue content (%) Swelling test: compession Soption Isothem: Compession -5MPa 3 25 Ealywood 2 Latewood ,2,4,6,8 1 elative humidity 27

28 adial stain [%] adial stain [%] tangential stain [%] tangential stain [%] 3 3 latewood ealywood adsoption desoption adsoption adsoption desoption adsoption RH [%] RH [%] latewood ealywood adsoption desoption adsoption adsoption desoption adsoption RH [%] RH [%]

29 Visualisation of ays by segmentation of voxel values Modeling the influence of ays on swelling

30 Swelling Stain Anisotopic swelling Restaining effect of the ays,16,14,12,1,8,6,4,2 Longitudinal Tangential Radial,1,2,3,4 Moistue Content(%) 3

31 Anisotopic swelling Unit Cell Model including a ow of ay cells Stess Stain 31

32 Computational homogenization High Resolution Finite Element Model selected fom -CT images 32

33 Computational homogenization Displacement configuations elated to six efeence stain states 33

34 Summay, too ealy fo conclusions Multiscale appoach: coupled behavio (mechanical and moistue) appopiate modeling at diffeent scales upscaling with ich infomation embedding components/mateial popeties micostuctue/macostuctue Towads study of influence of mophological and envionmental effects fo now, at steady state 34