Poroelastic modelling of the coupled mechanical moisture behaviour of wood
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- Όλυμπος Αλεξάκης
- 5 χρόνια πριν
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1 Ma terias Sci ence & Technoog y Poroeastic modeing of the couped mechanica moisture behaviour of wood M. Dresser, D. Derome, R. Guyer and J. Carmeiet
2 poroeastic modeing of wood - COST meeting October 00. objective Empa,,
3 poroeastic modeing of wood - COST meeting October 00 known effects of water - sweing B ϕ( p ) - moduus of easticity - Poisson s ratio - water sorption - stress dependent u Empa,, /6
4 poroeastic modeing of wood - COST meeting October 00 known effects of water - sweing 0.08 stressed in TT-direction stressed in RR-direction B ϕ( p ) stressed in LL-direction moduus of easticity - Poisson s 0.04 ratio sweing strain water sorption moisture content - mechano sorption moisture content moisture content F.-H. Neuhaus, Eastizitätszahen von Fichtenhoz in Abhängigkeit von der Hozfeuchtigkeit (easticity numbers of spruce as a function of wood moisture content), PhD thesis (in German), Institut für konstruktiven Ingenieurbau Ruhr-Universität Bochum (98) Empa,, /6 4
5 poroeastic modeing of wood - COST meeting October 00 known effects of water - sweing - moduus of easticity - Poisson s ratio u B C u ϕ( p ) - water sorption - stress dependent u Empa,, /6 5
6 poroeastic modeing of wood - COST meeting October 00 known effects of water - sweing moduus of easticity [MPa] moduus of easticity - Poisson s 000 ratio water sorption 00 data from Neuhaus cacuated vaues ue L E R E T B C u 000 ϕ( p ) E TL E LR stress dependent u moisture content E TR moisture content F.-H. Neuhaus, Eastizitätszahen von Fichtenhoz in Abhängigkeit von der Hozfeuchtigkeit (easticity numbers of spruce as a function of wood moisture content), PhD thesis (in German), Institut für konstruktiven Ingenieurbau Ruhr-Universität Bochum (98) Empa,, /6 6
7 poroeastic modeing of wood - COST meeting October 00 known effects of water - sweing Poisson's ratio moduus of easticity - Poisson s ratio ν TL u B C u ϕ( p ) ν TR ν RT ν RL - water sorption ν LT ν LR moisture content - stress dependent u moisture content moisture content F.-H. Neuhaus, Eastizitätszahen von Fichtenhoz in Abhängigkeit von der Hozfeuchtigkeit (easticity numbers of spruce as a function of wood moisture content), PhD thesis (in German), Institut für konstruktiven Ingenieurbau Ruhr-Universität Bochum (98) Empa,, /6 7
8 poroeastic modeing of wood - COST meeting October 00 constitutive equations - sweing - moduus of easticity - Poisson s ratio - water sorption - stress dependent u u u u B M B u ϕ( p C ϕ( p Empa,, /6 8 ) ) d = B( ) dϕ d = C( u) d du = M ( ) dϕ du = B( ϕ) d
9 poroeastic modeing of wood - COST meeting October 00 constitutive equations - sweing - moduus of easticity - Poisson s ratio - water sorption - stress dependent u u u u B M B u ϕ( p C ϕ( p Empa,, /6 9 ) ) d = B( ) dϕ d = C( u) d du = M ( ) dϕ du = B( ϕ) d d = Cd Bdp du = Mdp Bd J. Carmeiet, R. Guyer, D. Derome, 6 th Pant Biomechanics Conference, 009
10 poroeastic modeing of wood - COST meeting October 00. appication Empa,, 0
11 poroeastic modeing of wood - COST meeting October 00 resuts 4000 data from Neuhaus cacuated vaues 000 moduus of easticity [MPa] E L E R E TL E LR 00 E T moisture content moisture content E TR F.-H. Neuhaus, Eastizitätszahen von Fichtenhoz in Abhängigkeit von der Hozfeuchtigkeit (easticity numbers of spruce as a function of wood moisture content), PhD thesis (in German), Institut für konstruktiven Ingenieurbau Ruhr-Universität Bochum (98) Empa,, 5/6
12 poroeastic modeing of wood - COST meeting October 00 resuts....0 ν TL.0.0 Poisson's ratio ν TR ν RT ν RL ν LT ν LR moisture content moisture content moisture content F.-H. Neuhaus, Eastizitätszahen von Fichtenhoz in Abhängigkeit von der Hozfeuchtigkeit (easticity numbers of spruce as a function of wood moisture content), PhD thesis (in German), Institut für konstruktiven Ingenieurbau Ruhr-Universität Bochum (98) Empa,, 6/6
13 poroeastic modeing of wood - COST meeting October 00 resuts stressed in TT-direction stressed in RR-direction stressed in LL-direction UNstressed stressed data from Neuhaus sweing strain p kg -0.0 compressive stress 0, 0 MPa compressive stress 0, 0 MPa compressive stress 0, 0 MPa moisture content moisture content moisture content F.-H. Neuhaus, Eastizitätszahen von Fichtenhoz in Abhängigkeit von der Hozfeuchtigkeit (easticity numbers of spruce as a function of wood moisture content), PhD thesis (in German), Institut für konstruktiven Ingenieurbau Ruhr-Universität Bochum (98) Empa,, 7/6
14 poroeastic modeing of wood - COST meeting October 00 resuts stressed in RR-direction 0.0 stressed in LL-direction moisture content reative humidity reative humidity compressive stress 0, 0, 0 MPa p kg u reative humidity Empa,, 8/6 4
15 poroeastic modeing of wood - COST meeting October 00 resuts stressed in TT-direction stressed in RR-direction stressed in LL-direction p expeed moisture u(t=0) 5, 0 % u(t=0) 5, 0 % kg u 0.0 u(t=0) 5, 0 % compressive stress [MPa] compressive stress [MPa] compressive stress [MPa] Empa,, 9/6 5
16 poroeastic modeing of wood - COST meeting October 00 resuts 0 restrained in TT-direction restrained in RR-direction restrained in LL-direction p, start sweing stress [MPa] u(t=0) 0, 7.5, 5 % u(t=0) 0, 7.5, 5 % u(t=0) 0, 7.5, 5 % p moisture content moisture content moisture content Empa,, 0/6 6
17 poroeastic modeing of wood - COST meeting October 00 resuts 0.4 restrained in TT-direction RR-strain LL-strain 0.4 restrained in RR-direction TT-strain LL-strain 0.4 restrained in LL-direction TT-strain RR-strain p, start sweing strain u(t=0) 0, 7.5, 5 % u(t=0) 0, 7.5, 5 % u(t=0) 0, 7.5, 5 % p moisture content moisture content moisture content Empa,, /6 7
18 poroeastic modeing of wood - COST meeting October 00. physica background Empa,, 8
19 poroeastic modeing of wood - COST meeting October 00 couped moisture and mechanica behavior. tota differentia dω(, u) Ω Ω dω(, u) = d du u interna energy Ω(, u) Nm / m dω d d dω dt dt dω du du Empa,, /6 9
20 poroeastic modeing of wood - COST meeting October 00 couped moisture and mechanica behavior. tota differentia dω(, u) Ω Ω dω(, u) = d du u interna energy Ω(, u) Nm / m dω d d dω dt dt dω du du mode is isotherma Empa,, /6 0
21 poroeastic modeing of wood - COST meeting October 00 couped moisture and mechanica behavior. tota differentia dω(, u) Ω dω(, u) = d Ω Ω u Ω du u. Legendre transformation w(, p ) = Ω(, u) p u p Ω Ω p u Empa,, /6
22 poroeastic modeing of wood - COST meeting October 00 couped moisture and mechanica behavior. tota differentia dω(, u) Ω dω(, u) = d Ω Ω u. Legendre transformation w(, p ) = Ω(, u) p u dp p d u d. tota differentia d, du d = Ω du u p du = u p dp Empa,, /6
23 poroeastic modeing of wood - COST meeting October 00 couped moisture and mechanica behavior. tota differentia dω(, u) Ω dω(, u) = d Ω Ω u. Legendre transformation w(, p ) = Ω(, u) p u dp p d u d. tota differentia d, du d = Ω du u p du = u p dp strain capacity w C : = moisture capacity w M : = p couping coefficient w B : = p d = Bdp Cd du = Mdp Bd Empa,, /6
24 poroeastic modeing of wood - COST meeting October 00 couped moisture and mechanica behavior. tota differentia dω(, u) Ω dω(, u) = d Ω Ω u. Legendre transformation w(, p ) = Ω(, u) p u dp p d u d. tota differentia d, du d = Ω du u p du = u p dp strain capacity w Cijk = ij k moisture capacity M = w p couping coefficient B ij w = p ij d = C d B ij ijk k ij dp du = Mdp B ij d ij Empa,, /6 4
25 poroeastic modeing of wood - COST meeting October 00 energy function (D approach) w = w w stress water w couping Empa,, 4/6 5
26 Empa,, 6 energy function (D approach) 4/6 couping water stress w w w w = w stress = w stress poroeastic modeing of wood - COST meeting October 00
27 poroeastic modeing of wood - COST meeting October 00 energy function (D approach) w = w w stress water w couping w stress w stress = exampe: nd order approach wstress = water = 0 w C = = = const. w B = p = 0 w = 0 w couping w = d = Bdp Cd d = Cd = C Empa,, 4/6 7
28 poroeastic modeing of wood - COST meeting October 00 energy function (D approach) w = w w stress water w couping w stress w stress w water = u 0 u 0 = u0, FSP p v p g ρr TA ϕ / n w 0( ) water = u p dp u 0,FSP w = Ω(, u) p u dw = udp ϕ Empa,, 4/6 8
29 poroeastic modeing of wood - COST meeting October 00 energy function (D approach) w = w w stress water w couping w stress w stress = w water w water / nϕ p = u p dp u FSP p ρrvta 0 ( ) = 0, ( ϕ ) ρrvta ϕ n ϕ n ϕ Empa,, 4/6 9
30 Empa,, 0 energy function (D approach) 4/6 couping water stress w w w w = w stress w water w couping ( ) n FSP A u p u / 0, 0 / n ) ( = ϕ ϕ = R T p p Exp v g ρ ϕ = [0] [0] [0] 4 [0] [0] [0] 0 ) ( γ γ γ γ γ γ γ γ γ γ γ γ γ γ γ couping p u w ϕ ϕ ϕ ϕ ϕ ρ ρ n n R TA p R TA p u dp p u w n v v FSP water = = ) ( ) ( / 0, 0 poroeastic modeing of wood - COST meeting October 00 = w stress
31 poroeastic modeing of wood - COST meeting October 00 concusion Thermodynamic approach yieds set of two constitutive equations inking mechanica and moisture behavior d = Bdp Cd du = Mdp Bd Important effects of the couped moisture and mechanica behavior of wood are covered. Orthotropy of wood is taken into account. Empa,, 5/6
32 poroeastic modeing of wood - COST meeting October 00 Thank you Empa,, 6/6
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