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
poroeastic modeing of wood - COST meeting October 00. objective Empa,,
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
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 0.06 - moduus of easticity - Poisson s 0.04 ratio sweing strain 0.0 0.00 - water sorption -0.0 0.0 0. 0. 0. 0.0 0. 0. 0. 0.0 0. 0. 0. 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
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
poroeastic modeing of wood - COST meeting October 00 known effects of water - sweing moduus of easticity [MPa] 4000 000 00 - moduus of easticity - Poisson s 000 ratio 800 600 400 - water sorption 00 data from Neuhaus cacuated vaues ue L E R E T B C u 000 ϕ( p 800 600 400 00 ) E TL E LR 0 0.0 0. 0. 0. - stress dependent u moisture content E TR 0 0.0 0. 0. 0. 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
poroeastic modeing of wood - COST meeting October 00 known effects of water - sweing Poisson's ratio..0 0.8 - moduus of easticity - Poisson s ratio 0.6 0.4 ν TL..0 0.8 0.6 0.4 u B C u ϕ( p ) ν TR ν RT..0 0.8 0.6 0.4 ν RL - water sorption 0. 0. 0. ν LT ν LR 0.0 0.0 0.0 0.0 0. 0. 0. 0.0 0. 0. 0. 0.0 0. 0. 0. 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
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
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
poroeastic modeing of wood - COST meeting October 00. appication Empa,, 0
poroeastic modeing of wood - COST meeting October 00 resuts 4000 data from Neuhaus cacuated vaues 000 moduus of easticity [MPa] 000 00 000 800 600 400 E L E R 800 600 400 00 E TL E LR 00 E T 0 0.0 0. 0. 0. moisture content 0 0.0 0. 0. 0. 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
poroeastic modeing of wood - COST meeting October 00 resuts....0 ν TL.0.0 Poisson's ratio 0.8 0.6 0.4 0.8 0.6 0.4 ν TR ν RT 0.8 0.6 0.4 ν RL 0. 0. 0. ν LT ν LR 0.0 0.0 0. 0. 0. 0.0 0.0 0. 0. 0. 0.0 0.0 0. 0. 0. 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
poroeastic modeing of wood - COST meeting October 00 resuts stressed in TT-direction stressed in RR-direction stressed in LL-direction 0.08 0.06 UNstressed stressed data from Neuhaus sweing strain 0.04 0.0 0.00 p kg -0.0 compressive stress 0, 0 MPa compressive stress 0, 0 MPa compressive stress 0, 0 MPa 0.0 0. 0. 0. moisture content 0.0 0. 0. 0. 0.0 0. 0. 0. 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
poroeastic modeing of wood - COST meeting October 00 resuts 0.0 0.0 stressed in RR-direction 0.0 stressed in LL-direction 0.5 0.9 0.8 0.9 0.8 moisture content 0.0 0.5 0.0 0.05 0.7 0.990 0.995.000 reative humidity 0.7 0.990 0.995.000 reative humidity compressive stress 0, 0, 0 MPa p kg u 0.00 0.0 0. 0.4 0.6 0.8.0 reative humidity Empa,, 8/6 4
poroeastic modeing of wood - COST meeting October 00 resuts stressed in TT-direction stressed in RR-direction stressed in LL-direction p 0.05 0.04 expeed moisture 0.0 0.0 u(t=0) 5, 0 % u(t=0) 5, 0 % kg u 0.0 u(t=0) 5, 0 % 0.00 0 5 0 5 0 compressive stress [MPa] 0 5 0 5 0 0 5 0 5 0 compressive stress [MPa] compressive stress [MPa] Empa,, 9/6 5
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] -0-40 -60 u(t=0) 0, 7.5, 5 % u(t=0) 0, 7.5, 5 % u(t=0) 0, 7.5, 5 % p -80-00 0.0 0. 0. 0. moisture content 0.0 0. 0. 0. 0.0 0. 0. 0. moisture content moisture content Empa,, 0/6 6
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 0. 0. 0. sweing strain 0.0 0.08 0.06 0.04 0.0 u(t=0) 0, 7.5, 5 % 0.0 0.08 0.06 0.04 0.0 u(t=0) 0, 7.5, 5 % 0.0 0.08 0.06 0.04 0.0 u(t=0) 0, 7.5, 5 % p 0.00 0.0 0. 0. 0. moisture content 0.00 0.00 0.0 0. 0. 0. 0.0 0. 0. 0. moisture content moisture content Empa,, /6 7
poroeastic modeing of wood - COST meeting October 00. physica background Empa,, 8
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
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
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
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
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
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
poroeastic modeing of wood - COST meeting October 00 energy function (D approach) w = w w stress water w couping Empa,, 4/6 5
Empa,, 6 energy function (D approach) 4/6 couping water stress w w w w = w stress = 6 6 5 5 4 4 w stress poroeastic modeing of wood - COST meeting October 00
poroeastic modeing of wood - COST meeting October 00 energy function (D approach) w = w w stress water w couping w stress w stress = 4 4 5 5 6 6 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
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 = 4 4 5 5 6 6 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
poroeastic modeing of wood - COST meeting October 00 energy function (D approach) w = w w stress water w couping w stress w stress = 4 4 5 5 6 6 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
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 = 6 6 6 [0] 6 5 5 5 [0] 5 4 4 4 [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 = 6 6 5 5 4 4 w stress
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
poroeastic modeing of wood - COST meeting October 00 Thank you Empa,, 6/6