TY - JOUR
T1 - Modeling evolution of frost damage in fully saturated porous materials exposed to variable hygro-thermal conditions
AU - Koniorczyk, Marcin
AU - Gawin, Dariusz
AU - Schrefler, Bernhard A.
N1 - Funding Information:
The authors would like to acknowledge Prof. Nicolas Moës from Ecole Centrale de Nantes, France, for very fruitful discussions concerning modeling of damage. The first two authors’ research was partly funded by within the grant of National Science Center—Poland , No. UMO-2011/03/B/ST8/05963 entitled “Degradation of material properties due to development of expanding phases in building composites with a microstructure” realized at the Lodz University of Technology in years 2012–2015. Appendix Below the equations describing the elements of matrices in Eq. (58) are listed: (A.1) C L L = ∫ Ω N T N [ ϕ ( 1 − η C ) ρ L K L + ϕ η C ρ C K C + [ η C ρ C + ( 1 − η C ) ρ C ] ( b − ϕ ) K S ] d Ω + ∫ Ω N T N { ϕ ( η C − η L ) + [ η C ρ C + ( 1 − η C ) ρ C ] ( p C − p L ) ( b − ϕ ) K S } ∂ η C ∂ p L d Ω (A.2) C L T = ∫ Ω N T N [ ϕ ( 1 − η C ) α L ρ L + ϕ η C α C ρ C ] d Ω + ∫ Ω N T N { ϕ ( η C − η L ) + [ η C ρ C + ( 1 − η C ) ρ C ] ( p C − p L ) ( b − ϕ ) K S } ∂ η C ∂ T d Ω (A.3) C L u = ∫ Ω N T { ϕ ( 1 − η C ) ρ L + ϕ η C ρ C + [ η C ρ C + ( 1 − η C ) ρ C ] ( b − ϕ ) } Lm T N d Ω (A.4) C T T = ∫ Ω N T N [ ( 1 − ϕ ) ρ S C P , S + ϕ ( 1 − η C ) ρ L C P , L + ϕ η C ρ C C P , C ] d Ω (A.5) C T L = ∫ Ω N T N ρ C Δ H ∂ η C ∂ p L d Ω (A.6) K L L = − ∫ Ω ∇ N T ∇ N [ k k r L μ L ] d Ω (A.7) K T T = ∫ Ω ∇ N T ∇ N λ ef d Ω (A.8) K u L = ∫ Ω B T m T N d Ω (A.9) K u T = ∫ Ω B T Dm T ( β S / 3 ) N d Ω (A.10) K uu = − ∫ Ω B T DB d Ω (A.11) f L = − ∫ Γ N T q L d Γ (A.12) f T = − ∫ Ω N T N ρ C Δ H η ̇ C d Ω − ∫ Γ N T [ q T + h ( T − T ∞ ) ] d Γ (A.13) f u = ∫ Ω B T [ m T ( β S / 3 ) T 0 ] d Ω + ∫ Ω B T m T p ∗ d Ω + ∫ Ω B T N T [ ( ( 1 − n ) ρ s + n S w ρ w + n S g ρ g + n S p ρ p ) g ] d Ω − ∫ Γ N T t d Γ where (A.14) D = ( 1 − d ) E ( 1 + v ) ( 1 − 2 ν ) [ 1 − ν ν ν 0 0 0 v 1 − ν ν 0 0 0 ν ν 1 − ν 0 0 0 0 0 0 ( 1 − 2 ν ) 2 0 0 0 0 0 0 ( 1 − 2 ν ) 2 0 0 0 0 0 0 ( 1 − 2 ν ) 2 ] , (A.15) L = [ ∂ ∂ x 0 0 ∂ ∂ y 0 ∂ ∂ z 0 ∂ ∂ y 0 ∂ ∂ x ∂ ∂ z 0 0 0 ∂ ∂ z 0 ∂ ∂ y ∂ ∂ x ] T , (A.16) m = { 1 , 1 , 1 , 0 , 0 , 0 } T .
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PY - 2015/12/1
Y1 - 2015/12/1
N2 - Frost damage due to cyclic water freezing/ice thawing in the pores of building materials, is one of the main reasons jeopardizing durability of the structures in cold climates. A novel mathematical model of coupled hydro-thermo-mechanical phenomena in fully saturated porous materials exposed to water freezing/melting processes is proposed. The crystallization pressure, exerted by ice on the material pore walls and the related frost damage are considered. The kinetics of freezing/thawing phase change is modeled by means of a non-equilibrium approach. This kinetic description of the phase transformation allows avoiding numerical problems due to the strong sources of heat/mass accompanying the process. The frost deterioration is modeled by means of the isotropic nonlocal delayed damage theory in its rate formulation. The model equations are solved numerically by means of the finite element method in space and finite differences method in time. Three examples are solved to analyze the numerical performance of the model, to validate it by comparison with experimental results, and to present its application for modeling frost damage of a saturated concrete wall during cyclic freezing-thawing.
AB - Frost damage due to cyclic water freezing/ice thawing in the pores of building materials, is one of the main reasons jeopardizing durability of the structures in cold climates. A novel mathematical model of coupled hydro-thermo-mechanical phenomena in fully saturated porous materials exposed to water freezing/melting processes is proposed. The crystallization pressure, exerted by ice on the material pore walls and the related frost damage are considered. The kinetics of freezing/thawing phase change is modeled by means of a non-equilibrium approach. This kinetic description of the phase transformation allows avoiding numerical problems due to the strong sources of heat/mass accompanying the process. The frost deterioration is modeled by means of the isotropic nonlocal delayed damage theory in its rate formulation. The model equations are solved numerically by means of the finite element method in space and finite differences method in time. Three examples are solved to analyze the numerical performance of the model, to validate it by comparison with experimental results, and to present its application for modeling frost damage of a saturated concrete wall during cyclic freezing-thawing.
KW - Frost damage
KW - Nonequilibrium freezing/thawing modelling
KW - Rate type model of phase change
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U2 - 10.1016/j.cma.2015.08.015
DO - 10.1016/j.cma.2015.08.015
M3 - Article
AN - SCOPUS:84942036545
SN - 0045-7825
VL - 297
SP - 38
EP - 61
JO - Computer Methods in Applied Mechanics and Engineering
JF - Computer Methods in Applied Mechanics and Engineering
ER -