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

VL - 297

SP - 38

EP - 61

JO - Computer Methods in Applied Mechanics and Engineering

JF - Computer Methods in Applied Mechanics and Engineering

SN - 0045-7825

ER -