Some models for numerical simulations of brittle failure Kari Kolari - PowerPoint PPT Presentation

Some models for numerical simulations of brittle failure Kari Kolari 1 , Juha Kuutti 1 , Juha Hartikainen 2 , and Reijo Kouhia 2 firstname.lastname@vtt.fi or firstname.lastname@tkk.fi 1 VTT Technical Research Center of Finland 2 Helsinki University of Technology, Department of Structural Engineering and Building Technology NSCM-22, Aalborg, October 22-23, 2009 – p.1/11

OUTLINE � Motivation and materials � Numerical model � Constitutive models � Finite element procedures � Example simulations � Tensile test � Bending failure NSCM-22, Aalborg, October 22-23, 2009 – p.2/11

MOTIVATION AND MATERIALS Ice-structure interaction transition from continuous to discontinuous (a) crushing (b) bending NSCM-22, Aalborg, October 22-23, 2009 – p.3/11

MOTIVATION AND MATERIALS Ductile-to-brittle transition E. M. Schulson: Brittle failure of ice, Engineering Fracture Mechanics 68 (2001) 1839–1887. NSCM-22, Aalborg, October 22-23, 2009 – p.4/11

MOTIVATION AND MATERIALS Ice crushing against the lighthouse Norrströmsgrund NSCM-22, Aalborg, October 22-23, 2009 – p.5/11

NUMERICAL MODEL � Implemented in commercial code (Abaqus/Explicit) � Model update strategy � CDM-model for brittle failure � Model for ductile-to-brittle transition NSCM-22, Aalborg, October 22-23, 2009 – p.6/11

Model update strategy Element split based on damage vector Several advantages over element deletion process NSCM-22, Aalborg, October 22-23, 2009 – p.7/11

CDM-model for brittle behaviour � Vectorial damage model (Kolari 2007) � Crack-surface friction neglected � Stiffness recovery due to crack closure is taken into account � Softening by fictitious crack approac (Hillerborg et al. 1976) � Damage criterion F = η 1 ε e ii + η 2 ε e ii ε e jj + ε e ij ε e ij − B 0 − h ( w c , H ) κ = 0 σ σ � � Real crack Representative crack � � � NSCM-22, Aalborg, October 22-23, 2009 – p.8/11

CDM-model for brittle behaviour Damage evolution � � � H ( ε N ) ε N + D i = ˙ ε � i ε � n i + ε � ˙ λ i i � � � � � � � � � � � � � ε ε ε ε ε ε ε ε ε ε ε ε � ε ε ε ε � � � � NSCM-22, Aalborg, October 22-23, 2009 – p.9/11

Ductile-to-brittle transition Dissipation potential ϕ ( σ, Y ) = ϕ d ( Y ) ϕ tr ( σ ) + ϕ vp ( σ ) ϕ tr ≥ 0 ϕ tr ≈ 0 when � ˙ ǫ i � < η and ϕ tr > 1 when � ˙ ǫ i � > η 1.4 1.2 1 0.8 s 0.6 ◦ ǫ 0 = η ◦ 0.4 ǫ 0 = 5 η ◦ ǫ 0 = 10 η 0.2 ◦ ǫ 0 = 20 η 0 0 0.5 1.5 2.5 3 3.5 1 2 4 e NSCM-22, Aalborg, October 22-23, 2009 – p.10/11

NUMERICAL SIMULATIONS Tensile test simulation � Velocity (3 mm/s) controlled loading � C3D8R elements. Two elements in thickness direction (total 612 elements at initial stage) Animation NSCM-22, Aalborg, October 22-23, 2009 – p.11/11

NUMERICAL SIMULATIONS Bending failure with inclined structure � Level ice 30 cm thick � Initially 792 C3D8R elements Animation NSCM-22, Aalborg, October 22-23, 2009 – p.11/11