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

Some models for numerical simulations of brittle failure

Kari Kolari1, Juha Kuutti1, Juha Hartikainen2, and Reijo Kouhia2

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 = η1εe

ii + η2εe iiεe jj + εe ijεe ij − B0 − h(wc, H)κ = 0

• σ

σ

Representative crack Real crack

• NSCM-22, Aalborg, October 22-23, 2009 – p.8/11

CDM-model for brittle behaviour Damage evolution ˙ Di = ˙ λ

• H(εN)εN +
• ε

iε i

• ni + ε

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 ) = ϕd(Y )ϕtr(σ) + ϕvp(σ) ϕtr ≥ 0 ϕtr ≈ 0 when ˙ ǫi < η and ϕtr > 1 when ˙ ǫi > η

• ǫ0 = 20η
• ǫ0 = 10η
• ǫ0 = 5η
• ǫ0 = η

e s 4 3.5 3 2.5 2 1.5 1 0.5 1.4 1.2 1 0.8 0.6 0.4 0.2

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