9.9 Xfem Crack Element

The element is used to model cracks within the context of xfem (extended finite element) methods. The element current implementation is restricted to 2D problems.

CRACK_Xfem

Element_name = CRACK_Xfem, etc. …

< material data >

< connectivity data >.

9.9.1 Element Control Information

Note Variable Name Type Default Description

Element_name list [*] CRACK_Xfem

Element_type list [interface] Element type

Element_shape list [two_node_line] Element shape

Crack_growth list [off] Crack growth flag

on / off

Number_of_elements integer [*] Maximum number of elements

Enrichment_type list [none] Enrichment type

heaviside Heaviside only

heavi_crack_with_tip_1 Heaviside crack with tip 1

heavi_crack_with_tip_2 Heaviside crack with tip 2

crack_with_tip_1 Heaviside + asymptotic crack

function for tip 1

crack_with_tip_2 Heaviside + asymptotic crack

function for tip 2

crack Heaviside + asymptotic crack

functions for both tips 1 and 2

interface_with_tip_1 Heaviside + asymptotic crack

function for tip 1

interface_with_tip_2 Heaviside + asymptotic crack

function for tip 2

interface Heaviside + asymptotic crack

functions for both tips 1 and 2

(cont’d)

(cont’d)

Note Variable Name Type Default Description

shear_band Tangential discontinuity

joint Tangential + normal discontinuities

cohesive_with_tip_1 Heaviside + cohesive tip for tip 1

cohesive_with_tip_2 Heaviside + cohesive tip for tip 2

cohesive Heaviside + cohesive tip for both

tips 1 and 2

Interface_crack list [off] Interface crack flag

on / off

Crack_material list [off] Crack material data

on / off

9.9.2 Material Properties Data

Note Variable Name Type Default Description

Crack_material_model list [none] Title

Radius real [2.5] Radius for computing stress intensity

factors (fraction of h-elmt)

Critical_energy real [0.0] Critical energy release rate, G_c

Crack_growth_inc real [0.0] Maximum crack growth increment,

da_max

Growth_direction list [*] Growth direction

sigma_theta

straight

(1) Growth_formula list [*] Growth formula

none

hyperbolic_sin

logarithmic_formula

hyperbolic_tan

(1) Threshold_energy real [0.0] Threshold energy release rate G_th

(1) Growth_alpha real [0.0] Growth parameter alpha, α

(cont’d)

(cont’d)

Note Variable Name Type Default Description

(1) Growth_beta real [0] Growth parameter beta, β

(2) Interface_type lst [*] Interface type

perfect / contact

(2) Friction_angle real [0.0] Friction angle in degrees

(2) Normal_stiffness real [0.0] Normal stiffness

(3) Tangential_stiffness real [0.0] Tangential stiffness

(3) Number_of_integration integer [2] Number of integration points

(4) Cohesive_traction real [0.0] Cohesive strength f_u

(4) Fracture_energy real [0.0] Fracture energy G_F

Notes/

(1) The crack growth velocity is computed as:

- hyperbolic_sin formula:

- logarithmic formula:

- hyperbolic_tan formula:

(2) Only applicable to Joint interfaces.

(3) Only applicable to Joint and Shear Band interfaces.

(4) A linear strain softening bridging law is assumed, viz., the critical opening w_e defined as: w_e = 2G_F/f_u.

9.9.3 Nodal Connectivity Data

Consult Chapter 11 for details; for this element NEN=2.

References / Bibliography

1. Moës, N., J. Dolbow and T. Belytschko, “A Finite Element Method for Crack Growth without Remeshing,” International Journal for Numerical Methods in Engineering, Vol. 46, No. 1, (1999), pp. 131-150.

2. Daux, C., N. Moës, J. Dolbow, N. Sukumar and T. Belytschko, “Arbitrary Cracks and Holes with the Extended Finite Element Method,” International Journal for Numerical Methods in Engineering, Vol. 48, No. 2, (2000), pp. 1741-1760.

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