An open source ABAQUS/UEL implementation of the phase-field method to simulate brittle fracture

20 Pages·2017·1.7 MB·English

An open source ABAQUS/UEL
implementation of the phase‐field
method to simulate brittle fracture
Gergely Molnár and Anthony Gravouil
Content
Introduction to phase‐fields
1. Phase-field concept
2. Strain energy degradation
3. Staggered scheme
Parameters
1. Finite element mesh
2. Time step
3. Length-scale parameter
ABAQUS/UEL implementation
Conclusion
Introduction
undamaged zone (0 = d)
What is diffuse damage?
theoretical crack (d = 1)
damaged zone (0 < d < 1)
Solving fracture mechanics problem with
Partial Differential Equations (PDEs)
Introduction
What is diffuse damage?
Solving fracture mechanics problem with
Partial Differential Equations (PDEs)
Introduction
How do we approximate it with a phase‐field?

1. Brittle fracture   g Griffith, 1921
c
a
    
2. Minimization problem E u,     u d  g  d
c
 
Mumford & Shah, 1989
Francfort & Marigo, 1998
3. Crack energy density
 1 l 
E u, d    g d u d  g  d 2  c d 2 d
 
c
  2l 2
 
c
l  0  converges
Ambrosio & Tortorelli, 1990
c
 Bourdin et al., 2000
d  0
crack energy density ‐ γ
Amor et al., 2009
Miehe et al., 2010a
Prof. Dr.‐Ing.
Christian Miehe
(1956 – †2016)
Phase‐field method
Staggered scheme
Miehe et al., 2010b
Eu u, d 
Ed d, H 
n
  
H   u if H 
n 0 n1 0
Robustness!!!
Efficiency?
Molnár & Gravouil, 2017
Phase‐field method
Staggered scheme
Molnár & Gravouil, 2017
Phase‐field method
c - (2,2) element of the stiffness matrix
22
Single element solution
 2
  1 d  c
y y 22
2c
y 22
d 
g
c 2c
y 22
l
c
Molnár & Gravouil, 2017
Phase‐field method
Single element solution
analytic
 
y y
 
analytic

y
Miehe et al., 2010a
Parameters
How fine should the mesh be?

h  l / 2

  0.5 theoretical
  d
l
