multiPlas - Dynardo GmbH

Fig. 3-12 stress-strain relation in multiPlas (mlaw=0,2; mlaw = 1)
3.3.6.2 Nonlinear deformation behaviour during tensile load
Concrete tends to soften relatively brittle with local appearances of cracks. For including this into the
context of a continuum model, a homogenized crack and softening model is needed. The crack itself does
not appear in the topology description of the structure - but is described by its impact on stress and
deformation state [6-16],[6-21].
The softening process is formulated respectively to the energy dissipation caused by the occurance of
cracks. For the complete cracking, the fracture energy concerning the crack surface has to be
Gf -dissipated.
The used model has its origin within the crack band theory of Bažant / Oh [6-6]. It states that cracks
develop within a local process zone. Its width hPR (crack band width) is a material specific constant.
To avoid a mesh dependency of the softening and to assess the fracture energy correctly, a modification
of the work equation is necessary. For a given width of the crack band and a given fracture energy, the
volume fracture energy can be computed via:
G
f
g f =
h
(3-22)
PR
where:
gf volume fracture energy
Gf fracture energy
hPR crack band width
For meshing of the structure with elements which are larger than the expected width of the crack band the
stress-strain relationship has to be modified in such a way that the volume fracture energy reaches the
following value:
g
σd
Rd
σu
Rd/3
σr
f , INT
hPR
Gf
= gf
=
(3-23)
h h
where: gf,INT
εml εu εr
ε
volume fracture energy at the integration point
h equivalent length
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USER’S MANUAL, January, 2013