Cohesive Laws To Model Concrete Rupture – A Methodology That Takes Mesh Effects Into Consideration

Abstract

The cohesive surface method has been used intensively on numerical simulations of fracture
of metals and brittle materials. However, the constitutive cohesive laws (or traction versus crack
opening relationships) used for these materials are not adequate to simulate the concrete behavior
because they do not take into consideration effects related to the size of the finite elements and other
phenomena that characterize concrete rupture (e.g. development of a process zone at the crack tip).
In this work, some well-known post-peak constitutive equations for the cohesive surface are
explored. The shape of these equations changes overall results and it seems to be linked with the
development of the process zone, so the shape can be considered a material property as the fracture
energy. However, the present work also explores the effect of the pre-peak part of the cohesive law. It
is demonstrated that this part of the curve must be related to the size of the finite elements, in order to
have a mesh independent result.
As practical applications, cases in Mode I of propagation are presented (three-point bending),
where the effect of the post-peak relationship on load versus crack opening is shown. It could be
concluded that post-peak relationship is important to define maximum rupture load. Besides that,
different sizes of bodies were analyzed and the scale effect of concrete was captured (the smaller the
body, the greater the toughness). A good fit with literature results was obtained. It is demonstrated also
that results are mesh independent, depending on the pre-peak part of the cohesive law. Concrete
properties are not considered random fields.