Abstract

Cementitious materials such as mortar or concrete are brittle and have an inherent weakness in resisting tensile stresses. The addition of discontinuous fibers to such matrices leads to a
dramatic improvement in their toughness and remedies their deficiencies. It is generally
agreed that the fibers contribute primarily to the post-cracking response of the composite by
bridging the cracks and providing resistance to crack opening (Suwaka & Fukuyama 2006).

On the other hand, the multifield theory is a mathematical tool able to describe materials
which contain a complex substructure (Mariano & Stazi 2005). This substructure is endowed
with its own properties and it interacts with the macrostructure and influences drastically its
behavior. Under this mathematical framework, materials such as cement composites can be
seen as a continuum with a microstructure. Therefore, the whole continuum damage mechanics
theory, incorporating a new microstructure, is still applicable.

A formulation, initially based on the theory of continua with microstructure Capriz
(Capriz 1989), has been developed to model the mechanical behavior of the high performance
fiber cement composites with arbitrarily oriented fibers. This formulation approaches
a continuum with microstructure, in which the microstructure takes into account the fibermatrix
interface bond/slip processes, which have been recognized for several authors (Li
2003, Naaman 2007b) as the principal mechanism increasing the ductility of the quasi-brittle
cement response. In fact, the interfaces between the fiber and the matrix become a limiting
factor in improving mechanical properties such as the tensile strength. Particularly, in short
fiber composites is desired to have a strong interface to transfer effectively load from the
matrix to the fiber. However, a strong interface will make difficult to relieve fiber stress
concentration in front of the approaching crack. According to Naaman (Naaman 2003), in
order to develop a better mechanical bond between the fiber and the matrix, the fiber should
be modified along its length by roughening its surface or by inducing mechanical deformations.
Thus, the premise of the model is to take into account this process considering a microfield that represents the slipping fiber-cement displacement. The conjugate generalized stress
to the gradient of this micro-field verifies a balance equation and has a physical meaning.

This contribution includes the computational modeling aspects of the high fiber reinforced
cement composites (HFRCC) model. To simulate the composite material, a finite
element discretization is used to solve the set of equations given by the multifield approach
for this particular case. A two field discretization: the standard macroscopic and the microscopic
displacements, is proposed through a mixed finite element methodology. Furthermore,
a splitting procedure for uncoupling both fields is proposed, which provides a more convenient
numerical treatment of the discrete equation system.

The initiation of failure in HPFRCC at the constitutive level identified as the onset of
strain localization depends on the mechanical properties of the all compounds and not only
on the matrix ones. As localization criteria is considered the bifurcation analysis in combination
with the localized strain injection technique presented by Oliver et al. (Oliver et al.
2010a). It consists of injecting a specific localization mode during the localization stage, via
mixed finite element formulations, to the path of elements that are going to capture the
cracks, and, in this way, the spurious mesh orientation dependence is removed.

Model validation was performed using a selected set of experiments that proves the viability
of this approach. The numerical examples of the proposed formulation illustrated two
relevant aspects, namely: 1) the role of the bonding mechanism in the strain hardening behavior
after cracking in the HPFRCC and 2) the role that plays the finite element formulation in
capturing the displacement localization in the localization stage.