Macro – micro structures modeling of material failure in high performance fiber reinforced cementitious composites

DF. MORA; AE. HUESPE; JOLIVER

Viena

Congreso; ECCOMAS 2012, 6th European Congress on Computational Methods in Applied Sciences and Engineering; 2012

ECCOMAS

Cementitious materials such as mortar or concrete are brittle and have an inherent weakness inresisting tensile stresses. The addition of discontinuous fibers to such matrices leads to a dramaticimprovement in their toughness and remedies their deficiencies. It is generally agreed that the fiberscontribute primarily to the post-cracking response of the composite by bridging the cracks andproviding resistance to crack opening [1].On the other hand, the complex body theory is a mechanical/mathematical tool able to describematerials which contain a complex substructure [2]. This substructure is endowed with its ownproperties and it interacts with the macrostructure and influences drastically its behaviour. Under thismathematical framework, materials such as cement composites can be seen as a continuum with amicrostructure. Therefore, the whole continuum damage mechanics theory, incorporating a newmicrostructure, is still applicable.A formulation, initially based on the theory of complex bodies of Capriz [3], has been developed tomodel the mechanical behaviour of the high performance fiber cement composites with arbitrarilyoriented fibers. This formulation approaches a continuum with microstructure, in which themicrostructure takes into account the fiber-matrix interface bond/slip processes, which have beenrecognized for several authors [4-5] as the principal mechanism increasing the ductility of the quasibrittlecement response. In fact, the interfaces between the fiber and the matrix become a limitingfactor in improving mechanical properties such as the tensile strength. Particularly, in short fibercomposites is desired to have a strong interface to transfer effectively load from the matrix to thefiber. However, a strong interface will make difficult to relieve fiber stress concentration in front ofthe approaching crack. According to Naaman [6], in order to develop a better mechanical bondbetween the fiber and the matrix, the fiber should be modified along its length by roughening itssurface or by inducing mechanical deformations. Thus, the premise of the model is to take intoaccount this process considering a micro field that represent the slipping fiber-cement displacement.The conjugate generalized stress to the gradient of this micro-field verifies a balance equation havinga physical meaning.This contribution faces the computational modelling of those high fiber reinforced cementcomposites (HFRCC). To simulate the composite material, a finite element discretization is used tosolve the set of equations given by the complex bodies theory for this particular case. Moreover, atwo field discretization: the standard macroscopic and the microscopic displacements, is proposedthrough a mixed finite element methodology. Furthermore, a splitting procedure for uncoupling bothfields is proposed, which provides a more convenient numerical treatment of the discrete equationsystem.The initiation of failure in HPFRCC at the constitutive level identified as the onset of strainlocalization depends on the mechanical properties of the all compounds and not only on the matrixones. As localization criteria is considered the bifurcation analysis in combination with the localizedstrain injection presented by Oliver et al. [7]. It consists of injecting a specific localization modeduring the localization stage, via mixed finite element formulations, to the path of elements that aregoing to capture the cracks, and, in this way, the spurious mesh orientation dependence is removed.Validation of the obtained numerical results with a selected set of experiments proves the viability ofthis approach. The numerical examples of the proposed formulation illustrated two relevant aspects,namely: 1) the role of the bonding mechanism in the strain hardening behaviour after cracking in theHPFRCC and 2) the role that plays the finite element formulation in capturing the displacementlocalization in the localization stage.