Keywords: quasi-brittle fracture, fracture process zone, energy dissipation, physical discretization, nonlinear dynamic system, CUDA implementation.

Recently, the authors have been expending much effort in the development of an efficient technique for the determination of the fracture properties of cementitious quasi-brittle materials from experimental tests on laboratory specimens. In order to eliminate the effects of the specimen's size and geometry on the determined values of fracture-mechanical characteristics, the possibilities of specification of the energy dissipated within the fracture process zone (FPZ) by its volume rather than by the cracked ligament area, have been investigated and proposed for the developing procedure. An amalgamation of classical nonlinear fracture models for concrete, multi-parameter fracture mechanics and plasticity theory has been proposed for a reconstruction of the volume of the FPZ (termed the ReFraPro technique [4]) by which the amount of the energy consumed during the fracture should be specified.

This method, however, is not easy to validate experimentally, as only a limited number of works on this topic are available in the literature. For better evidence and understanding of fundamental issues of the developing ReFraPro method numerical simulations of fractures are being carried out by means of physical discretization of the continuum [2]. This discretiazation technique is similar to lattice models and uses a procedure developed for rigid body spring networks [1]. The computational code developed for the simulations by the authors (termed the FyDiK program) is based on a nonlinear dynamical description of the problem.

In the paper the ReFraPro procedure is adequately illustrated using an experiment from the literature [3]. The results of the FyDiK model simulation of the test are presented and discussed too. The overall extent of the failure zone is very similar for the ReFraPro and the FyDiK approaches and fits to the experimental data very well.

The paper presents an analysis for the verification and validation of the (semi-) analytical technique for estimation of the extent (size and shape) of the fracture process zone in quasi-brittle silicate-based composites during tensile failure (ReFraPro). The author's own implementation of the computational model (FyDiK) was successfully employed for a partial verification of the developed ReFraPro method. A parallelized version implemented in the nVidia CUDA environment was effectively used for solving on a small Tesla C1060 supercomputer.

1

J.E. Bolander, K. Yoshitake, J. Thomure, "Stress analysis using elastically uniform rigid-body-spring networks", J. Struct. Mech. Earthquake Eng., 633, 125-132, 1999.

2

P. Frantík, "FyDiK application", 2007-2011. http://www.kitnarf.cz/fydik

3

H. Mihashi, N. Nomura, "Correlation between characteristics of fracture process zone and tension-softening properties of concrete", Nuclear Engineering and Design, 165, 359-376, 1996. doi:10.1016/0029-5493(96)01205-8

4

V. Veselý, P. Frantík, "ReFraPro - Reconstruction of Fracture Process", Java application, 2008-2011.

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