L. E. Kosteski et alii, Frattura ed Integrità Strutturale, 34 (2015) 226-236; DOI: 10.3221/IGF-ESIS.34.24 226 Focussed on Crack Paths Applications of lattice method in the simulation of crack path in heterogeneous materials L. E. Kosteski Prof. at Unipampa University, Alegrete, Rio Grande do Sul, Brazil luiskosteski@gmail.com F. S. Soares Student of PROMEC/UFRGS, Mechanical post-graduation Program, Federal Univ. Rio Grande do Sul Brazil szs.fernando@gmail.com I. Iturrioz Prof. of PROMEC/UFRGS, Brazil ignacio@mecanica.ufrgs.br A BSTRACT . The simulation of critical and subcritical crack propagation in heterogeneous materials is not a simple problem in computational mechanics. These topics can be studied with different theoretical tools. In the crack propagation problem it is necessary to lead on the interface between the continuum and the discontinuity, and this region has different characteristics when we change the scale level point of view. In this context, this work applies a version of the lattice discrete element method (LDEM) in the study of such matters. This approach lets us to discretize the continuum with a regular tridimensional truss where the elements have an equivalent stiffness consistent with the material one wishes to model. The masses are lumped in the nodes and an uni-axial bilinear relation, inspired in the Hilleborg constitutive law, is assumed for the elements. The random characteristics of the material are introduced in the model considering the material toughness as a random field with defined statistical properties. It is important to highlight that the energy balance consistence is maintained during all the process. The spatial discretization lets us arrive to a motion equation that can be solved using an explicit scheme of integration on time. Two examples are shown in the present paper; one of them illustrates the possibilities of this method in simulating critical crack propagation in a solid mechanics problem: a simple geometry of grade material. In the second example, a simulation of subcritical crack growth is presented, when a pre-fissured quasi-brittle body is submitted to cyclic loading. In this second example, a strategy to measure crack advance in the model is proposed. Finally, obtained results and the performance of the model are discussed. K EYWORDS . Lattice Model; Dynamic Crack propagation; Subcritical propagation. I NTRODUCTION he crack propagation in heterogeneous materials has some particular issues, as the localization phenomenon and the influence of clusters of microfissures which are some of the effects that characterize this problem. The study of this problem from a continuum mechanics point of view let advance, but it is necessary to overpass the homogenization of anisotropic damage with a non-homogeneous distribution. An alternative to the continuum approach is to simulate T

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