Applications of lattice method in the simulation of crack path in heterogeneous materials
Journal Title: Frattura ed Integrità Strutturale - Year 2015, Vol 9, Issue 34
Abstract
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.
Authors and Affiliations
L. Kosteski, F. Soares, I. Iturrioz
Numerical study of fracture arrest on snow cover
Under the hypothesis of a perfectly brittle phenomenon, avalanche triggering can be investigated numerically by means of Linear Elastic Fracture Mechanics (LEFM). Since, however, the real phenomenon is intrinsically dyna...
Effect of nonlinearity of restrainer and supports on the elasto-plastic seismic response of continuous girder bridge
During an earthquake, the nonlinearity of the bridge structure mainly occurs at the supports, bridge piers and restrainers. When entering nonlinear stage, members of the bridge structure affect the elasto-plastic...
Numerical experiments in 2D variational fracture
In the present work we present some results of numerical experiments obtained with a variational model for quasi-static Griffith-type brittle fracture. Essentially the analysis is based on a recent formulation by Francfo...
A non-linear procedure for the numerical analysis of crack development in beams failing in shear
In this work, a consistent formulation for the representation of concrete behavior before and after cracking has been implemented into a non-linear model for the analysis of reinforced concrete structures, nam...
Applications of lattice method in the simulation of crack path in heterogeneous materials
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 crac...