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CivilComp Proceedings
ISSN 17593433 CCP: 75
PROCEEDINGS OF THE SIXTH INTERNATIONAL CONFERENCE ON COMPUTATIONAL STRUCTURES TECHNOLOGY Edited by: B.H.V. Topping and Z. Bittnar
Paper 57
3D Simulation of Concrete Cracking: Probabilistic Formulation in a Parallel Environment C.N.M. Paz+, L.F. Martha+, E.M.R. Fairbairn*, J.L.D. Alves*, N.F.F. Ebecken* and A.L.G.A. Coutinho*
+Department of Civil Engineering and Technology Group on Computer Graphics, Pontifical Catholic University of Rio de Janeiro, Brazil
C.N.M. Paz, L.F. Martha, E.M.R. Fairbairn, J.L.D. Alves, N.F.F. Ebecken, A.L.G.A. Coutinho, "3D Simulation of Concrete Cracking: Probabilistic Formulation in a Parallel Environment", in B.H.V. Topping, Z. Bittnar, (Editors), "Proceedings of the Sixth International Conference on Computational Structures Technology", CivilComp Press, Stirlingshire, UK, Paper 57, 2002. doi:10.4203/ccp.75.57
Keywords: parallel processing, high performance computing, discrete cracking concrete, probabilistic crack approach, material heterogeneity, size effects, tensile strength domain, Monte Carlo method, nonlinear analysis, finite elements.
Summary
This work presents a probabilistic crack approach (Rossi et al [1]), based on the
Monte Carlo method, that was recently implemented in a 3D fully parallelized finite
element code (Paz, [2]). The cracking scheme used is the discrete crack approach
introduced by means of 3D interface elements. In this approach the heterogeneity of
the material is taken into account by considering the properties (tensile strength,
Young Modulus, etc.) to vary spatially following a normal distribution determined
by the mean the standard deviation of the considered material properties. samples
of a vector of these properties are generated and the corresponding solutions are
computed by the FE code. Hence, the average response of the samples
corresponding to a Monte Carlo simulation is a function of the mean value and of
the standard deviation that define the Gauss density function. If the heterogeneous
characteristics of the material are well established and quantified by the statistical
moments it is possible that the model displays the size effects related to the material
heterogeneity. The problem with this approach is that these statistical moments are
not known a priori for the characteristic volume of the finite elements used in the
analysis. However, some methods have been proposed to determine these
parameters by means of inverse analysis using neural networks [2,3].
The stochastic process is introduced at the material local scale considering that cracks are created within the concrete with different energy dissipation depending on the spatial distribution of constituents and initial defects. The local material behavior in concrete is assumed to be a perfect elastic brittle behavior. This the random distribution of local cracking energies can be replaced by a random distribution of local strengths. Fracturing is modeled by 3D interface elements that are generated in a previously defined region within the mesh. The interface elements are triangular base prisms connecting adjacent faces of neighboring tetrahedra. These elements simulate crack opening through relative displacements between the triangular faces. The model is based on the assumption the some particularities of the cracking behavior of concrete, such as strain softening, cracking evolution, and sizeeffects are derived from the heterogeneous characteristics of the material. The code achieved a very good level for both parallel performance and vetorization. The most demanding routines, which implement the matrixvector multiply computational kernel for the interface and tetrahedral elements, are "fully" parallelized and responsible for over 80 emphasizes the suitability of the implemented code on the parallelvector machine, CRAY T90 for 2 CPU's, which presented a flop rate of 614 Mflop/s and a parallel speedup of 3.8 for 4 CPU's. Extensive use of elementbyelement techniques within the computational kernels comprised in the iterative solution drivers provided a natural way for achieving high Flop rates and good parallel speedup's. Furthermore, elementbyelement techniques avoid completely the formation and handling of large sparse matrices. Therefore, the computational strategies presented herein provide a natural way to deal with more complex scenarios, particularly those involving threedimensional problems. References
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