Begell House Inc.
International Journal for Multiscale Computational Engineering
JMC
1543-1649
1
4
2003
PREFACE
1
Pierre
Ladeveze
University Paris VI
Jacob
Fish
Civil Engineering and Engineering Mechanics, Columbia University, New York, New York
10027, USA
An Energy-Based Statistical Model for Multiple Fractures in Composite Laminates
22
K. P.
Herrmann
Department of Mechanical Engineering, University of Paderborn, Paderborn, Germany
Junqian
Zhang
Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai, China
Jinghong
Fan
Alfred University, Alfred, New York, USA; Research Center for Materials Mechanics, Chongqing University, Chongqing, China
A theory is developed to predict the evolution of transverse ply cracking in a composite laminate as a function of the underlying statistical fracture toughness and the applied load. The instantaneous formation of a matrix crack spanning both the ply thickness and the ply width is assumed to be governed by the energy criterion associated with the material fracture toughness, Γ, at the ply level. Assume multiple matrix fractures occur quasistatically and sequentially such that the ply cracks form one after another under the constant external load imposed on the specimen. The number of cracks, n, within the gauge length, 2L, is a discrete random variable for a given applied load, σ, because the fracture toughness varies with the location of fractures in a given specimen as well as from specimen to specimen. The probability function f(n, σ, L) of the discrete random variable, n, is determined from the fracture toughness distribution and the solution for the potential energy release rate. Consequently, the distribution of the crack density, dn = n/2L, is obtained. Finally, the mean crack density is formulated as a function of the applied load.
Homogeneous Analysis of Periodic Assemblies of Elastoplastic Disks in Contact
22
Hongwu
Zhang
Department of Engineering Mechanics, Faculty of Vehicle Engineering and Mechanics, State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian 116024, P. R. China
D. P.
Boso
Department of Constructions and Transportations, University of Padua, Via Marzolo, 9, I-35131 Padova, Italy
Bernhard
Schrefler
Department of Ingegneria Civile, Edile e Strutturale e Trasporti University of Padua, Via Marzolo 9, 35131 Padua, Italy
The objective of this article is to capture the macroscopic behavior of an assembly of elastic and inelastic disks in contact by means of a numerical homogenized constitutive relation. An important feature of this work is that the evolving yield surfaces at the macroscopic level are defined through a quasi-static frictional contact analysis of the microstructure composed of deformable elastic and inelastic disks by means of a parametric quadratic programming principle and its corresponding algorithm in numerical analysis. The flow rule and the hardening parameters needed for an elastic—plastic analysis at macroscopic level are directly obtained from the numerically constructed yield surfaces in a self-consistent manner. The generality of the algorithm for the homogeneous analysis is pointed out and, in principle, can be applied to any kind of nonlinear behavior affecting the representative volume element. Numerical examples are given to demonstrate the efficiency of the algorithm presented in this article.
MultiScale First-Order and Second-Order Computational Homogenization of Microstructures towards Continua
16
Marc
Geers
Eindhoven University of Technology
Varvara G.
Kouznetsova
Department of Mechanical Engineering, Eindhoven University of Technology P.O. Box 513, 5600 MB Eindhoven; and Netherlands Institute for Metals Research, Rotterdamseweg 137 2628 AL Delft, The Netherlands
W. A. M.
Brekelmans
Department of Mechanical Engineering, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
This paper addresses a first-order and a second-order framework for the multiscale modelling of heterogeneous and multiphase materials. The macroscopically required (first-order or second-order) constitutive behavior is retrieved directly from the numerical solution of a boundary value problem at the level of the underlying microstructure. The most important features of computational homogenization schemes are: no constitutive assumptions on the macro level; large deformations and rotations on the micro and macro level; arbitrary physically nonlinear and time-dependent material behavior on the micro level; independent of the solution technique used on the micro level; applicable to evolving and transforming microstructures. In particular, a second-order computational homogenization scheme deals with localization and size effects in heterogeneous or multiphase materials. Higher-order continua are naturally retrieved in the presented computational multiscale model, through which the analysis of size and localization effects can be incorporated. The paper sketches a brief introductory overview of the various classes of multiscale models. Higher-order multiscale methods, as typically required in the presence of localization, constitute the main topic. Details on the second-order approach are given, whereas several higher-order issues are addressed at both scales, with a particular emphasis on localization phenomena. Finally, the applicability and limitations of the considered first-order and second-order computational multiscale schemes for heterogeneous materials are high-lighted.
A Multi-Time-Scale Strategy for Multiphysics Problems: Application to Poroelasticity
14
David
Dureisseix
Laboratoire de Mécanique et Génie Civil (LMGC), Laboratoire de Micromécanique et d'lntégrité des Structures (MIST), IRSN DPAM, CNRS UMR 5508, University Montpellier 2, F-34095 Montpellier CEDEX 5, France
Pierre
Ladeveze
University Paris VI
David
Neron
LMT-Cachan (ENS Cachan / CNRS / University Paris 6), 61, avenue du President Wilson, F-94235 Cachan CEDEX, France
Bernhard
Schrefler
Department of Ingegneria Civile, Edile e Strutturale e Trasporti University of Padua, Via Marzolo 9, 35131 Padua, Italy
Usually, multiphysics phenomena and coupled-field problems lead to computationally intensive structural analysis. Strategies to keep these problems computationally affordable are of special interest. For coupled fluid-structure problems, for instance, partitioned procedures and staggered algorithms are often preferable to direct analysis.
In a previous article, a new strategy derived from the LArge Time INcrement (LATIN) method was described. This strategy was applied to the consolidation of saturated porous soils, which is a highly coupled fluid-solid problem. The feasibility of the method and the comparison of its performance with that of a standard partitioning scheme (the so-called ISPP method) was presented.
Here, we go one step further and use the LATIN method to take into account the different time scales that usually arise from the different physics. We propose a multi-time-scale strategy, which improves the existing method.
Adaptive Mesh Computation of a Shell-Like Problem with Singular Layers
18
C. A.
De Souza
Department of Mechanical Engineering, Federal University of Brasilia, Brasilia, 70910-900, Brazil
D.
Leguillon
Laboratoire de Modelisation en Mecanique, Universite Pierre et Marie Curie - Paris 6, 4, Place Jussieu — case 162 — 75252, Paris Cedex 05, France
Evariste
Sanchez-Palencia
Laboratoire de Modélisation en Mécanique, Université Pierre et Marie Curie 4, place Jussieu, Paris, 75252, France
Solutions to very thin shell problems exhibit in some cases singularities that propagate along given characteristic lines. Often, deformation and energy concentrate along such curves (singular layers); so, an accurate computation needs much refinement in these regions. Herein, we propose an adaptive mesh procedure for solving a model problem (allowing explicit description of the singularities) corresponding to these kind of situations. It generates elements which are, in the layer region, small and elongated.
Parallel Computational Strategies for Multicontact Problems: Applications to Cellular and Granular Media
12
Pierre
Alart
Laboratoire de Mecanique et Genie Civil, Equipe Systemes Multi-Contacts, UMR 5508, Universite Montpellier 2 -CNRS, cc048, Place Eugene Bataillon, 34095 Montpellier Cedex 05, France
Michael
Barboteu
Laboratoire de Theorie des Systemes, Universite de Perpignan, 52 Av. de Villeneuve, 66860 Perpignan, France
Mathieu
Renouf
Laboratoire de Mecanique et Genie Civil, Equipe Systemes Multi-Contacts, UMR 5508, Universite Montpellier 2 -CNRS, cc048, Place Eugene Bataillon, 34095 Montpellier Cedex 05, France
In this article, we compare strategies for introducing parallelism in solving multicontact problems. Two typical problems are distinguished, to emphasize both common and different features, in terms of mechanical modeling, mathematical formulation, and numerical solutions. These two parallel computational approaches are tested on two applications: cellular and granular media. It shows that two different problems using similar equations may lead to the adoption of two very different strategies in order to be efficient: either a sophisticated approach based on a domain decomposition method, or a multithreading procedure that is easy to carry out. The challenges in these research fields reveal the potential of parallel computing.
Acoustic Wave Propagation in a Composite of Two Different Poroelastic Materials with a Very Rough Periodic Interface: a Homogenization Approach
10
Robert P
Gilbert
Miao-jung
Ou
Department of Mathematics, University of Central Florida, Orlando, FL 32817, U.S.A.
Homogenization is used to analyze the system of Biot-type partial differential equations in a domain of two different poroelastic materials with a very rough periodic interface. It is shown that by using homogenization, such a rough interface can be replaced by an equivalent flat layer within which a system of modified differential equations holds. The coefficients of this new system of equations are certain "effective" parameters. These coefficients are determined by solutions of the auxiliary problems which involve the detailed structure of the interface. In this paper, the auxiliary problems are derived and the homogenized system of equations is given.
Micromechanical Analyses of Saturated Granular Soils
20
Mourad
Zeghal
Rensselaer Polytechnic Institute
U. El
Shamy
Civil and Environmental Engineering Department Rensselaer Polytechnic Institute, Troy, NY 12180
Mark S.
Shephard
Rensselaer Polytechnic Institute
R.
Dobry
Civil and Environmental Engineering Department Rensselaer Polytechnic Institute, Troy, NY 12180
Jacob
Fish
Civil Engineering and Engineering Mechanics, Columbia University, New York, New York
10027, USA
T.
Abdoun
Civil and Environmental Engineering Department Rensselaer Polytechnic Institute, Troy, NY 12180
Phenomenological (macroscale) models are commonly used in analyses of saturated soil systems. In these models, the momentum exchange between the solid and fluid phases is generally accounted for using Darcy's law. A hydromechanical model is presented herein to study the coupled mesoscale pore water flow and microscale solid matrix deformation of granular soils. The fluid motion is idealized using averaged Navier-Stokes equations, and the discrete element method is employed to model soil particles. Fluid-particle interactions are addressed using established semi-empirical relationships. The proposed approach was validated using published experimental results. Numerical simulations were conducted to investigate the liquefaction of soil deposits subjected to a critical hydraulic gradient. Pore water flow through a liquefied coarse sandy soil was shown to deviate from Darcy's law and eventually become locally nonlaminar. At steady state, the associated permeabilities were found to be comparable to those at subcritical conditions.
Indices to Volume 1
4