Begell House Inc.
International Journal for Multiscale Computational Engineering
JMC
1543-1649
10
6
2012
FOREWORD
vii-ix
Patrizia
Trovalusci
Department of Structural Engineering and Geotechnics
Sapienza University of Rome
Via Gramsci 53, 00197 Rome, Italy
Bernhard
Schrefler
Department of Ingegneria Civile, Edile e Strutturale e Trasporti University of Padua, Via Marzolo 9, 35131 Padua, Italy
Special Issue on MULTISCALE MECHANICAL MODELLING OF COMPLEX MATERIALS AND ENGINEERING APPLICATIONS 3
EVALUATION OF GENERALIZED CONTINUUM SUBSTITUTION MODELS FOR HETEROGENEOUS MATERIALS
527-549
Duy Khanh
Trinh
MINES ParisTech, Centre des materiaux, CNRS UMR 7633, BP 87, F−91003 Evry Cedex, France
Ralf
Janicke
Ruhr-Universitat Bochum, Institut fur Mechanik-Kontinuumsmechanik, IA 3/28, Universitatsstr. 150, D−44780 Bochum, Germany
Nicolas
Auffray
Laboratoire Modelisation et Simulation Multi-echelles (MSME), UMR 8208 CNRS, Universite Paris-Est Marne-la-Vallee, 5 Bd Descartes, D−77454 Marne-la-Vallee, France
Stefan
Diebels
Universitat des Saarlandes, Lehrstuhl fuer Technische Mechanik, Postfach 1511 50, D−66041 Saarbrucken, Germany
Samuel
Forest
Several extensions of standard homogenization methods for composite materials have been proposed in the literature that rely on the use of polynomial boundary conditions enhancing the classical affine conditions on the unit cell. Depending on the choice of the polynomial, overall Cosserat, second gradient, or micromorphic homogeneous substitution media are obtained. They can be used to compute the response of the composite when the characteristic length associated with the variation of the applied loading conditions becomes of the order of the size of the material inhomogeneities. A significant difference between the available methods is the nature of the fluctuation field added to the polynomial expansion of the displacement field in the unit cell, which results in different definitions of the overall stress and strain measures and higher order elastic moduli. The overall higher order elastic moduli obtained from some of these methods are compared in the present contribution in the case of a specific periodic two-phase composite material. The performance of the obtained overall substitution media is evaluated for a chosen boundary value problem at the macroscopic scale for which a reference finite element solution is available. Several unsatisfactory features of the available theories are pointed out, even though some model predictions turn out to be highly relevant. Improvement of the prediction can be obtained by a precise estimation of the fluctuation at the boundary of the unit cell.
THEORETICAL AND ALGORITHMIC FORMULATION OF MODELS FOR ENERGETIC GND-BASED HARDENING IN SINGLE CRYSTALS
551-565
Swantje
Bargmann
Institute of Mechanics, Dortmund University of Technology, Germany
Bob
Svendsen
Material Mechanics, Juelich Aachen Research Alliance, RWTH Aachen University
In this work, a model for energetic hardening due to deformation incompatibility at large deformation is formulated in the context of continuum thermodynamics and extended crystal plasticity. In particular, this is carried out using a rate variational approach for the corresponding initial boundary value problem. This involves, in particular, the formulation of rate potentials whose form is determined in general by that of (i) the free energy density for energetic processes, (ii) the dissipation potential for kinetic processes, (iii) the boundary conditions, and (iv) the evolution relations for the internal variablelike quantities on which the free energy and dissipation potential depend. In the current context, these latter quantities include, for example, the inelastic local deformation and dislocation densities, in particular for geometrically necessary dislocations. The algorithmic formulation of the resulting model is carried out with the help of direct, and discrete variational, explicit time integration methods. To demonstrate that the model indeed predicts lengths-cale-dependent hardening behavior, simulation results are shown for the case of a 16-grain synthetic crystalline aggregate in two dimensions.
CONTINUUM TO DISCONTINUUM TRANSITION DURING FAILURE IN NONLOCAL DAMAGE MODELS
567-580
David
Gregoire
Laboratoire des Fluides Complexes, UMR5150, Universite de Pau et des Pays de I'Adour, France
Laura B.
Rojas-Solano
Laboratoire des Fluides Complexes, UMR5150, Universite de Pau et des Pays de I'Adour, France
Gilles
Pijaudier-Cabot
Laboratoire des Fluides Complexes, UMR5150, Universite de Pau et des Pays de I'Adour, France
The purpose of this paper is to discuss how boundary and emerging boundary effects can be folded into a new nonlocal damage formulation based on integral models that provides a consistent transition toward discrete cracking. Several enhancements of the original nonlocal damage model inspired from micromechanics of interacting defects are considered. The goals of the modified nonlocal formulation are threefold: (i) the distribution of damage at failure should be mesh independent; (ii) the model should be able to capture the continuous-discontinuous transition involved in the process of failure due to increasing stresses; (iii) the discontinuous displacements fields resulting from complete failure should be approached as closely as possible. A 1D example illustrates the capabilities of the original and enhanced models. It is found that a combination of increasing/decreasing interactions and nonlocal effects during failure provides the most suitable results.
GRADIENT-DEPENDENT CONSTITUTIVE LAWS FOR A MODEL OF MICROCRACKED BODIES
581-597
Malika Bongue
Boma
Department of Mechanical and Manufacturing Engineering, University of Calgary
Les
Sudak
Department of Mechanical and Manufacturing Engineering, University of Calgary
Salvatore
Federico
Department of Mechanical and Manufacturing Engineering, University of Calgary
The aim of this paper is to propose nonlocal constitutive laws for a model of microcracked bodies. To do so, we use a multiscale approach: we call macroscopic the description in which the body is considered as a continuum and we refer to the microscopic scale when a crack is studied at a closer view. We first propose an approximation of the stress and strain fields in the vicinity of a crack, considering the neighboring discontinuities. We then use equivalence principles between micro- and macroscopic scales in order to determine the expression of the macroscopic constitutive assignments of the body. The latter are written not only in terms of the local values of the deformation and the local values of the geometrical variables representative of the crack field, but also in terms of their gradients. Numerical implementations are performed; we compare constitutive laws obtained from local and nonlocal approaches.
MICROMORPHIC CONTINUA: APPLICATION TO THE HOMOGENIZATION OF DIATOMIC MASONRY COLUMNS
599-613
Ioannis
Stefanou
Ecole des Ponts ParisTech, UR Navier/MSA, 68 av. B. Pascal, F 77455 Marne la Vallee cdx 2, France
J.
Sulem
Ecole des Ponts ParisTech, UR Navier/CERMES, 68 av. B. Pascal, F 77455 Marne la Vallee cdx 2, France
In the frame of continuum mechanics, the theory of general micromorphic continua is a key element for modeling mechanical systems of discrete building blocks such as masonry structures. This stems from the fact that the kinematics of the particle, in the terminology of Germain (Germain, P., The Method of Virtual Power in Continuum Mechanics, Part 2: Microstructure. SIAM J. Appl. Math., vol. 25, pp. 556-575, 1973), is quite rich to cover the various degrees of freedom of the discrete microstructure. In the present paper, we derive a third-order micromorphic continuum for modeling diatomic masonry columns. Our analysis is extended to the dynamic regime. For linear elastic interfaces, the derived continuum is compared with the discrete model in terms of the dispersion curves. It is shown that the continuum approximates well the discrete structure for wavelengths five to ten times bigger than the size of the elementary cell. Therefore, the presented model may be the base for future engineering applications in the field of cultural heritage assets, because it might be an alternative approach in the mechanical modeling of ancient colonnades, whose study is mostly performed with the discrete element method. As it is well known, continuum models are quite flexible, computationally cheaper, and may give insight to the fundamental properties of the systems at hand.
MULTISCALE VISCOELASTICâˆ’VISCOPLASTIC MODEL FOR THE PREDICTION OF PERMANENT DEFORMATION IN FLEXIBLE PAVEMENTS
615-634
Elisabeth
Aigner
Austrian Institute for Construction Engineering, Schenkenstrasse 4, A-1010 Vienna, Austria
Roman
Lackner
Material Technology Innsbruck, University of Innsbruck, Innsbruck, Austria
Josef
Eberhardsteiner
Institute for Mechanics of Materials and Structures, Vienna University of Technology, Karlsplatz 13/202, A-1040 Vienna, Austria
Creep/relaxation of asphalt consisting of the thermorheological binder material (bitumen), inclusions (aggregates), and air voids may lead to considerable permanent deformations (rutting). Although viscoelastic models are suitable to describe the asphalt behavior at low stress levels and in the low-temperature regime, material models taking plastic deformation into account are needed in order to capture the thermorheological behavior of asphalt at elevated temperature regimes. In this paper, the deformation behavior of asphalt is described by means of a creep/relaxation function, which, in a second step, is extended toward viscoplastic deformation. The underlying model parameters describing the thermorheological nature of asphalt are determined from a multiscale model considering five observation scales. The model, implemented into a Finite Element program, is used for determination of permanent deformations, as illustrated by the reanalysis of triaxial cyclic compression tests and the prediction of rutting in flexible pavements.
DEFINITION OF THE STIFFNESS MATRIX OF A HIERARCHICAL STRUCTURE BY USING VIRTUAL TESTING AND ARTIFICIAL NEURAL NETWORKS
635-648
Daniela
Boso
Department of Structural and Transportation Engineering, University of Padova, Via Marzolo 9, 35131 Padova, Italy
M.
Lefik
Geotechnical Engineering and Engineering Structures, Technical University of Lodz, Poland
In this paper, we consider structures characterized by a definite geometrical hierarchy, such as multilayer wire ropes. We investigate the mechanical behavior, namely, the influence of the hierarchical helix geometry on the stiffness of the cable. It is shown how the stiffness matrix of these structures is different from the usual stiffness matrix of Euler-Bernoulli beams. Furthermore, the dependence of the stiffness coefficients on the twist pitches of the multilevel helixes is also analyzed. A hybrid finite element{artificial neural network approach (ANN-FE) is proposed, suggesting that suitably trained ANNs can replace the module that usually provides the stiffness matrix in an FE code. Finally, a comparison is shown, where results obtained via the FE method are compared with those calculated by an ANN-FE procedure.