Begell House Inc.
International Journal for Multiscale Computational Engineering
JMC
1543-1649
6
5
2008
PREFACE
vii
Multiscale Modeling of Material Failure: From Atomic Bonds to Elasticity with Energy Limiters
393-410
Konstantin Y.
Volokh
Faculty of Civil and Environmental Engineering, Technion-Israel Institute of Technology, Haifa 32000, Israel
Separation of two particles is characterized by a magnitude of the bond energy, which limits the accumulated energy of the particle interaction. In the case of a solid comprising many particles, there exist a magnitude of the average bond energy, the failure energy, which limits the energy that can be accumulated in an infinitesimal material volume under strain. The energy limiter controls material softening; the softening indicates failure. Thus, by limiting the stored energy density, we include a description of material failure in the constitutive model. When the failure energy, that is, the energy limiter, is introduced in the constitutive model, it can be calibrated in macroscopic experiments. Traditional material models do not have energy limiters, and they allow for unlimited energy accumulation under the strain increase, which is unphysical because no material can sustain large enough strains without failure. We review the applications of the new approach based on the use of the energy limiters to failure of soft biological tissues and fracture of brittle materials. In addition, we consider new developments concerning the rate-dependent failure in solids and the drop of viscosity in fluids.
Finite Strain Micromechanical Modeling of Multiphase Composites
411-434
Jacob
Aboudi
Faculty of Engineering, Tel Aviv University, Ramat Aviv 69978, Israel
This paper reviews a series of articles in which finite strain micromechanical analyses were developed for the prediction of the macroscopic (global) behavior of multiphase composites undergoing large deformations. The finite strain constituents in these composites can be modeled as hyperelastic, thermoelastic (based on entropic elasticity), viscoelastic (including quasilin-ear viscoelasticity, which is suitable for the modeling of biological tissues), thermoviscoelastic, rate-dependent thermoinelastic (viscoplastic), and rate-independent thermoinelastic (elastoplastic). In all cases, the micromechanical analyses are based on the homogenization technique for periodic composites. These analyses provide the instantaneous mechanical, thermal, and inelastic concentration tensors that relate the local induced strain in the phase to the current externally applied strains and temperature. In addition, these micromechanical analyses yield the macroscopic constitutive equations of the multiphase composite in terms of its instantaneous stiffness and thermal stress tensors. In any one of these micromechanical analyses, the local field distribution among the various constituents of the composite can be also determined at any instant of loading. The finite strain micromechanically established macroscopic constitutive equations can be employed in a structural analysis to determine the behavior of composite structures and biological tissues underging large deformations, thus forming a micro macrostructural multiscale analysis.
Employing the Discrete Fourier Transform in the Analysis of Multiscale Problems
435-449
Michael
Ryvkin
School of Mechanical Engineering, Tel Aviv University, Ramat Aviv 69978, Israel
The idea of employing the discrete Fourier transform casted as the representative cell method for the solution of multiscale problems is illustrated. Its application in combination with analytical (structural mechanics methods, Wiener-Hopf method, integral transform methods) and numerical (finite element method, higher-order theory) methods is demonstrated. Both cases of 1-D and 2-D translational symmetry are addressed. In particular, the problems for layered, cellular, and perforated materials with and without flaws (cracks) are considered. The method is shown to be a convenient and universal analysis tool. Its numerical efficiency allowed us to solve optimization problems characterized by multiple reanalysis.
A Multiscale Approach to Nonlinearity in Piezoelectric-Ferroelectric Smart Structures: From Micromechanics to Engineering
451-468
Oded
Rabinovitch
Faculty of Civil and Environmental Engineering, Technion, Israel Institute of Technology, Technion City, Haifa, 32000, Israel
Uri
Kushnir
Faculty of Civil and Environmental Engineering, Technion, Israel Institute of Technology, Technion City, Haifa, 32000, Israel
A multiscale approach to the nonlinear electromechanical analysis of piezoelectric and ferroelectric structural elements is presented. The multiscale modeling ranges from the unit cell scale, in which the phenomena of domain switching originate, and goes through the grain scale, the material point scale, the continuum scale, and up to the structural element scale. A multiscale approach for the numerical solution of the governing equations of the nonlinear structural model is also presented. This approach accounts for the loading history dependency and the nonlinearity of the ferroelectric behavior by implementing an incremental iterative procedure and separate discretizations for the grain, the material point, and the structure scales. A numerical example of a ferroelectric beam under combined bending, compression, and electrical loading demonstrates the various multiscale aspects of the model and, particularly, the influence of the domain switching on the response at the different physical and mathematical scales. The findings of the article designate the multiscale approach as a meaningful step toward the implementation of ferroelectric materials in advanced smart structures with enhanced capabilities.
Postbuckling of Layered Composites by Finite Strain Micromechanical Analysis
469-481
Rivka
Gilat
Department of Civil Engineering, Faculty of Engineering, Ariel University Center, Ariel 44837, Israel
Jacob
Aboudi
Faculty of Engineering, Tel Aviv University, Ramat Aviv 69978, Israel
A finite deformation micromechanical analysis that includes the effect of initial geometrical imperfection is formulated and employed to demonstrate its capability to predict the mechanical and thermal postbuckling of periodic bilayered composites. This micromechanical model, is based on the analysis of doubly periodic composites in conjunction with the homogenization technique. The field equations are modified to incorporate the effect of initial wavy imperfection, which is essential for development and analysis of the postbuckling phenomenon. Nonlinear, compressible neo-Hookean law is adopted for representing the behavior of the composites constituents. The offered approach is employed to predict the postbuckling behavior of layered composites under compressive mechanical loading. In addition, the possibility of the occurrence of postbuckling as a result of thermal stresses developing during the application of a temperature drop is examined.
Subject-Specific p-FE Analysis of the Proximal Femur Utilizing Micromechanics-Based Material Properties
483-498
Zohar
Yosibash
Department of Mechanical Engineering, Ben-Gurion University, Beer-Sheva 84105, Israel
Nir
Trabelsi
Department of Mechanical Engineering, Ben-Gurion University, Beer-Sheva 84105, Israel
Christian
Hellmich
Institute for Mechanics of Materials and Structures, Vienna University of Technology, A-1040 Vienna, Austria
Novel subject-specific high-order finite element models of the human femur based on computer tomographic (CT) data are discussed with material properties determined by two different methods, empirically based and micromechanics based, both being determined from CT scans. The finite element (FE) results are validated through strain measurements on a femur harvested from a 54-year-old female. To the best of our knowledge, this work is the first to consider an inhomogeneous Poisson ratio and the first to compare results obtained by micromechanics-based material properties to experimental observations on a whole organ. We demonstrate that the FE models with the micromechanics-based material properties yield results which closely match the experimental observations and are in accordance with the empirically based FE models. Because the p-FE micromechanics-based results match independent experimental observations and may provide access to patient-specific distribution of the full elasticity tensor components, it is recommended to use a micromechanics-based method for subject-specific structural mechanics analyses of a human femur.
Development of a Concrete Unit Cell
499-510
Erez
Gal
Department of Structural Engineering, Ben-Gurion University, Beer-Sheva, 84105, Israel
Avshalom
Ganz
Department of Structural Engineering, Ben-Gurion University, Beer-Sheva, 84105, Israel
Liran
Hadad
Department of Structural Engineering, Ben-Gurion University, Beer-Sheva, 84105, Israel
Roman
Kryvoruk
Department of Structural Engineering, Ben-Gurion University, Beer-Sheva, 84105, Israel
This paper describes the development of a unit cell for concrete structures. Executing a multiscale analysis procedure using the theory of homogenization requires solving a periodic unit cell problem of the material in order to evaluate the material macroscopic properties. The presented research answers that need by creating a concrete unit cell through using the concrete paste generic information (i.e., percentage of aggregate in the concrete and the aggregate distribution). The presented algorithm manipulates the percentage of the aggregate weight and distribution in order to create a finite element unit cell model of the concrete to be used in a multiscale analysis of concrete structures. This algorithm adjusts the finite element meshing with respect to the physical unit cell size, creates virtual sieves according to adjusted probability density functions, transforms the aggregate volumes into a digitized discrete model of spheres, places the spheres using the random sampling principle of the Monte Carlo simulation method in a periodic manner, and constructs a finite element input file of the concrete unit cell appropriate for running a multiscale analysis using the theory of homogenization.