Construction of models of dispersive elastodynamic behavior of periodic composites: A computational approach (original) (raw)

Effective elastoplastic properties of the periodic composites

Computational Materials Science, 2001

The article presented deals with the homogenization of composite materials with elastoplastic constituents. The transformation ®eld analysis (TFA) approach is presented and applied to compute the eective nonlinear behavior of multicomponent periodic composite structure. Computational implementation of the method consists in special utilization of the program ABAQUS, which makes it possible to homogenize n-component periodic composites with relatively general con®guration of the periodicity cell. Numerical example of homogenization of a three-component periodic composite shows the comparison between the nonlinear behavior of a real composite and of a homogenized one in a speci®c boundary problem de®ned on its representative volume element (RVE).

Apparent elastic and elastoplastic behavior of periodic composites

International Journal of Solids and Structures, 2001

We investigate scale and boundary conditions eects on the elastic and elastoplastic behavior of periodic ®berreinforced composites. Four boundary conditions, including displacement controlled, traction controlled, mixed (normal displacements and zero shear tractions speci®ed on each boundary) and periodic boundary conditions, are considered. In¯uence of several factors ± such as the window size, the mismatch between component phases' properties, and the types of boundary conditions ± on the apparent mechanical response (elastic and elastoplastic) is studied. It is shown that the apparent properties obtained under our mixed and periodic conditions are the same within numerical accuracy, and they are bounded by those obtained using displacement and traction controlled boundary conditions. From our study of elastic case, it is found that the bounds are very sensitive to the mismatch of phase moduli: the higher the mismatch, the wider are the bounds. In the study of elastoplastic case, monotonically increasing proportional loading is applied to dierent sized windows under each of the above four boundary conditions. An explanation of response curves can be reached through the observation of shear bands, under these various boundary conditions. Ó

Homogenization and effective elastoplasticity models for periodic composites

Communications in Numerical Methods in Engineering, 1994

Techniques for stress-and strain-controlled in situ homogenization of inelastic periodic composites are presented. The results of homogenization computations on a specific elastoplastic composite solid are then employed to validate the form of an orthotropic elastoplasticity model with a tensorial kinematic hardening law.

Overall Dynamic Properties of 3-D periodic elastic composites

2011

A method for the homogenization of 3-D periodic elastic composites is presented. It allows for the evaluation of the averaged overall frequency dependent dynamic material constitutive tensors relating the averaged dynamic ?eld variable tensors of velocity, strain, stress, and linear momentum. The formulation is based on micromechanical modeling of a representative unit cell of a composite proposed by Nemat-Nasser & Hori (1993), Nemat-Nasser et. al. (1982) and Mura (1987) and is the 3-D generalization of the 1-D elastodynamic homogenization scheme presented by Nemat-Nasser & Srivastava (2011). We show that for 3-D periodic composites the overall compliance (stiffness) tensor is hermitian, irrespective of whether the corresponding unit cell is geometrically or materially symmetric.Overall mass density is shown to be a tensor and, like the overall compliance tensor, always hermitian. The average strain and linear momentum tensors are, however, coupled and the coupling tensors are shown to be each others' hermitian transpose. Finally we present a numerical example of a 3-D periodic composite composed of elastic cubes periodically distributed in an elastic matrix. The presented results corroborate the predictions of the theoretical treatment.

Effective properties of elastic periodic composite media with fibers

Journal of The Mechanics and Physics of Solids, 2007

A series solution to obtain the effective properties of some elastic composites media having periodically located heterogeneities is described. The method uses the classical expansion along Neuman series of the solution of the periodic elasticity problem in Fourier space, based on the Green's tensor, and exact expressions of factors depending on the shape of the inclusions. Some properties of convergence

Localized Effects in Periodic Elastoplastic Composites

A method is applied for the study of the field distributions in metal matrix fiber reinforced composites with periodic microstructure in which localized damage exists in the form of complete or partial fiber loss and crack. In addition, the behavior of ceramic/metal periodically layered composites with a single broken ceramic layer is determined. The proposed analysis is based on continuum damage mechanics considerations, and the method of solution combines three distinct approaches. In the first one, referred to as the representative cell method, the periodic composite domain is reduced, in conjunction with the discrete Fourier transform to a finite domain problem of a single representative cell. This method has been previously applied on linear thermoelastic, smart and electrostrictive composites, but is presently extended and applied on elastoplastic composites (presently deformation and incremental plasticity). In the second approach, the appropriate far-field boundary conditions in the transform domain are applied in conjunction with the high-fidelity generalized method of cells micromechanical model for the prediction of the macroscopic behavior of the inelastic composite. The third approach consists of the application of the inelastic higher-order theory for the computation of the elastoplastic field in the transform domain. An inverse transform provides the actual field. The effect of damage is included in the analysis in the form of eigenstresses which are a priori unknown. Hence an iterative procedure is employed to obtain a convergent solution. The proposed method is verified by a comparison with an analytical solution, and several applications illustrate the applicability of the method for metal matrix composites with localized damage in the form of a crack or fiber loss.

Overall dynamic constitutive relations of layered elastic composites

Journal of The Mechanics and Physics of Solids, 2011

A method for homogenization of a heterogeneous (finite or periodic) elastic composite is presented. It allows direct, consistent, and accurate evaluation of the averaged overall frequency-dependent dynamic material constitutive relations. It is shown that when the spatial variation of the field variables is restricted by a Bloch-form (Floquet-form) periodicity, then these relations together with the overall conservation and kinematical equations accurately yield the displacement or stress modeshapes and, necessarily, the dispersion relations. It also gives as a matter of course point-wise solution of the elasto-dynamic field equations, to any desired degree of accuracy. The resulting overall dynamic constitutive relations however, are general and need not be restricted by the Bloch-form periodicity. The formulation is based on micro-mechanical modeling of a representative unit cell of the composite proposed by Nemat-Nasser and coworkers; see, e.g., [1] and [2].

Homogenization of elastoplastic composites with generalized periodicity in the microstructure

International Journal Plasticity

In this paper, a consistent theory of homogenization for complex heterogeneous elastoplastic structures with generalized periodicity is proposed. The structures under consideration are not necessarily periodic, but their properties (geometry and material) exhibit periodicity with respect to non-linear periodicity functions. The proposed theory is based on an adequate definition of the admissible deformation fields and the corresponding functional setting, and results from the generalization of the two-scale convergence theory. Moreover, the discrete variational formulation is presented, for both the global and local problems. Additionally, the implicit formulation of the homogenization problem is proposed for elastic-J2-plastic constituents with linear hardening in the context of infinitesimal elastoplasticity, including the numerical scheme for homogenization and the derivation of the consistent elastoplastic tangent modulus. Finally, the computational algorithm for the proposed theory is deployed, consisting of four interacting problems, the macroscale, the microscale, the iterative plastic scheme and the effective tangent modulus problem. The theory and the numerical and computational scheme are supplemented by two examples, one of a wavy multilayered structure and one of a multilayered tube.

Elastic properties of composite materials

Mathematical Models and Computer Simulations, 2010

A developed system is presented for computer aided calculation of the effective elastic properties of composite materials (CM) with various reinforcement structure (3D reinforced, 4D reinforced, textile reinforcement). The computation was based on the finite element method for the solution of the so called local problems L pq arising on applying the asymptotic homogenization method worked out by N.S. Bakhvalov and B.Ye. Pobedrya. The calculation results for effective elastic properties of CM obtained by the developed software system are presented as well as some character istics of the system application to the above listed types of reinforcement structures. CM (composites), which have been intensively developed since the 1960s, are still one of the leading classes of engineering materials due to their outstanding properties, i.e., low weight (even in comparison with aluminum alloys), high stiffness and strength, as well as their high chemical resistance, machinability, etc. The greatest disadvantage of these materials is their high price, which had earlier limited the scope of its application in civil engineering, but it has largely been overcome, since the price of the end product (e.g., aircraft or sea vessels) is now much less dependent on the prices of components and materials.