Elastic-plastic Composites Research Articles

A simple analytical estimate for the elastic-plastic behavior of two-phase bi-continuous isotropic composites

A simple modeling is proposed to estimate the elastic-plastic behavior of two-phase isotropic composites made of interpenetrated co-continuous phases. This nonlinear modeling, without equivalent so far, is based on the extension of an explicit Laminate System (LS) scheme proposed previously for linear elastic behavior of such co-continuous composites. Considering monotonic radial loadings, the effective nonlinear stiffness of bi-continuous elastic-plastic composites is estimated from stepwise linearizing the composite overall and phase behaviors using a classical secant linearization procedure. The efficiency of this proposed modeling is checked on some comparisons with rare experimental literature data and with other classical analytical homogenization estimate schemes.

Packing and size effects in elastic-plastic particulate composites: Micromechanical modelling and numerical verification

The issue of applicability of the Morphologically Representative Pattern (MRP) approach to elastic-plastic composites is addressed. The extension to the regime of non-linear material behaviour is performed by employing the concept of incremental linearization of the material response in two basic variants: tangent and secant. The obtained predictions are evaluated through comparison with the outcomes of numerical analyses. Finite Element simulations are carried out using periodic unit cells with cubic arrangements of spherical particles and representative volume elements (RVE) with 50 randomly placed inclusions. In addition to the analysis of the packing effect in two-phase composites, the size effect is also studied by assuming an interphase between the matrix and inclusions. It is concluded that the MRP approach can be used as an effective predictive alternative to computational homogenization, not only in the case of linear elasticity but also in the case of elastic-plastic composites.

Multiscale modeling of deformation and damage of elasticplastic particle reinforced composites

A model is proposed for the deformation of elastic-plastic particle reinforced composite materials of a periodic structure with allowance for the damage. The model is based on a variant of the deformation theory of plasticity under active loading, in which the damage parameter is introduced, taking into account the difference in the accumulation of damage in phases during shear, tension and compression. The method of asymptotic homogenization of periodic structures was used to model the effective characteristics of elastic-plastic composites. Examples of numerical calculation are carried out for particle-reinforced metal composite - aluminum matrix filled with SiC particles.

Hierarchical simulations for the design of supertough nanofibers inspired by spider silk

Biological materials such as spider silk display hierarchical structures, from nano to macro, effectively linking nanoscale constituents to larger-scale functional material properties. Here, we develop a model that is capable of determining the strength and toughness of elastic-plastic composites from the properties, percentages, and arrangement of its constituents, and of estimating the corresponding dissipated energy during damage progression, in crack-opening control. Specifically, we adopt a fiber bundle model approach with a hierarchical multiscale self-similar procedure which enables to span various orders of magnitude in size and to explicitly take into account the hierarchical topology of natural materials. Hierarchical architectures and self-consistent energy dissipation mechanisms (including plasticity), both omitted in common fiber bundle models, are fully considered in our model. By considering one of the toughest known materials today as an example application, a synthetic fiber composed of single-walled carbon nanotubes and polyvinyl alcohol gel, we compute strength and specific energy absorption values that are consistent with those experimentally observed. Our calculations are capable of predicting these values solely based on the properties of the constituent materials and knowledge of the structural multiscale topology. Due to the crack-opening control nature of the simulations, it is also possible to derive a critical minimal percentage of plastic component needed to avoid catastrophic behavior of the material. These results suggest that the model is capable of helping in the design of new supertough materials.

On Full Two-Scale Expansion of the Solutions of Nonlinear Periodic Rapidly Oscillating Problems and Higher-Order Homogenised Variational Problems

We consider a scalar quasilinear equation in the divergence form with periodic rapid oscillations, which may be a model of, e.g., nonlinear conducting, dielectric, or deforming in a restricted way hardening elastic-plastic composites, with “outer” periodicity conditions of a fixed large period. Under some natural growth assumptions on the stored-energy function, we construct for uniformly elliptic problems a full two-scale asymptotic expansion, which has a precise “double-series” structure, separating the slow and the fast variables “in all orders”, so that its “slowly varying” part solves asymptotically an “infinite-order homogenised equation” (cf. Bakhvalov, N.S., Panasenko, G.P.: Homogenisation: Averaging Processes in Periodic Media. Nauka, Moscow, 1984 (in Russian); English translation: Kluwer, 1989), and whose higher-order terms depend on the higher gradients of the slowly varying part. We prove the error bound, i.e., that the truncated asymptotic expansion is “higher-order” close to the actual solution in appropriate norms. The approach is extended to a non-uniformly elliptic case: for two-dimensional power-law potentials we prove the “non-degeneracy” using topological index methods. Examples and explicit formulae for the higher-order terms are given. In particular, we prove that the first term in the higher-order homogenised equations is related to the first-order corrector to the “mean” flux, and has in general the form of a fully nonlinear operator which is quadratic with respect to its highest (second) derivative being a linear combination of the second minors of the Hessian with coefficients depending on the first gradient, and in dimension two is of Monge-Ampere type. We show that this term is present at least for some examples (three-phase power-law laminates).

Micromechanical analysis of composites by the generalized cells model

In the original formulation of the micromechanical method of cells, designated for the analysis of fibrous composites with periodic structure, the repeating volume element consists of four interacting subcells. The various capabilities and reability of the micromechanical model were verified in a recent review paper and a monograph. The present investigation offers a generalization of the method to an arbitrary number of subcells for the modeling of multiphase periodic composites. Such a generalization is particularly advantageous when dealing with elastic-plastic composites, since yielding and plastic flow of a metallic phase may take place at different locations. Effective constitutive laws that govern overall behavior of the elastic-viscoplastic composite material are established. These laws are given in terms of relationships between the average stress-rate and strain-rate of the inelastic multiphase composite. Comparisons between the response of boron/aluminum composite obtained by the present model and a finite element solution are given.

A nonstandard approach to the micromodelling of large deformations in incompressible elastic-plastic composites

The aim of this paper is to present a new homogenized model of periodic composites made of incompressible elastic-plastic Prandtl-Reuss materials with isotropioc work hardening. The nonstandard method of modelling is applied. The considerations are carried out within the large deformation theory. As an example the steady simple extension of a laminate is calculated.

Bounds on overall instantaneous properties of elastic-plastic composites

M inimum principles of plasticity are used to derive upper and lower bounds on ordered eigenvalues and on diagonal terms of instantaneous stiffness and compliance matrices of elastic-plastic composite aggregates subjected to uniform overall stress or strain increments. The method is implemented with the help of a periodic model of binary fibrous composites ; overall properties are derived from incremental solutions of an inclusion problem in a small unit cell. Actual results are found with displacement and equilibrium formulations of the finite element method. In this implementation the instantaneous properties of the inelastic phases of the composite are known only in terms of the approximate values calculated at each step, hence the bounds are valid for an aggregate in which the actual properties have been replaced by the approximate ones. Examples are presented for the fibrous B-A1 system. The technique can be used to evaluate instantaneous element properties in a finite element program for analysis of metal matrix composite structures.

Elastic-plastic composites at finite strains

For elastic-plastic composites at finite strains and rotations. Hill’s self-consistent method is used to estimate the overall instantaneous elastic-plastic moduli. Results are applied to a porous metal whose matrix constitutive relations are characterized by a generalized J2 plasticity model. As an illustration, uniaxial deformation of a porous elastic-plastic solid is considered, and conditions under which the overall uniform deformation becomes unstable by localized deformations, are examined.