Strain Concentration Tensors Research Articles

Modeling of structures in the mechanics of composites

One possible general statement of a quasi-static problem in the mechanics of composites is considered. It is assumed that a composite is characterized not only by the heterogeneity of a regular structure, but also by the presence of imperfections, impurities, cracks, and the roughness of surfaces, which are partly taken into account by introducing appropriate couple stresses. Two statements, “in displacements” and “in stresses,” are considered together with the statement of the same problems in the case where the constitutive relations are linear integral operators. The boundary-value problem remains nonlinear due to the nonlinearity of a scattering function which enters into the heat equation. The theory of effective moduli for a nonpolar medium is discussed in more detail. The equilibrium equations for a homogeneous medium with reduced characteristics and the equation of heat inflow, introduced in nonlinear (in an explicit form) and linear variants, are examined. For a simple laminated composite, all effective mechanical and thermophysical characteristics are found in an explicit form. The effective material functions for a transversely isotropic medium are constructed on the basis of a unique dimensionless relaxation kernel with the use of several Il'ushin kernels. Based on the known solution of the boundary-value problem for the reduced medium, the stress and strain concentration tensors, at any point of a simple laminated composite, are also constructed in an explicit form. In this case, the changes in the structure are taken into account.

Micromechanics modeling of composite with ductile matrix and shape memory alloy reinforcement

A quantitative micromechanics-based analysis on the role of microstructure and constituent properties in the overall behavior of shape memory alloy (SMA) composite is carried out in the present work. The composite consists of ductile matrix and SMA second phase inclusions. The macroscopic constitutive relations of the composite are established by using self-consistent approach where the micro–macro correlation is realized by volume averaging and by introducing the concept of stress and strain concentration tensors. In this micromechanics modeling, the internal stress and strain in both matrix and SMA and their evolution are derived as function of externally applied thermomechanical loading as well as the degree of phase transformation in SMA. As an application of the present theory in the microstructural design of this novel composite, the constitutive response of composites with spherical SMA particulate embedded in two different elastoplastic matrixes under uniaxial tension is calculated. The obtained results demonstrate several interesting deformation features of the new composite, which are expected to have potential applications in the future.

A generalized self‐consistent mori‐tanaka scheme for prediction of the effective elastic moduli of hybrid multiphase particulate composites

AbstractA generalized self‐consistent Mori‐Tanaka method (GSCMTM) is developed in this paper. The method starts with the formulation of the problem of heterogeneous elasticity proposed by Dederichs and Zeller and incorporates the strain equivalence condition of Christensen's generalized self‐consistent method (GSCM) and Hill's interfacial operator theory into the evaluation of the strain concentration tensors of constituents. For a two‐phase composite with spherical inclusions, the effective moduli predicted by GSCMTM coincide with those predicted by the Mori‐Tanaka method (MTM). By a two‐step homogenization technique, GSCMTM was successfully extended to multiphase composites. The effective moduli predicted by GSCMTM for multiphase hybrid particulate composites agree well with the existing theoretical and experimental results and can be expressed in a simple explicit form.

Stress and Strain Concentration Tensors for Damaged Fibrous Composites

As composite materials undergo damage, the corresponding stress and strain concentration tensors do not remain constant even for the case of elastic deformations.These tensors are derived and presented here for fibrous composites that undergo damage in both the constituents and the interfacial surface. The damage in the matrix includes nucleation and growth of voids, etc., while in the fibers includes micro-fracture, etc. In addition, interfacial damage is described as the damage due to debonding. The damaged stress and strain concentration tensors are obtained for the elasto-plastic states of the composite material. Expressions are derived and presented here for the elasto-plastic stress and strain concentration tensors for fibrous composite materials in the damaged conigurations. The fibers are assumed to be continuous in this work. The elastic strain and stress concentration tensors using the Mori-Tanaka method for the case of undamaged fiberous composites are formulated by Chen, et al. (1992). These elastic concentration tensors are constant in the undamaged or effective configuration due to the fact that damage effects in the material are ignored. However, these damaged elasto-plastic concentration tensors are a function of the fourth order damage tensors in the damaged configuration.