Showing papers on "Micromechanics published in 2003"

Mechanics of composite structures

Abstract: Preface List of symbols 1. Introduction 2. Displacements, strains, stresses 3. Laminated composites 4. Thin plates 5. Sandwich plates 6. Beams 7. Beams with shear deformation 8. Shells 9. Finite element analysis 10. Failure criteria 11. Micromechanics Appendix A. Cross-sectional properties of thin-walled composite beams Appendix B. Buckling loads and natural frequencies of orthotropic beams with shear deformation Appendix C. Typical material properties Index.

Development of a self-consolidating engineered cementitious composite employing electrosteric dispersion/stabilization

Abstract: A self-consolidating engineered cementitious composite (ECC) reinforced with hydrophobic polyethylene fibers has been developed by combining micromechanics based design and rheological design, in a compatible manner. The previously developed micromechanics based design selects material ingredients for tensile ductility in the hardened state. The rheological design, which is the focus in this paper, modifies the material ingredients for self-consolidation behavior in the fresh state. For this purpose, the rheological design adopts a complementary electrosteric dispersion and stabilization technique to obtain cement pastes with desirable flow properties at constant particle concentrations dictated by the micromechanics based design. Such stabilization is realized by optimizing the dosages of strong polyelectrolyte and non-ionic polymer and by controlling the mixing procedure of the polymers. The fresh cement paste designed thereby leads to fresh mortar mix with desirable deformability, cohesiveness, and high consistency, and thus satisfies the self-consolidating performance of fresh ECC mix. In addition, ductile strain-hardening performance of the self-consolidating ECC is confirmed through uniaxial tensile test. This ductile composite with excellent fluidity can be broadly utilized for a variety of applications, e.g. in repair of deteriorated infrastructures requiring horizontal formworks, or in seismic-resistant structures with dense reinforcements and requiring high ductility.

An accurate scheme for mixed‐mode fracture analysis of functionally graded materials using the interaction integral and micromechanics models

Abstract: SUMMARY The interaction integral is a conservation integral that relies on two admissible mechanical states for evaluating mixed-mode stress intensity factors (SIFs). The present paper extends this integral to functionally graded materials in which the material properties are determined by means of either continuum functions (e.g. exponentially graded materials) or micromechanics models (e.g. self-consistent, Mori–Tanaka, or three-phase model). In the latter case, there is no closed-form expression for the material-property variation, and thus several quantities, such as the explicit derivative of the strain energy density, need to be evaluated numerically (this leads to several implications in the numerical implementation). The SIFs are determined using conservation integrals involving known auxiliary solutions. The choice of such auxil

Interfacial cracks between piezoelectric and elastic materials under in-plane electric loading

Abstract: A new experimental technique for accelerated fatigue crack growth tests was recently developed (Du et al., 2001). The technique, which uses piezoelectric actuators, enables application of cyclic loading at frequencies several orders higher than that by mechanical loading. However, the validity of this technique relies on the equivalence between piezoelectric and mechanical loading. In this paper, the behavior of an interfacial crack between a piezoelectric material and an elastic material under in-plane electric loading is studied. The displacement mismatch along a bonded interface due to electric potential loading on the piezoelectric material is modeled by inserting an array of uniformly distributed dislocations along the interface. By means of Fourier transformation methods, the governing equations are converted to an integral equation, which is then converted to a standard Hilbert problem. A closed form solution for stresses, electric field, and electric displacements along the bonded interface is obtained. The results agree very well with those obtained from numerical simulations. The results show that the closed form solution is accurate not only for far field distributions of stresses and electric variables, but also for the asymptotic distributions near the crack tip. The solution also suggests the likelihood of domain switching in the piezoelectric material near the crack tip, a process that may influence the interfacial fracture resistance.

General Techniques for Exploiting Periodicity and Symmetries in Micromechanics Analysis of Textile Composites

Abstract: General formulas for obtaining boundary conditions for micromechanics analysis of textile composites are developed based on the concept of equivalent subcell, which is the smallest region that has

Micromechanics Study on Top-Down Cracking:

Abstract: Top-down cracking is a type of cracking that rivals the severity and prevalence of reflective cracking It significantly reduces the pavement's quality service life Yet the nature of top-down cracking has not been completely understood Recent studies of the causes of top-down cracking have focused on identifying the mechanisms that induce tensile stresses at the surface by applying different combinations of surface tractions and the finite element method Asphalt concrete is treated as a uniform linear elastic material A new and different approach is presented for investigating the causes of top-down cracking by means of micromechanics In this approach, asphalt concrete is viewed as a bonded granular material, and the microstructure, including aggregate particle configuration and mastic stiffness, is considered Theories that predict the existence of tensile stress under compressive loading were reviewed Both qualitative and quantitative experimental methods were developed to observe the location of

Micromechanics-Based Modeling of Woven Polymer Matrix Composites

Abstract: A novel approach is combined with the generalized method of cells (GMC) to predict the elastic properties of plain-weave polymer matrix composites (PMCs). The traditional one-step three-dimensional homogenization procedure that has been used in conjunction with GMC for modeling woven composites in the past is inaccurate due to the lack of shear coupling inherent in the model. However, by performing a two-step homogenization procedure in which the woven composite repeating unit cell is homogenized independently in the through-the-thickness direction prior to homogenization in the plane of the weave, GMC can now accurately model woven PMCs. This two-step procedure is outlined and implemented, and predictions are compared with results from the traditional one-step approach as well as other model and experimental results from the literature. Full coupling of this two-step technique within the recently developed Micromechanics Analysis Code with GMC software package will result in a widely applicable, efficient, and accurate tool for the design and analysis of woven composite materials and structures.

Fracture Toughness of Carbon Foam

Abstract: Mode I fracture toughness of open cell carbon foam was measured using single edge notched four-point bend specimens. A micromechanical model was developed assuming a rectangular prism as the unit-cell. A small region surrounding the crack tip was modeled using finite elements. Displacement boundary conditions were applied to the boundary of the region based on linear elastic fracture mechanics for orthotropic materials. From the finite element results the Mode I stress intensity factor that will cause failure of a crack tip element was determined and it was taken as the predicted fracture toughness of the foam. A simpler model in which the foam consisted of struts of square cross section was also considered. The micromechanical simulations were used to study the variation of fracture toughness as a function of solidity of the foam. The good agreement between the finite element and experimental results for fracture toughness indicates that micromechanics can be an effective tool to study crack propagation in cellular solids.

Two exact micromechanics-based nonlocal constitutive equations for random linear elastic composite materials

Abstract: A Hashin–Shtrikman–Willis variational principle is employed to derive two exact micromechanics-based nonlocal constitutive equations relating ensemble averages of stress and strain for two-phase, and also many types of multi-phase, random linear elastic composite materials. By exact is meant that the constitutive equations employ the complete spatially-varying ensemble-average strain field, not gradient approximations to it as were employed in the previous, related work of Drugan and Willis (J. Mech. Phys. Solids 44 (1996) 497) and Drugan (J. Mech. Phys. Solids 48 (2000) 1359) (and in other, more phenomenological works). Thus, the nonlocal constitutive equations obtained here are valid for arbitrary ensemble-average strain fields, not restricted to slowly-varying ones as is the case for gradient-approximate nonlocal constitutive equations. One approach presented shows how to solve the integral equations arising from the variational principle directly and exactly, for a special, physically reasonable choice of the homogeneous comparison material. The resulting nonlocal constitutive equation is applicable to composites of arbitrary anisotropy, and arbitrary phase contrast and volume fraction. One exact nonlocal constitutive equation derived using this approach is valid for two-phase composites having any statistically uniform distribution of phases, accounting for up through two-point statistics and arbitrary phase shape. It is also shown that the same approach can be used to derive exact nonlocal constitutive equations for a large class of composites comprised of more than two phases, still permitting arbitrary elastic anisotropy. The second approach presented employs three-dimensional Fourier transforms, resulting in a nonlocal constitutive equation valid for arbitrary choices of the comparison modulus for isotropic composites. This approach is based on use of the general representation of an isotropic fourth-rank tensor function of a vector variable, and its inverse. The exact nonlocal constitutive equations derived from these two approaches are applied to some example cases, directly rationalizing some recently-obtained numerical simulation results and assessing the accuracy of previous results based on gradient-approximate nonlocal constitutive equations.