Anisotropic Constitutive Equations Research Articles

Propagation of harmonic waves in a layered elasto-piezoelectric composite

The exact analytical treatment of the propagation of harmonic waves in an infinitely extended, periodically layered, elastic and piezoelectric composite is presented. The general anisotropic constitutive equations including the terms of piezoelectric and anti-piezoelectric effects are used. The electric field is assumed as quasi-static. The continuity and the Floquet condition are assumed as boundary conditions on the field variables, leading to a dispersion equation of an 8 × 8 determinantal form. This dispersion equation is solved to investigate the dispersion characteristics of a composite. Numerical computations are made for a composite consisting of zinc oxide, gallium arsenide, and lithium tantalate. The influence of the piezoelectric effect of materials on the phase velocity of waves is investigated.

Flow and Fiber Orientation Calculations in Reinforced Thermoplastic Extruded Tubes

Abstract A calculation of fiber orientation of reinforced thermoplastics in two tube die geometries is presented. The flow field and fiber motion are calculated using coupled anisotropic constitutive equation and equation of change for fiber orientation. A finite element method is used for the flow field computation, and a simplified characteristic method for the fiber orientation. Results show that fibers orient parallel to the tube axis in a classical die of constant radius in the final land whereas fibers have a more isotropic orientation in a die with a final divergent land. Experimental observations and quantification of fiber orientation in reinforced thermoplastic tubes extruded with the two dies are presented. Results of the calculation agree well with the experimental data for the classical die. For the diverging die, the agreement is good at the tube surface, but the calculation underestimates the degree of orientation perpendicular to the tube axis in the core of the tube.

Near-tip field of an anti-plane crack in a micro-cracked power-law solid

Asymptotic near-tip field is investigated for an anti-plane (mode III) crack in a power-law solid permeated by a distribution of micro-cracks. The micro-crack location is assumed to be random, while the micro-crack orientation is taken to be non-random. The anisotropic nature of this kind of damage gives rise to anisotropic constitutive equations for the overall macroscopic strains and stresses. The structure of the asymptotic field at a macro-crack tip is analyzed by solving a nonlinear eigenvalue problem. It is shown that under the assumptions made in this analysis the asymptotic crack tip field of the damaged solid has the same structure as the mode III HRR-field of the undamaged solid. Numerical results are presented for the angular functions, the contours of constant effective shear stress, the normalization constant arising in the near-tip field, and the crack opening displacement. By means of these results, the effects of the micro-crack density and orientation on the crack-tip field will be explored.

A description of creep anisotropy induced by plastic pre-strain. (2nd Report. A form based on a mapped effective stress).

A mapped (effective) stress defined by a linear transformation of four rank was applied to formulate an anisotropic creep constitutive equation. First, a reduced version of the polynomial representation of isotropic strain rate function was discussed in connection with an effective stress mapped by a four-rank anisotropic tensor. Then, a rational effective stress defined by the four-rank anisotropic tensor proposed by Baltov-Sawczuk was examined, and it was extended so as to incorporate both isotropic and anisotropic hardenings. By using the proposed anisotropic effective stress tensor, a form of anisotropic creep constitutive relation was develpoed and embodied by using the functional form of Bailey-Norton creep law. The proposed model was applied to the anisotropic creep behavior after plastic deformation for 316 stainless steel at elevated temperature. A comparison between the predicted and experimental results showed reasonable agreement.

Tensor Functions Representations as Applied to Deriving Constitutive Relations for Skewed Anisotropy

AbstractAn irreducible, non‐polynomial representation is established for an anisotropic constitutive equation being an explicit relation between two symmetric, second‐order tensors. The considered material anisotropy is characteristic of two non‐orthogonal and mechanically non‐equivalent privileged directions in plane. Particular cases of orthotropy and of cubic symmetry are analyzed in detail. An illustrative example referring to infinitesimal elasticity is presented in order to compare the developed representation with the classical Hooke law.

A Variational Principle for the Linear Coupled Thermoelastodynamic Analysis of Mechanism Systems

A variational principle is presented which provides the basis for developing the equations governing the coupled thermoelastic response of planar flexible mechanism systems subjected to both mechanical and thermal loading. These systems are modeled as chains of continua with anisotropic elastic constitutive equations. By permitting arbitrary independent variations of the system parameters for each link, approximate equations of motion and boundary conditions may be systematically constructed. As an illustrative example, the derivation of the problem definition of a flexible connecting rod of a slider crank mechanism subjected to thermal shock is presented.

Composite Laminates with Negative Through-the-Thickness Poisson's Ratios

A simple analysis using two-dimensional lamination theory combined with the ap propriate three-dimensional anisotropic constitutive equation is presented to show some rather surprising results for the range of values of the through-the-thickness ef fective poisson's ratio vxz for angle-ply laminates. Results for graphite-epoxy show that the through-the-thickness effective poisson's ratio can range from a high of 0.49 for a [90] laminate to a low of -0.21 for a [±25]S laminate. It is shown that negative values of vxz are also possible for other laminates.

General Constitutive Equations of Anisotropic Thermal-Elastic-Plastic Materials

General thermal-elastic plastic constitutive equations for any anisotropic materials are discussed theoretically. First, the general anisotropic thermal-elastic constitutive equations are obtained, and a plastic potential, which is a function of stress and entropy, is assumed. Then from the concept of von Mises and from the assumption of the perfect plasticity, the general thermal-elastic-plastic constitutive equations are derived. The special case of quadratic form of the plastic potential with respect to the stress and entropy is analysed. The _??_-representation is also discussed, where the constitutive equations are expressed in terms of six or seven dimensional vectors in _??_6 or _??_7.

Thermo-acoustical waves in linear thermo-elastic materials

Coupled waves of thermal and mechanical jumps in linear thermo-elastic materials are analysed. General linear anisotropic constitutive equations of thermo-elastic materials are derived from the Clausius-Duhem inequality and Vernotte's heat conduction law is adopted. The waves are defined to have jumps in acceleration and in temperature rate and the four-dimensional thermo-acoustical propagation condition is obtained. The differential equations which govern the variation of the wave amplitudes are obtained. For waves in linear isotropic thermo-elastic materials, there are four principal waves. Two shear waves are purely mechanical and propagate with constant amplitude, while two thermo-longitudinal waves have different propagation velocities: one is larger and other smaller than the purely mechanical longitudinal wave velocity, and their amplitudes decay, in general, exponentially in time.

Shear-dependent deformation of erythrocytes in rheology of human blood.

Shear-dependent deformation of erythrocytes in rheology of human blood.

STRESS FIELD AND FRACTURING OF SOLID PROPELLANT DURING ROCKET FIRING

T occurrence of crazing, cracking, or fracturing in viscoelastic .materials has been attributed to its strong association with the presence of tensile stress.2 In the problem of studying fracturing of solid propellant during rocket firing, the determination of the stress distribution in the solid propellant must be made as a prerequisite. However, because of the development of the anisotropic properties of the solid propellant as a result of microscopic nonhomogeneity in its constituents, the stress analysis must be based upon anisotropic viscoelastic considerations. Using general indicial notations and summation convention over repeated diagonal indices, the anisotropic constitutive equations in linear infinitesimal viscoelasticity may be deduced from invariant considerations. Under certain restrictions the stress tensor cr(x,l) at time t can be related to the history of the infinitesimal strain tensor aj(x,t — T) where 0 < r < <», i.e., -£ (1)