Micromechanically Based Constitutive Relations for Polycrystalline Solids

A basic method to estimate the overall mechanical response of solids which contain periodically distributed defects is presented. The method estimates the shape and growth pattern of voids periodically distributed over the grain boundaries in a viscous matrix. The relaxed moduli are obtained for a polycrytalline solid that undergoes relaxation by grain boundary sliding which accounts for the interaction effects. The overall inelastic nonlinear response at elevated temperatures in terms of a model which considers nonlinear power law creep within the grains, and linear viscous flow in the grain boundaries is discussed

Torsional Instability of Cantilevered Bars Subjected to Nonconservative Loading

Cantilever bar torsional instability under nonconservative compression loadin

On the stability of equilibrium of continuous systems Technical report no. 65-1

Stability of equilibrium of linear elastic continuum - Galerkin metho

On the Stability Equilibrium of Continuous Systems

Sufficiency theorem for stability of linearly viscoelastic solid subjected to partial follower surface traction

Destabilizing effect of velocity-dependent forces in nonconservative continuous systems Technical report no. 65-4

Velocity dependent force destabilizing effect in cantilevered continuous pipe conveying fluid at constant velocit

Interaction Between an Incident Wave and a Dynamically Transforming Inhomogeneity

Transformation-toughening of ceramics has attracted considerable attention [1,2,3] in recent years. The key mechanism in this toughening is the stress-induced phase transformation of the partially stabilized zirconia (PSZ) inhomogeneities, which accompanies volumetric expansion. Due to this expansion, the composite material consisting of PSZ inhomogeneities in a brittle matrix becomes more resistant to fracturing. While this problem has been studied for guasi-static loadings [4,5], the corresponding dynamic case has remained relatively unexplored

Deformation and Failure of Amorphous Solidlike Materials

Since the 1970's, theories of deformation and failure of amorphous, solidlike materials have started with models in which stress-driven, molecular rearrangements occur at localized flow defects via "shear transformations". This picture is the basis for the modern theory of "shear transformation zones" (STZ's), which is the focus of this review. We begin by describing the structure of the theory in general terms and by showing several applications, specifically: interpretation of stress-strain measurements for a bulk metallic glass, analysis of numerical simulations of shear banding, and the use of the STZ equations of motion in free-boundary calculations. In the second half of this article, we focus for simplicity on what we call an "athermal" model of amorphous plasticity, and use that model to illustrate how the STZ theory emerges within a systematic formulation of nonequilibrium thermodynamics.Comment: 28 pages, 4 figures, submitted to Annual Reviews of Condensed Matter Physic

Models demonstrating instability of nonconservative mechanical systems Technical report no. 66-4

Models demonstrating instability on nonconservative mechanical system

Effect of Microstructural Damage on Ultrasonic Velocity and Elastic Moduli of Partially Stabilized Zirconia

Zirconia toughened ceramics, such as magnesia partially stabilized zirconia (Mg-PSZ), have received considerable attention due to their high strength and fracture toughness [1]. These properties are a consequence of stress-induced microstructural changes which inhibit crack propagation and provide a degree of ‘damage tolerance1 not common to other ceramic materials. Ultrasonic testing can aid in the characterization of microstructural changes associated with transformation plasticity [2]. The present paper presents measurements of ultrasonic velocity as a function of microstructural damage in Mg-PSZ loaded in compression at high strain rates. Observed changes in elastic moduli are compared to a model of a solid containing randomly distributed penny-shaped microcracks which are all oriented parallel to the axis of compression

Overall Dynamic Properties of 3-D periodic elastic composites

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 field 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.Comment: 26 pages, 2 figures, submitted to Proceedings of the Royal Society