Jace W. Nunziato

LINEAR ELASTIC MATERIALS WITH VOIDS

A linear theory of elastic materials with voids is presented. This theory differs significantly from classical linear elasticity in that the volume fraction corresponding to the void volume is taken as an independent kinematical variable. Following a discussion of the basic equations, boundary-value problems are formulated, and uniqueness and weak stability are established for the mixed problem. Then, several applications of the theory are considered, including the response to homogeneous deformations, pure bending of a beam, and small-amplitude acoustic waves. In each of these applications, the change in void volume induced by the deformation is determined. In the final section of the paper, the relationship between the theory presented and the effective moduli approach for porous materials is discussed.In the two year period between the submission of this manuscript and the receipt of the page proof, there have been some extensions of the results reported here. In the context of the theory described, the classical pressure vessel problems and the problem of the stress distribution around a circular hole in a field have uniaxial tension have been solved [19,22]. The solution given in the present paper for the pure bending of a beam when the rate effect of the theory is absent is extended to case when the rate effect is present in [21]. The various implications of the rate effect in the void volume deformation are pursued all the subsequent works [19,20,21,22].

Recent results in nonlinear viscoelastic wave propagation

Abstract In this article we present a review of some recent theoretical and experimental developments in the field of nonlinear viscoelastic wave propagation. Confining our attention to the case of one-dimensional strain, we review the theories of shock and acceleration wave propagation in general materials with memory and discuss the correlation of these theoretical predictions with some recent experimental results obtained for a particular polymeric solid. Fundamental to this work is the existence of steady shock waves and the fact that they can be generated in a one-dimensional experimental configuration. Using such experimental steady wave observations, a procedure is outlined for determining the material response functions necessary for predicting the growth or decay of shock and acceleration waves in viscoelastic materials. It is further shown that by using a particular constitutive assumption (either purely mechanical or thermomechanical) the complete one dimensional constitutive equation governing the material response can be evaluated from steady shock wave measurements.

An experimental and theoretical study of deflagration-to-detonation transition (DDT) in the granular explosive, CP☆

Abstract In this paper, we present results of an experimental and theoretical study of the combustion processes associated with deflagration-to-detonation transition in the granular explosive, CP. Image-enhanced, high-speed streak photography recorded the various stages of flame spread within heavily confined charges as viewed through a Lexan window in a thick-wall, stainless steel tube. To characterize the phenomena, we applied a multiphase reactive flow model based on the theory of mixtures. This nonequilibrium model treated each phase as fully compressible and incorporated a compaction model for the granular reactant. Formulation of the constitutive models included a pressure-dependent burn rate and experimentally determined porous bed permeability. Predictions of this model were in good agreement with experimental observations.

Acoustical determination of stress relaxation functions for polymers

An analysis of acoustic waves in viscoelastic materials reveals that the stress relaxation function for such materials can be evaluated from acoustic dispersion data. In this paper we illustrate this method by evaluating the longitudinal stress relaxation function for the solid polymer, polymethyl methacrylate (PMMA) using previously reported acoustic data. From this result, we deduce the relaxation function appropriate for describing the shock wave response of PMMA by specifying the time‐scale characteristic of plate impact experiments. This relaxation function compares well with the function determined from the experimental observations of steady shock waves in PMMA.

The behavior of one-dimensional acceleration waves in an inhomogeneous granular solid

Abstract In this paper we study the propagation of 1-dimensional acceleration waves in a particular granular solid. Experimental data on the average wave speed and the wave amplitude are reported for two different initial amplitudes. These results are then compared with the predictions of a recently developed theory of granular materials. The theoretical predictions are shown to agree well with the experimental observations.

The unloading and reloading behavior of shock‐compressed polymethyl methacrylate

Samples of polymethyl methacrylate (PMMA) have been shock compressed to ?0.82 GPa and then further compressed by a reloading wave which approximately doubled the initial compressive stress. The reloading waves were observed to be acceleration waves rather than shocks. Assuming the material is Maxwellian, these waves have been analyzed to determine certain material properties characterizing the stress‐strain response of the material. These properties were found to be different than those obtained from previously reported unloading waves also propagating in shock‐compressed PMMA at ?0.82 GPa. This difference in stress‐strain response supports the existence of a yield‐type phenomenon previously suggested in PMMA at ?0.75 GPa.

The thermal ignition time for homogeneous explosives involving two parallel reactions

Abstract An expression is derived for the thermal ignition time of a homogeneous explosive which is exothermically decomposing by two parallel Arrhenius reactions. The result involves the thermal ignition time of each reaction alone, and is expressed in terms of the hypergeometric function. Application of this analysis to the case of nitromethane ignition is illustrated.

Amplitude behavior of shock waves in a thermoviscoelastic solid

Abstract Recent theoretical studies of the propagation of one-dimensional shock waves in nonlinear viscoelastic materials have considered the influence of the strain gradient immediately behind a propagating shock front on the amplitude of the wave. In particular, the growth or decay behavior of the wave depends upon the relative magnitude of the strain gradient and a critical strain gradient which depends upon the material response properties. Here we apply the results of these studies to a particular constitutive model for a thermoviscoelastic material and determine the critical strain gradient and shock amplitude equation in terms of material response functions and thermophysical properties. The results are exhibited for a particular polymeric solid (PMMA) and compared to experimental results obtained in steady wave studies.

Thermodynamic restrictions on the relaxation functions of the theory of heat conduction with finite wave speeds

In this paper we establish the restrictions imposed by the Second law of Thermodynamics on the relaxation functions which arise in the theory of heat conduction with finite wave speeds. We show that (i) the initial values of the energy relaxation function and the heat flux relaxation function are non-negative, (ii) the initial slope of the heat flux relaxation function is non-positive, and (iii) the equilibrium conductivity is non-negative. These results have important implications with regard to the behavior of waves and the uniqueness of solutions.ZusammenfassungIn dieser Arbeit werden die durch den zweiten Hauptsatz der Thermodynamik gegebenen Beschränkungen der Relaxationsfunktionen aufgezeigt, die in der Theorie der Wärmeleitung mit endlicher Ausbreitungsgeschwindigkeit auftreten. Es wird gezeigt, dass erstens die Anfangswerte der Energie-Relaxationsfunktion und der Wärmefluss-Relaxationsfunktion nicht negativ sind, zweitens die Anfangsableitung der Wärmefluss-Relaxationsfunktion nicht positiv ist, drittens die Gleichgewichts-Wärmeleit fähigkeit nicht negativ ist. Diese Resultate haben wichtige Konsequenzen in Bezug auf das Verhalten der Wellenausbreitung und die Eindeutigkeit der Lösungen.

Evolution of steady shock waves in polymethyl methacrylate

The observation of steady shock wave profiles plays an important role in the characterization of the dynamic response of viscoelastic solids. Here we consider the evolution of such wave profiles in polymethyl methacrylate (PMMA) in plate‐impact experiments. On the basis of some experimental observations, we determine a lower bound on the propagation distance required for the development of a steady wave for a given impact velocity. This result can then be used to estimate the minimum sample thickness required for the observation of steady shock waves in PMMA and in other polymers with similar structure.