This paper is concerned with a possible material instability arising from a non-unique dependence of stress on deformation and leading to localization of stress in otherwise homogeneous deformations. A recently published work cites several constitutive theories and certain experimental evidence indicating this type of constitutive behavior, and it provides an analysis of quasi-static bifurcation of in the steady exten-sional deformation of certain idealized isotropic elastic solids and viscoelastic fluids. The principle objective is to raise the question as to whether the ubiquitous "force chains" observed in experiments and computer simulation of non-cohesive granular media represent stress localization. As a prelude to a more complete investigation, consideration is given to the question of the statistical distribution of contact forces in sphere assemblies. The maximum-entropy estimator of statistical thermodynamics is employed to derive the statistical distribution of contact forces in a static assembly of nearly-rigid grains. However, instead of the usual constraint of stationary energy, stationarity of stress is assumed. It is shown that under fairly general circumstances one obtains a distribution with exponential tail in contact-force magnitude, which is found in various experiments and numerical simulations. This result is exact for frictionless monodispcrse sphere assemblies subject to isotropic confinement. According to the present model, the exponential tail does not depend on special models of "force propagation" in granular assemblies, of the type postulated in the contemporary physics literature. According to the above principle, the precise form of the probability density for force depends on the weight (a priori probability) assigned to elementary volumes in the state-space of contact forces. Various weight functions are discussed and the resulting distributions are compared to experiment and simulation. In its present form, the analysis given here does not apply to the "two-phase" structure associated with force chains in granular media.
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