Biaxial isotropic stochastic viscoelastic creep (Q1058884)

This is second part of a paper dealing with the formulation of constitutive equations for statistically isotropic multi-axial visco- elastic stochastic creep in terms of a second moment white noise field model [for part I see ibid. 19, 873-883 (1983; Zbl 0524.73041)]. Herein the biaxial linearized model is studied. After an extensive retrospective introduction recapitulating the basic concepts, the paper presents the solution to the spatial covariance structure of a stress field history which is homogeneous in the mean. Result for the corresponding strain field are also presented. It turns out to be necessary to let the spatial second moment white noise character of the strain tensor fields history for given deterministic stress tensor history be approached through a sequence of genuine covariance functions corresponding to isotropic random fields. In the limit the variances of both stress and strain become infinite. Interesting asymptotic results show up in this connection. The appendices give some useful mathematical results concerning Fourier transforms related to the Laplace operator and covariance functions of isotropic random fields.