CONSTITUTIVE-OPERATOR SMOOTHING BY CONDENSATION

An existing condensation model reduction theory is modified so as to p erform degree-of-freedom elimination on the constitutive operators of semi-discrete system models while retaining system-response-prediction fidelity in those degrees-of-freedom that remain. For the important s pecial case for which this process corresponds to homogenizing/smoothi ng of the constitutive behavior of deterministic, heterogeneous media, such as composites, the spatially-discrete version of the macroscale constitutive operator is fully and directly calculated from the given, spatially discrete microscale-constitutive and material-independent o perators, the composition of which forms the spatially discrete system operator. (In this paper, ''micro'' is taken to mean the scale of the heterogeneity, such as the inclusion-matrix scale of a composite comp onent, and ''macro'' is taken to mean a scale which is globally small but large compared to the heterogeneity, such as the local-structural- response scale of a composite component. Some refer to this definition of microscale as the mesoscale.) The form of structural-scale composi te constitutive operators, as well as their content, are hence amenabl e to systematic deduction in this semi-discrete setting. (Linear-elast ic and viscoelastic forms are examples of stress-strain constitutive o perator forms for solids.) This contrasts with current ''guess the for m and fit its parameters'' techniques. In fact, it is shown that the s emi-discrete kernel of a wide class of nonlocal macroscale constitutiv e operators can be computed directly. The condensation method of this paper is applicable to nonlinear constitutive relations as well as lin ear ones, at least to an extent comparable to the condensation model r eduction theory from which it originated. As both a demonstration and a validation check, the method is applied to the computation of the ma croscale stress-displacement operator for both a periodic and a nonper iodic linear elastic laminate.