Probabilistic Modeling of Hysteretic Behavior of Elastomers Under 3-D Cyclic Loading

Existing methods to analyze the hysteretic behavior of elasto mers are primarily based on a deterministic point of view, ignoring scatter of material properties. To overcome this limitation, a probabilistic model is proposed to describe random hysteretic energy loss of viscoelastic materials under two- or three-dimensional (2- or 3-D) cyclic loading. The model takes into consideration the random nature of material properties along with a signi ficant nonlinearity of deformation. Simple analytical solutions to predict major statistical characteristics of random energy loss (mean values, standard deviations) are offered. A generalization of the 3-D model is proposed, where cyclic functions of loading may be different in different directions. A problem of experimental characterization of random material properties is systematically considered on examples of two representative elastomers.