Viscoelastic material response with a fractional-derivative constitutive model

Abstract

A rubber coupon is modeled as a viscoelastic material by a fractional-derivative constitutive law to capture the material behavior over a broad frequency range. The coupon, of finite length, is clamped at one end and subject to either a forced loading or a deflection at the other end. The physical response profile of the material for this distributed model is examined in terms of a relaxation response, associated with a branch-cut integration, and a modal response.