Bounds on the Isotropic Response of Viscoelastic Composites: From Shear to Volumetric Components
Author: Jasmin Martinez
Faculty Supervisor: Ornella Mattei
Department: Mathematics
Composites, which are mixtures of at least two distinct homogeneous materials, are ubiquitous, and it is of paramount importance to derive mathematical models able to predict their mechanical response. Specifically, given the mechanical response of the constituent materials and their arrangement geometry, the goal is to extrapolate the behavior of the composite as a whole, as if it behaved like a homogeneous material.
For isotropic materials, deformation and corresponding stress can be conceptualized as a combination of shear and volumetric components: shear deformations are responsible for a change of shape only, whereas volumetric deformations are responsible for a change of volume only. When the material is viscoelastic, then if either a constant shear or volumetric deformation is applied, the corresponding stress will not be constant in time but it will decrease, a phenomenon called stress relaxation.
Previous research and literature have established bounds on the shear stress of viscoelastic composites in time, by using the analytic properties of the function describing the shear response of the composite. This study aims to extend this understanding to encompass the volumetric component as well. However, determining the precise mechanical response of composite materials is often unattainable. Thus, establishing bounds, especially if tight, on the material response proves invaluable.