Theoretical and numerical studies of relaxation differential approach in viscoelastic materials using generalized variables

The phenomenon of incrementalization in the time domain, for linear non-ageing viscoelastic materials undergoing mechanical deformation, is investigated. Analytical methods of solution are developed for linear viscoelastic behavior in two dimensions utilizing generalized variables and realistic material properties. This is accomplished by the use of time-dependent material property characterization through a Dirchilet series representation, thus the transformation of the viscoelastic continuum problem from the integral to a differential form is achieved. The behavior equations are derived from linear differential equations based on the discrete relaxation spectrum. This leads to incremental constitutive formulations using the finite difference integration, thus the difficulty of retaining the strain history in computer solutions is avoided. A complete general formulation of linear viscoelastic strain analysis is developed in terms of increments of generalized stresses and strains.