Generalized Collocation Method using Stiffness Matrices in the Context of the Theory of Linear Viscoelasticity (GUSTL)

Abstract

This paper presents a methodology called GUSTL (Generalized collocation method using Stiffness matrices in the context of the Theory of Linear visco elasticity), which is designed to efficiently estimate the parameters of a Prony series representation using measured data of the complex modulus E∗ of a viscoelastic material obtained via a dynamic mechanical thermal analysis (DMA or DMTA). The methodology is based on the idea of solving aninverse problem, which is established as a physically motivated system of linear equations. The“stiffness matrix“of this problem is derived out of the interdepencies of the single elements of the Generalized–Maxwell–Elements. Further extensions of the method to the incorporation of the time–temperature–superposition (TTS) principle as well as uncertainty quantification tasks are also highlighted. The whole methodology is validated against sample data from an epoxy–coated carbon reinforcement grid for concrete structures and from a PVB–interlayer material for laminated safety glass.