Implementation of the Maxwell, Kelvin-Voigt, Boltzmann and Zener rheological models for numerical description of the viscoelastic creep behavior based on the Positional Finite Element Method

Juliano dos Santos Becho¹; Felício Bruzzi Barros¹; Marcelo Greco¹

¹ Federal University of Minas Gerais

doi:10.20906/CPS/CILAMCE2017-0047

Resumo

The present paper presents the formulations and computational implementations of four different rheological models for the numerical description of the viscoelastic creep behavior. The formulations developments are based on the Positional Finite Element Method, developed for analysis of truss elements. This method considers the nodal positions of a structure as variables of the problem, regarding a fixed coordinate system in the space in order to describe the kinematics of the finite elements (i. e. a total Lagrangian description). The stress-strain relations required in the formulations are obtained through rheological models, physically described by springs and dashpots associations. These relations, called rheological relations, take into account the time variable and are used to describe the viscoelastic behavior of the elements. The different formulations developed using the rheological relations for the Maxwell, Kelvin-Voigt, Boltzmann and Zener models are then presented and implemented numerically. As an example, a bar under traction is analyzed using the implementations developed with each model. The responses obtained for deformation along time under constant stress (creep phenomena) are compared among themselves and regarding the respective behaviors expected by the theory of viscoelasticity. The results confirm the capacity of the Positional Finite Element Method to describe different creep behaviors through the adoption of appropriate rheological relation. Furthermore, the behavior of a spatial lattice structure is simulated with the different models and the results are analyzed and discussed in light of the viscoelasticity and structure theories.

Palavras-chave: Creep; Viscoelasticity; Positional Finite Element Method; Rheological Model; Truss