Geometric nonlinear elastic and thermoelastostatic analysis of the nylon springs with negative thermal expansion

Abstract

For geometric nonlinear elastic and thermoelastostatic analysis of the nylon springs (artificial muscles) with negative thermal expansion an innovative geometrically nonlinear nylon spring finite element is established. This straight two-noded finite element is based on the Updated Lagrange Formulation (ULF) at finite displacements. The stiffness matrix of the spring finite element containing a linear and nonlinear part is established without any linearization. The required and measured initial parameters of the nylon spring finite element are its length, the linear spring constant, and the compressive prestress force. The additionally measured negative thermal spring expansion coefficient is included into the thermomechanical load. Numerical experiments using the herein proposed algorithm are performed based on nonlinear elastic and thermoelastic analysis of the Nylon Twisted Coiled Spring (NTCS) which is also known as an artificial muscle. Additionally, a geometrically nonlinear elastostatic analysis of the passive nylon damper is performed. The established nonlinear finite element equations of the nylon spring systems are solved using Newton's incremental method. Selected numerical results are verified experimentally using a physical model of the nylon spring system. These measurements indicate perfect accuracy of the proposed numerical approach, and it turns out that large extension of the nylon spring can only be captured by nonlinear calculations. This innovative procedure can be used in modelling and dimensioning of artificial muscles, special thermoelastic actuators as well as in the design of flexible storage of small stationary or mobile systems.