Formulation, validation, and application of a finite element model for elastomeric lag dampers

Abstract

A time-domain finite element model has been developed to model the dynamic behavior of nonlinear viscoelastic elastomers. Motivated by helicopter lag damper applications, a member in pure shear (one-dimension) is analyzed. The current approach is based on the method of Anelastic Displacement Fields (ADF). This approach extends the linear ADF approach to model the strain-dependent behavior characteristic of elastomeric materials. Material nonlinearities are introduced via nonlinear functions that describe the dependence of the unrelaxed and relaxed material moduli, and the anelastic strain rate on the instantaneous total and anelastic strains. The parameters that characterize the nonlinear material behavior are identified through harmonic strain controlled experimental tests. Experimental stress data for only two strain amplitudes (10% and 100%, zero static offset) are used to determine the ADF model parameters. The modeling approach is validated against linearized complex moduli data and stress-strain hysteresis loops at various strain amplitudes and static strain offsets. The new ADF method is used to model two elastomeric systems, a silicon based high-damping elastomer, and a black rubber low-damping, high-stiffness elastomer. Nonlinear finite element equations are obtained in terms of the resulting ADF parameters. The potential of the subject technique is explored through a two element two material elastomeric snubber-damper model. The combined snubber-damper finite element equations are integrated in the time-domain and a limit cycle scenario, in the presence of an inherent initial instability is demonstrated.