On the explicit dynamics implementation and validation of partitioned rate-type constitutive relation for dampers

Abstract

We propose a simple 3D nonlinear rate-type constitutive relation with just three parameters for elastomeric dampers capable of emulating double-shear data in frequency and strain sweep mode. The nonlinear relation derived using two scalar functions, namely Helmholtz free energy and the rate of dissipation function [1], result in a partitioned constitutive relation: Cauchy stress tensor is described in terms of the left Cauchy-Green stretch tensor and a tensor describing instantaneous elastic response, and the evolution equation for the instantaneous elastic response is derived by maximizing the rate of dissipation function. A compressible version of this model is implemented in Abaqus® The constitutive relation and the implementation are validated by comparing with known semi-inverse solutions obtained by specializing rate-type relation to special deformations. Material parameters are obtained for dampers made of synthetic and natural rubber by fitting the predictions of the model with that of double shear data. By using the same parameters, three dimensional simulations of a cylindrical damper subjected to sinusoidal force akin to that of an unbalanced machinery predict different hysteresis curves in compression/tension and shear. To that end, we show that the non-linear 3 parameter model is one of the simple models that can be formulated within the thermodynamic framework which can predict the inherent non-linearity of the damper operating under combined harmonic loading situations. A robust implementation (VUMAT) of the developed model is included with the article. We believe that this can aid engineers in tailoring dampers for its controlled dissipation across multiple modes of deformation as well as academicians in adding more value by building and implementing sophisticated models within this framework.