A material model is presented, which describes the material behavior of rubbery materials in the case of uniaxial tension/compression. It includes the characteristic nonlinearity of rubber at large strains as well as strain induced softening called Mullins effect. The generalization to arbitrary deformations is done with the concept of representative directions, published by Freund & Ihlemann [2] utilizing a numerical integration on a unit sphere. An FE simulation of a chassis bushing shows that the Mullins effect is reproduced appropriately, verifying the preceding material characterization. Uniaxial modeling of rubber behaviorRubbers are characterized by a variety of more or less sharply described effects. The present phenomenological model aims to cover the most relevant effects such as high nonlinearity, strain induced softening and time-dependent behavior. A parent model of this visco-elastoplastic version has been described earlier by Freund et al. [1]. The scalar-valued implementation serves for uniaxial stress-strain-states only. It has an additive structure of three 1st PK stress contributions:The hyperelastic part T he results from the non-affine tube model with non-Gaussian extension, the elastoplastic part T ep from a generalized Prandtl element (microplasticity) of Rabkin et al.[3] and the viscoelastic part T ve from a generalized Maxwell element. In the present work the viscoelastic part is deactivated resulting in a 9-parameter model covering time-independent rubber behavior. The theory of a strain amplification factor is applied (Mullins & Tobin [4]), which decreases with increasing prestrain controlled by a two-parameter formulation and hereby causes strain induced softening. The generalization of the model for simulation of arbitrary spatial deformation processes is done applying the concept of representative directions proposed by Freund & Ihlemann [2]. The concept utilizes the evaluation of the uniaxial material model in several equally distributed directions and numerical integration in order to obtain a tensorial model for FE simulations. Adaption of the generalized material lawThe model is adapted to data on rubber buffers under tension/compression (Fig.1). The force-deflection data of these buffers are converted into stress-strain data applying the effective length and cross section of the specimen, which are the result of a preceding optimization process. The data are fitted well in a range of -50% to 100% engineering strain.
In this contribution a new measurement strategy is presented, which enables in combination with an optimized specimen-setup the investigation of strains up to a compression level of −70%. The specimen-setup itself consists of a slender dumbbell structure and a mounting geometry. The main idea of the new measurement strategy is, that for almost incompressible materials the average strain in the symmetry plane can be derived from the tangential strain at the surface. For this, the new measurement strategy is derived, simulated and experimentally tested. Finally, phenomenological characteristics of rubber, like Payne effect, Mullins effect, permanent set, relaxation and creep can be investigated at such extreme compression levels.This is an open access article under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs Licence 4.0, which permits use and distribution in any medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made.
The present paper introduces a material model following the Prandtl‐Reuss theory of time‐independent elasto‐plasticity. Applying a hypo‐elastic relation a material model for uniaxial tension/compression is derived which is completely based on scalar kinematics. Combined isotropic and kinematic hardening is provided in terms of nonlinear formulations showing saturation. The proof of thermodynamic consistency is supplied. Further, the model is generalized by the concept of representative directions and implemented for finite element application, so that arbitrary spatial deformation processes can be simulated. Especially, the elastic response of the model is investigated. Comparative simulations give evidence that spurious phenomena such as shear oscillation and numerically induced ratcheting are absent for the presented generalized material model. Distinct distortional hardening is obtained after generalization describing metal plasticity adequately. Finally the model is extended to show tension/compression anisotropy.
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