The Polar-corotational Constitutive Characterization Of Filled Rubbers At Large Deformation:Theoretical And Numerical Aspects

Due to the special physical and mechanical behavior,filled rubbers are widely ap-plied in industry and private life,the constitutive characterization and numerical imple-mentation of the hypoelasticity coupled with viscoelasticity,elastoplasticity and isotropic damage presented by filled rubbers have received more and more attention of many re-searchers in materials and mechanics.Similar to the strategy used in the constitutive char-acterization conducted by Lin and schomburg on the basis of the experimental obser-vations and the phenomenological model shown in the articles of Lion and Miehe and Keck,the thesis presents,in the polar corotational frame,a new elastic-viscoelastic-elastoplastic material law coupled with isotropic Mullins damage for filled rubbers,and provides the relevant numerical algorithms and finite element program.These theoreti-cal and numerical products will provide a basis for the design and application of rubber components.The following aspects haven been conducted in the work:? On the basis of the phenomenological model consisting of the parallel-connected elastic,viscoelastic and elastoplastic branches coupled with isotropic damage,a constitutive setting suitable for filled rubbers at infinitesimal deformation is de-rived.? By virtue of the work-conjugate pair described in the polar corotational frame,the Clausius-Planck inequality describing the internal dissipation in inelastic deforma-tion and damage are derived.On the basis of these inequalities,the convex property of the potential functions for inelastic flows and the theory of maximum dissipa?tion,the evolution equations described in the polar corotational frame for inelastic strains and isotropic damage are constructed.Therefore,the current constitutive setting is consistent with the second law of thermodynamics.? The algorithms for updating stress and computing the consistent tangent moduli are derived.The corresponding finite element subroutine is coded and integrated in the general finite element program ABAQUS.? The subroutine is used to simulate the uniaxial cyclic tension test of a rubber block and the uniaxial tension test of a rubber strip with hole conducted by Miehe and Keck ,the obtained numerical results agree well with the experimental observa-tions,this conclusion proves that the current constitutive law and the numerical algorithms are effective for filled rubbers.? The current constitutive law is systematically compared with the material law pre-sented in Lin and Schomburg by using them to predict the stress responses of rubber parts in several representative deformation processes.The results show that the predictions of both laws are the same for the uniaxial tension of rubber block.For the simple shear with large rotation,there exist differences between their corre-sponding stresses of the viscoelastic and elastoplastic branches,but for the simple shear with small rotation,both laws can present the identical stress responses for the viscoelastic and elastoplastic branches.Because the stresses of the inelastic branches are far smaller than the stress of the elastic branch,the differences be-tween the corresponding stress components of the inelastic branches presented by both laws cannot lead to a clear difference in the total stresses of both cases.But,the stresses of the inelastic branches are the key factor causing the stress hysteresis phenomenon in cyclic deformation processes.The novel aspects of the thesis are presented by the last four points above.The consti-tutive law,algorithms and finite element subroutine will be conducive to the design and application of filled rubber components.