Nonlinear Finite Element Analysis for Elastomeric Materials under Finite Strain (original) (raw)
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Computer Methods in Applied Mechanics and Engineering, 1984
Finite element models for elasto-plastic incremental analysis are derived from a three-field variational principle. The Newton-Raphson method is applied to solve the nonlinear system of equations which is obtained from the stationarity condition of this principle. The iterative schemes are discussed in detail for pure displacement and for pure equilibrium models from which iterative schemes for hybrid models folfow directly. In the displacement model, the compatibility of the strains and the plasticity criterium are satisfied during the whole iterative process, while the equilibrium of the stresses is restored only in the mean after convergence. In the equilibrium model, the plasticity criterium and the compatibility of the strains are verified in the mean during the iterative process; when convergence is achieved, the stresses are locally in equilibrium with the applied external loads. In both cases, a tangential stiffness matrix can be constructed, even for perfectly plastic materials and it allowsone to obtain always very good convergence properties. Examples are shown for plane stress and axisymmetric cases.
Computer Methods in Applied Mechanics and Engineering, 1977
The paper discusses numerical solution techniques of problems in continuum mechanics in the presence of finite elastic as well as plastic strain components. The paper is based on the natural finite element formulation of large deformations. The proposed model requires the determination of an intermediate (stress-free) configuration at each step of the loading process. Certain approximations are adopted and comparisons are made to assess the difference between the natural approach with an intermediate reference configuration and conventional models for large displacements and small strains. Some numerical illustrations are given.
Finite element formulation for modeling nonlinear viscoelastic elastomers
Computer Methods in Applied Mechanics and Engineering, 2008
Nonlinear viscoelastic response of reinforced elastomers is modeled using a three-dimensional mixed finite element method with a nonlocal pressure field. A general second-order unconditionally stable exponential integrator based on a diagonal Padé approximation is developed and the Bergström-Boyce nonlinear viscoelastic law is employed as a prototype model. An implicit finite element scheme with consistent linearization is used and the novel integrator is successfully implemented. Finally, several viscoelastic examples, including a study of the unit cell for a solid propellant, are solved to demonstrate the computational algorithm and relevant underlying physics.
A remark on the application of the Newton-Raphson method in non-linear finite element analysis
Computational Mechanics, 2005
Usually the notion ''Newton-Raphson method'' is used in the context of non-linear finite element analysis based on quasi-static problems in solid mechanics. It is pointed out that this is only true in the case of non-linear elasticity. In the case of constitutive equations of evolutionary-type, like in viscoelasticity, viscoplasticity or elastoplasticity, the ''Multilevel-Newton algorithm'' is usually applied yielding the notions of global and local level (iteration), as well as the consistent tangent operator. In this paper, we investigate the effects of a consistent application of the classical Newton-Raphson method in connection with the finite element method, and compare it with the classical Multilevel-Newton algorithm. Furthermore, an improved version of the Multilevel-Newton method is applied.
Communications in Numerical Methods in Engineering, 2001
This paper presents an objective formulation for the anisotropic elastic–plastic problems at large strain plasticity. The constitutive equations are written in a rotating frame. The multiplicative decomposition of the deformation gradient is adopted and the formulation is hyperelastic based. Since no stress rates are present and the incremental constitutive law was formulated in a rotating frame, the formulation is numerically objective in the time integration. Explicit algorithm was proposed and has been optimized with regard to stability and accuracy. The incremental law was integrated in fast Lagrangian analysis of continua (FLAC) method to model anisotropic elastic–plastic problems at finite strain. Structural tests are carried out for isotropic and orthotropic materials. Copyright © 2001 John Wiley & Sons, Ltd.
Computational modelling of elastomeric materials to fit experimental data
Computational Methods and Experimental Measurements XVII, 2015
The mitigation of the vibrations of components and structures, through the use of rubber mounts, is a common practice in many industries, such as in automotives and aeronautics or energy. It is a very important issue, because it is a key factor not just for the fatigue life but also for matters of comfort. On the other side, these industries make extensive use of finite element models to predict the dynamic behaviour of structures. Therefore, it means that the non-linear constitutive equations of rubber mount devices need to be properly integrated into the global analytical model. The quasi-static and dynamic behaviour of these devices can be quite complex, because they are usually done by a steel cover with an elastomer inside. Experimental test campaigns are usually carried forward to characterize the quasi-static and dynamic behaviour in terms of dynamic stiffness and loss factor. The experiments are designed to determine dependency on the frequency, the dynamic amplitude, the temperature and the preload. In this paper an optimization methodology, combining hyper-elasticity, viscoelasticity and elasto-plasticity constitutive equations will be presented to obtain representative elastomeric behaviour, able to fit the experimental data in hand and to predict the rubber mount behaviour in load conditions different from those tested. The numerical results obtained are in very good agreement with the experimental data.
An Isoparametric Finite Element Model for Large-Strain Elastostatics
Journal of Research of the National Bureau of Standards, 1981
This paper describes a simple finite element model for large-strain elastostatics. The realization of the model in a small-scale computer-code is described. The purpose of the model is to produce test problems for research on the application of penalty techniques in nonlinear elasticity. For this reason the code must balance the requirements of reasonable flexibility with those of computational economy. The current code employs multilinear isoparametric elements. The model is capable of generalization to a variety of element types. The solution method employed is that of incremental loading combined with the Newton-Raphson method. Symmetric, banded systems of equations are produced which are solved in-core. Two-and three-dimensional symmetric bodies which are isoparametric images of a reference "brick" may be modeled. An example comparing two-and three-dimensional models of a "dogbone"-shaped A.S.T.M. rubber tensile-test specimen is presented. The results shed some light on the nature of stress-concentrations which occur in specimens of this geometry.
Nonlinear Visco-Hyperelastic Constitutive Modeling for Filled Elastomeric Materials
2013
The mechanical behavior of filled elastomeric materials (rubber or rubber-like materials) is known to be incompressible, or nearly-incompressible, hyperelastic and time-dependent, or viscoelastic. This complex behavior of rubbery materials needs more understanding, and a good knowledge is required for such behavior in order to attain a constitutive modeling for better design of a rubber component for a specific application. To achieve this objective, theoretical and experimental works are presented in this paper. Theoretical works are considered for modeling the hyperelastic and viscoelastic behaviors of rubber. The hyperelastic behavior is modeled using Mooney-Rivlin constitutive model. While the time-dependent behavior (viscoelasticity) was modeled by using Prony series. Modeling and parameters identification, for both hyperelastic and viscoelastic behaviors, were performed and compared with ANSYS 14. To do this, different tests were performed on filled rubber in the present work,...
The present study is devoted to the problem of optimal loading pressure identification by the prescribed displacements vector. The mathematical model of large elastocreep deformations is used. The problem of deformation of the material in the vicinity of microdefect was considered. Integrodifferential equations for the external pressure, irreversible deformations and displacements were derived. The optimization algorithm for this problem was proposed. The optimal strainstress state parameters were computed and analyzed.