A novel model of rubber elasticity—the extended tube-model—is introduced. The model considers the topological constraints as well as the limited chain extensibility of network chains in filled rubbers. It is supplied by a formulation suitable for an implementation into a finite element code. Homogeneous states of deformation are evaluated analytically to yield expressions required e.g., for parameter identification algorithms. Finally, large scale finite element computations compare the extended tube-model with experimental investigations and with the phenomenological strain energy function of the Yeoh-model. The extended tube-model can be considered as an interesting approach introducing physical considerations on the molecular scale into the formulation of the strain energy function which is on the other hand the starting point for the numerical realization on the structural level. Thus, the gap between physics and numerics is bridged. Nevertheless, this study reveals the importance of a proper parameter identification and adapted experiments.
Purely elastic material models have a limited validity. Generally, a certain amount of energy absorbing behaviour can be observed experimentally for nearly any material. A large class of dissipative materials is described by a time-and frequency-dependent viscoelastic constitutive model. Typical representatives of this type are polymeric rubber materials. A linear viscoelastic approach at small and large strains is described in detail and this makes a very efficient numerical formulation possible. The underlying constitutive structure is the generalized Maxwell-element. The derivation of the numerical model is given. It will be shown that the developed isotropic algorithmic material tensor is even valid for the current configuration in the case of large strains. Aspects of evaluating experimental investigations as well as parameter identification are considered. Finally, finite element simulations of time-dependent deformations of rubber structures using mixed elements are presented.
El proceso de fractura del concreto se describe mediante el criterio de fallo de William -Warnke y el modelo material de Microplanos, los cuales han sido formulados en el método de los elementos finitos, considerando deformaciones infinitesimales y cargas estáticas.Se simuló el ensayo estandarizado de compresión de cilindros de concreto con 20% de participación volumétrica del agregado, considerando agregado grueso de arenisca o de caliza blanda, y 20 distribuciones granulométricas aleatorias.Como resultado se obtuvo la evolución de la fractura del mortero y el agregado, y la respuesta mecánica del concreto. Lo anterior permitió: identificar la inclinación de la fisura a escala macroscópica, observar las zonas de compresión triaxial y los conos de corte, y definir una ecuación del módulo de elasticidad del concreto en función de los respectivos módulos de sus componentes.Palabras clave: Método de los elementos finitos, comportamiento mecánico del concreto, mecánica de la fractura, modelos mesoscópicos, criterio de williamwarnke, modelo de microplanos.
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