Dynamics of structures

https://hal.archives-ouvertes.fr/hal-00773015/document

A review on the Mullins effect

https://www.giref.ulaval.ca/~deteix/bois/documents_references/article4.pdf

A theory of finite viscoelasticity and numerical aspects

The review describes recent research about reinforcement in elastomers where the main intention is to gain insight into the relationship between disordered filler structure on different length scales and reinforcement and to microscopic mechanisms of strain enhancement. Several theoretical concepts will be discussed together with very recent experimental findings related to hydrodynamic reinforcement, rigid filler aggregates with fractal structure and polymer adsorption on heterogeneous filler surfaces. Based on the new concepts, we present several recent efforts to understand typical effects in filled rubbers that have an extraordinary practical importance (for example, stress softening of carbon black filled rubbers during repeated large strain stretching and during small strain dynamic excitations).

Reinforcement of Elastomers

Damping studies in fiber-reinforced composites : a review

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.

/pdf/formulation-and-implementation-of-three-dimensional-1r8zlwi2bh.pdf

Formulation and implementation of three-dimensional viscoelasticity at small and finite strains

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...

An extended tube-model for rubber elasticity : Statistical-mechanical theory and finite element implementation

A formulation of elasticity and viscoelasticity for fibre reinforced material at small and finite strains

Theoretical and numerical formulation of a molecular based constitutive tube-model of rubber elasticity

Phase-field crack approximation relies on the proper definition of the crack driving strain energy density to govern the crack evolution and a realistic model for the modified stresses on the crack surface. A novel approach, the directional split, is introduced, analyzed and compared to the two commonly used formulations, which are the spectral split and the volumetric---deviatoric split. The directional split is based on the decomposition of the stress tensor with respect to the crack orientation, specified by a local crack coordinate system, into crack driving and persistent components. Accordingly, a modified stress strain relation is proposed to model fundamental crack characteristics properly, and a thermodynamically consistent crack driving strain energy density is postulated. The split is applied to numerical examples of initially cracked specimens and compared to results obtained by the two standard approaches.

Michael Kaliske

Papers

Formulation and implementation of three-dimensional viscoelasticity at small and finite strains

An extended tube-model for rubber elasticity : Statistical-mechanical theory and finite element implementation

A formulation of elasticity and viscoelasticity for fibre reinforced material at small and finite strains

Theoretical and numerical formulation of a molecular based constitutive tube-model of rubber elasticity

A phase-field crack model based on directional stress decomposition