Comparison of discontinuous damage models of Mullins-type

The Mullins effect is a characteristic property of filled rubber materials whose accurate and efficient modelling is still a challenging task. Innumerable constitutive models for elastomers are described in the literature. Therefore, this contribution gives a review on some widely used approaches, presents a classification, proves their thermodynamic consistency, and discusses reasonable modifications. To reduce the wide range of models, the choice is restricted to those which reproduce the idealised, discontinuous Mullins effect. Apart from the theoretical considerations, two compounds were produced and tested under cyclic uniaxial and equibiaxial tension as well as pure shear. Based on this experimental data, a benchmark that compares the fitting quality of the discussed models is compiled and favourable approaches are identified. The results are a sound basis for establishing novel or improving existing rubber models

Numerical explorations of solvent borne adhesives: A lattice-based approach to morphology formation

The internal structure of adhesive tapes determines the effective mechanical properties. This holds true especially for blended systems, here consisting of acrylate and rubber phases. In this note, we propose a lattice-based model to study numerically the formation of internal morphologies within a four-component mixture (of discrete particles) where the solvent components evaporate. Mimicking numerically the interaction between rubber, acrylate, and two different types of solvents, relevant for the technology of adhesive tapes, we aim to obtain realistic distributions of rubber ball-shaped morphologies -- they play a key role in the overall functionality of those special adhesives. Our model incorporates the evaporation of both solvents and allows for tuning the strength of two essentially different solvent-solute interactions and of the temperature of the system.Comment: 8 page

Multi-Mechanism Models - Theory and Applications

Multi-mechanism models (MM models) are used studying various materials and mechanical effects. In this work, a general concept of modeling with MM models of serial type is introduced within the framework of continuum mechanics. Contrary to many authors, the thermoelastic strain is not regarded as a special separated strain. The modular principle of MM models is illustrated by several basic, advanced and generalized mechanisms and MM models. We specify the modeling of linear viscoelasticity with MM models and apply the concept of MM models to the phenomena of transformation-induced plasticity. In the case of viscoelasticity, we present the 3d mathematical problems of a thermoelastic-(N)-coupled-Kelvin-Voigt-element model and an isothermal-(N)-coupled-Kelvin-Voigt-element model. The latter model is mathematically analyzed according to its weak solvability as a mixed boundary value problem by transforming the original problem into an equivalent system of integro-differential equations. Therefore, the presented approach of proving an existence and uniqueness result is nonstandard. In case of a 1d rod, the modeling and the mathematical treatment are provided related to the isothermal-(2)-coupled-Kelvin-Voigt-element model. We conduct numerical simulations of the isothermal-(2)-coupled-Kelvin-Voigt-element model for 3d and 1d situations. The results underline the quality of the introduced viscoelastic model covering material effects like ratcheting without predicting instantaneous elasticity. The phenomena of transformation-induced plasticity can occur for materials which undergo phase transformations when moderate stresses are applied. A detailed test evaluation for experiments characterizing the interaction of classic plasticity and transformation-induced plasticity of the steel 100Cr6 (SAE 52100) is presented. A MM model considering the interaction of classic plasticity and transformation-induced plasticity is verified by these experiments. Therefore, we develop numerical schemes of the model suited for uniaxial situations and perform systematical parameter identifications for some selected experiments

Mehrmechanismen-Modelle - Theorie und Anwendungen

Multi-mechanism models (MM models) are used studying various materials and mechanical effects. In this work, a general concept of modeling with MM models of serial type is introduced within the framework of continuum mechanics. Contrary to many authors, the thermoelastic strain is not regarded as a special separated strain. The modular principle of MM models is illustrated by several basic, advanced and generalized mechanisms and MM models. We specify the modeling of linear viscoelasticity with MM models and apply the concept of MM models to the phenomena of transformation-induced plasticity. In the case of viscoelasticity, we present the 3d mathematical problems of a thermoelastic-(N)-coupled-Kelvin-Voigt-element model and an isothermal-(N)-coupled-Kelvin-Voigt-element model. The latter model is mathematically analyzed according to its weak solvability as a mixed boundary value problem by transforming the original problem into an equivalent system of integro-differential equations. Therefore, the presented approach of proving an existence and uniqueness result is nonstandard. In case of a 1d rod, the modeling and the mathematical treatment are provided related to the isothermal-(2)-coupled-Kelvin-Voigt-element model. We conduct numerical simulations of the isothermal-(2)-coupled-Kelvin-Voigt-element model for 3d and 1d situations. The results underline the quality of the introduced viscoelastic model covering material effects like ratcheting without predicting instantaneous elasticity. The phenomena of transformation-induced plasticity can occur for materials which undergo phase transformations when moderate stresses are applied. A detailed test evaluation for experiments characterizing the interaction of classic plasticity and transformation-induced plasticity of the steel 100Cr6 (SAE 52100) is presented. A MM model considering the interaction of classic plasticity and transformation-induced plasticity is verified by these experiments. Therefore, we develop numerical schemes of the model suited for uniaxial situations and perform systematical parameter identifications for some selected experiments

Crack path comparisons of a mixed phase‐field fracture model and experiments in punctured EPDM strips

Working on quasi-static phase-field fracture modeling in nearly incompressible solids for crack propagation is a challenging task. To avoid arising locking effects therein, a mixed form for the solid displacement equation is developed, resulting in two unknowns: a displacement field and a hydro-static pressure variable. In order to fulfil an inf-sup condition, stable Taylor-Hood elements are employed for the displacement-pressure system. The irreversibility condition of the crack evolution is handled by help of a primal-dual active set method. To get both a sharper crack and reasonable computational costs, adaptive meshes are used based on a predictor-corrector scheme. The crack paths from the numerical simulations are compared on the experimentally observed crack paths in carbon black filled ethylene propylene diene monomer (EPDM) rubber strips. The punctured EPDM strips with a hole and a given notch at different heights are stretched till total failure