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Loehnert S.,Institute of Continuum Mechanics
Computational Mechanics

In this contribution a simple, robust and efficient stabilization technique for extended finite element (XFEM) simulations is presented. It is useful for arbitrary crack geometries in two or three dimensions that may lead to very bad condition numbers of the global stiffness matrix or even ill-conditioning of the equation system. The method is based on an eigenvalue decomposition of the element stiffness matrix of elements that only possess enriched nodes. Physically meaningful zero eigenmodes as well as enrichment scheme dependent numerically reasonable zero eigenmodes are filtered out. The remaining subspace is stabilized depending on the magnitude of the respective eigenvalues. One of the main advantages is the fact that neither the equation solvers need to be changed nor the solution method is restricted. The efficiency and robustness of the method is demonstrated in numerous examples for 2D and 3D fracture mechanics. © 2014 Springer-Verlag Berlin Heidelberg. Source

Harish A.B.,Institute of Continuum Mechanics | Wriggers P.,Institute of Continuum Mechanics | Jungk J.,Continental Reifen Deutschland GmbH | Hojdis N.,Continental Reifen Deutschland GmbH | Recker C.,Continental Reifen Deutschland GmbH
Computational Mechanics

Elastomers are exceptional materials owing to their ability to undergo large deformations before failure. However, due to their very low stiffness, they are not always suitable for industrial applications. Addition of filler particles provides reinforcing effects and thus enhances the material properties that render them more versatile for applications like tyres etc. However, deformation behavior of filled polymers is accompanied by several nonlinear effects like Mullins and Payne effect. To this day, the physical and chemical changes resulting in such nonlinear effect remain an active area of research. In this work, we develop a heterogeneous (or multiphase) constitutive model at the mesoscale explicitly considering filler particle aggregates, elastomeric matrix and their mechanical interaction through an approximate interface layer. The developed constitutive model is used to demonstrate cluster breakage, also, as one of the possible sources for Mullins effect observed in non-crystallizing filled elastomers. © 2016 Springer-Verlag Berlin Heidelberg Source

Avci B.,Institute of Continuum Mechanics | Wriggers P.,Institute of Continuum Mechanics
Computational Methods in Applied Sciences

Multiphase flows consisting of a continuous fluid phase and a dispersed phase of macroscopic particles are present in many engineering applications. In general, a main task in the study of the particle-laden fluid flow of an application is to make predictions about the system's nature for various boundary conditions, since, depending on the volume fraction and mass concentration of the dispersed phase a fluid-particle system shows quite different flow properties. Unfortunately, often it is impossible to investigate such a system experimentally in detail or even at all. An option to capture and to predict its properties is performing a direct numerical simulation of the particulate fluid. For this purpose, a model approach based on a fictitious domain method is proposed in this contribution. Here, the fluid and the particle phase are treated, respectively, within the framework of the finite element method and the discrete element method. The coupling scheme, which accounts for the phase interaction, is realized at the particle scale. For the computation of the forces that the fluid exerts on a particle an approach is used in which they are determined directly from the flow field in the vicinity of its surface. © 2014 Springer International Publishing Switzerland. Source

Wellmann C.,Institute of Continuum Mechanics | Wriggers P.,Institute of Continuum Mechanics
Computational Methods in Applied Sciences

Within this contribution the mechanical behavior of dry frictional granular material is modeled by a three-dimensional discrete element method (DEM). The DEM uses a superquadric particle geometry which allows to vary the elongation and angularity of the particles and therefore enables a better representation of real grain shapes compared to standard spherical particles. To reduce computation times an efficient parallelization scheme is developed which is based on the Verlet list concept and the sorting of particles according to their spatial position. The macroscopic mechanical behavior of the particle model is analyzed through standard triaxial tests of periodic cubical samples. A technique to accurately apply stress boundary conditions is presented in detail. Finally, the triaxial tests are used to analyze the influence of the sample size and the particle shape on the resulting stress-strain behavior. © Springer Science+Business Media B.V. 2011. Source

Loehnert S.,Institute of Continuum Mechanics | Prange C.,Institute of Continuum Mechanics | Wriggers P.,Institute of Continuum Mechanics
International Journal of Fracture

The accurate and efficient prediction of the interaction of microcracks with macrocracks has been a challenge for many years. In this paper a discretization error controlled adaptive multiscale technique for the accurate simulation of microstructural effects within a macroscopic component is presented. The simulation of cracks is achieved using the corrected XFEM. The error estimation procedure is based on the well known Zienkiewicz and Zhu method extended to the XFEM for cracks such that physically meaningful stress irregularities and non-smoothnesses are accurately reflected. The incorporation of microstructural features such as microcracks is achieved by means of the multiscale projection method. In this context an error controlled adaptive mesh refinement is performed on the fine scale where microstructural effects may lead to highly complex mechanical behavior. The presented method is applied to a few examples showing its validity and applicability to arbitrary problems within fracture mechanics. © 2012 Springer Science+Business Media Dordrecht. Source

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