DEM-FEM coupled numerical investigation of granular materials to increase crashworthiness of double-hull vessels

In this contribution, a novel design strategy is investigated for improving the crashworthiness of double-hull vessels, which involves usage of granular materials. For numerical simulation, a framework based on coupling of the Discrete Element and the Finite Element Method is used to study load bearing capacity of granular materials during uniaxial compression. In addition, the effect of Young's modulus of particles is also investigated with respect to the load transferability. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Random homogenization analysis in linear elasticity based on analytical bounds and estimates

In this work, random homogenization analysis of heterogeneous materials is addressed in the context of elasticity, where the randomness and correlation of components’ properties are fully considered and random effective properties together with their correlation for the two-phase heterogeneous material are then sought. Based on the analytical results of homogenization in linear elasticity, when the randomness of bulk and shear moduli, the volume fraction of each constituent material and correlation among random variables are considered simultaneously, formulas of random mean values and mean square deviations of analytical bounds and estimates are derived from Random Factor Method. Results from the Random Factor Method and the Monte-Carlo Method are compared with each other through numerical examples, and impacts of randomness and correlation of random variables on the random homogenization results are inspected by two methods. Moreover, the correlation coefficients of random effective properties are obtained by the Monte-Carlo Method. The Random Factor Method is found to deliver rapid results with comparable accuracy to the Monte-Carlo approach.     

An axisymmetrical quasi-Kirchhoff-type shell element for large plastic deformations

Summary An axisymmetrical shell element for large plastic strains is developed. The theory is based on the multiplicative decomposition of the material deformation gradient into an elastic and a plastic part. For quasi-Kirchhoff-type axisymmetric shells this leads to a product of the elastic and plastic stretches. By introduction of logarithmic strains the decomposition becomes additive. Plastic incompressibility is fulfilled in an exact manner.Support for this work was provided by the Deutsche Forschungsgemeinschaft (DFG) under contract Wr 19/7-1. The financial aid for the first and second author is gratefully acknowledged.     

Modelling thermoplastic material behaviour of dual-phase steels on a microscopic length scale - numerical treatment

On a microscopic length scale dual-phase steels exhibit a polycrystalline microstructure consisting of ferrite and martensite. In this work it is assumed that the martensitic phase behaves purely thermoelastic while for the ferritic phase a thermoplastic material model was developed based on the assumption that the driving mechanism for persistent deformation is the movement of dislocations on preferred planes in preferred directions. The necessary shear stress to move dislocations at a certain temperature and deformation rate is assumed to possess contributions from the atomic lattice, alloying atoms and the dislocation structure. To consider the influence of the dislocation structure, dislocation densities are introduced as state variables for which temperature and deformation rate dependent evolution equations are formulated. Since for general loading histories the model equations cannot be integrated analytically, a time discretized form of the model equations with an appropriate solution algorithm is presented. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A Finite Element Algorithm for Electromechanical Contact Problems

In the last hundred years a lot of work is done in describing and measuring the influence of the pressure on the resistance and wear in electrical contacts. But up to now there exists a lack of knowledge in predicting and optimizing the behavior of electrical contacts with numerical simulation tools considering the pressure dependency. The present work provides a new constitutive model for the contact interface in the case of current flow and a new friction law including electrical wear phenomena. Additionally numerical investigations are made to compare the numerical results with experimental data. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

About the Microstructural Effects of Polycrystalline Materials and their Macroscopic Representation at Finite Deformation

In the sheet bulk metal forming field, the strict geometrical requirements of the workpieces result in a need of a precise prediction of the material behaviour. The simulation of such forming processes requires a valid material model, performing well for a huge variety of different geometrical characteristics and finite deformation. Because of the crystalline nature of metals, anisotropies have to be taken into account. Macroscopically observable plastic deformation is traced back to dislocations within considered slip systems in the crystals causing plastic anisotropy on the microscopic and the macroscopic level. A finite crystal plasticity model is used to model polycrystalline materials in representative volume elements (RVEs) of the microstructure. A multiplicative decomposition of the deformation gradient into elastic and plastic parts is performed, as well as a volumetric-deviatoric split of the elastic contribution. In order to circumvent singularities stemming from the linear dependency of the slip system vectors, a viscoplastic power-law is introduced providing the evolution of the plastic slips and slip resistances. The model is validated with experimental microstructural data under deformation. The validation on the macroscopic scale is performed through the reproduction of the experimentally calculated initial yield surface. Additionally, homogenised stress-strain curves from the microstructure build the outcome for a suitable effective material model. Through optimisation techniques, effective material parameters can be determined and compared to results from real forming processes. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A finite element formulation based on the Cosserat point theory

The theory of Cosserat points is the basis of a 3D finite element formulation for large deformations in structural mechanics, that recently was presented by [1]. First investigations [2] have revealed, that this formulation is free of showing undesired locking or hourglassing-phenomena. It additionally shows excellent behaviour for any type of incompressible material, for large deformations and sensitive structures such as plates or shells. The formulation initially was restricted to a Neo-Hookean material. This work will present the extension to a general elastic Ogden material and the verification of the chosen model. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Three-dimensional modelling of discrete particles by superellipsoids

Discrete Elements are used for the simulation of granular materials (sand, ballast) as well as for molecular assemblies. Circles (2D) and spheres (3D) are often used in literature on the Discrete Element Method (DEM) however they represent a strong idealisation of the real geometry. Superellipsoids provide the opportunity to generate a wide variety of three-dimensional geometrical shapes (e.g. sphere, cube, cylinder). The motion of each particle is described by means of rigid body dynamics. Suitable numerical integration methods are necessary which are able to conserve the essential physical quantities like momentum energy etc.. Possible choices are e.g. the explicit Verlet-Leapfrog method for the translation and the explicit fourth order Runge-Kutta method for the rotation. The implemented contact formulation takes damping as well as friction into account. Efficient implementation of the contact search is the main aim of this part of the work. It is subdivided into the neighbourhood search and the local search. A bisection algorithm is used to calculate the gap between two superellipsoids within the search. For the neighbourhood search two binning algorithms were implemented and compared for several packages of particles. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Notes on a novel finite element for anisotropy at large strains

A locking phenomenon can be observed in the case of anisotropic elasticity, due to high stiffness in preferred directions. In this contribution we propose a formulation with the goal to overcome this locking problem. We apply a Simplified Kinematic for the Anisotropic part of the free-energy by means of a constant approximation of the right Cauchy-Green tensor. For the tested boundary value problem the SKA-element performs excellent and behaves extremely robust. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)