An Adaptive Finite Element Approach for Brittle Fracture

The extension of the finite element method to take discrete fracture and failure modes into account is a current field of research. In recent times, first results in terms of cohesive element formulations have been introduced into commercial applications. Such element formulations are able to cover the discrete behaviour of interfaces between different materials or the mechanical processes of thin layers. These approaches are not suitable for simulations with unknown crack paths in homogeneous materials, due to the initial elastic phase of the material formulation and the necessity to define potential crack paths a priori. The presented strategy starts with an unextended model and modifies the structure during the computations in terms of an adaptive procedure. The idea is to generate additional elements, based on the cohesive element formulation, to approximate arbitrary crack paths. For this purpose, a failure criterion is introduced. For nodes where the limiting value is reached, cohesive elements are introduced between the volume element boundaries of accordingly facets and corresponding nodes are duplicated. Necessary modifications for this application on system level as well as the element and the material formulation are introduced. By means of some numerical examples, the functionality of the presented procedure is demonstrated. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Simulation model for anisotropic fibrous materials

Paper and paper–based materials such as cardboard are used in a wide variety of applications and in the development of new applications such as boxes an accurate simulation model is of major importance. Industrially made paper material typically has an orthotropic fibrous structure, due to the manufacturing process, where the fibers tend to align in the direction of motion in the machine. In this work a plasticity–based material model allowing for finite strains is developed. The model is suitable for materials with an anisotropic fibrous structure such as paper. The general framework is based on separate mappings describing the deformations of the continuum and the substructure and a multiplicative split of these mappings into elastic and plastic parts. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Simulation and Measurements of Rolling Tire Dynamics

The simulation of rolling tires including stationary rolling, modal analysis, excitation with roughness of road surfaces and sound radiation is presented for state of the art industrial tire models. The target of this research, part of the german project “Leiser Straßenverkehr”, is the reduction of trafic noise, whereas the main source, namely the tire/road system, is investigated in contrast to other techniques like sound insulating walls. The needs and methods for the solution of the resulting large scale problems are discussed next to special properties of rotating structures, high frequency behavior of rubber material and approaches for the reduction of computational cost. For the validation of the model measurements of real tires and roads are used. These include shaker tests of the standing tire and acoustics of tires rolling on a drum. The same set–ups are applied to the simulation for the comparison of frequency response functions and sound pressure levels. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Extended multiscale FEM for design of beams and frames with complex topology

A numerical method for design of beams and frames with complex topology is proposed. The method is based on extended multi-scale finite element method where beam finite elements are used on coarse scale and continuum elements on fine scale. A procedure for calculation of multi-scale base functions, up-scaling and downscaling techniques is proposed by using a modified version of window method that is used in computational homogenization. Coarse scale finite element is embedded into a frame of a material that is representing surrounding structure in a sense of mechanical properties. Results show that this method can capture displacements, shear deformations and local stress-strain gradients with significantly reduced computational time and memory comparing to full scale continuum model. Moreover, this method includes a special hybrid finite elements for precise modelling of structural joints. Hence, the proposed method has a potential application in large scale 2D and 3D structural analysis of non-standard beams and frames where spatial interaction between structural elements is important.     

Theoretical and numerical analysis for the quasi-continuum approximation of a material particle model

In many applications materials are modeled by a large number of particles (or atoms) where any one of particles interacts with all others. Near or nearest neighbor interaction is expected to be a good simplification of the full interaction in the engineering community. In this paper we shall analyze the approximate error between the solution of the simplified problem and that of the full-interaction problem so as to answer the question mathematically for a one-dimensional model. A few numerical methods have been designed in the engineering literature for the simplified model. Recently much attention has been paid to a finite-element-like quasicontinuum (QC) method which utilizes a mixed atomistic/continuum approximation model. No numerical analysis has been done yet. In the paper we shall estimate the error of the QC method for this one-dimensional model. Possible ill-posedness of the method and its modification are discussed as well.

     

Simulation of powder metallurgical coating by radial axial ring rolling

The process integrated powder coating by radial axial rolling of rings is expected to provide a new hybrid production technique to apply different kinds of powder metallurgical functional surfaces to ring–shaped work pieces. The main advantages compared with conventional manufacturing processes in this field can be found in lower costs, shorter process cycles and larger producible work pieces. In order to meet the requirements for an industrial application of this new process it is important to proof its capability particularly with regard to reproducibility and to investigate its boundaries. A reliable process simulation will provide a deeper insight into the governing parameters and reduce the money and time consuming experimental tests. Considering a numerical simulation using the FE method two challenges can be named. First one requires a material model to describe the compaction of metal powder at different elevated temperatures. As second the simulation of the ring rolling process itself is still very time consuming. A fine spatial discretization due to large deformations in the rolling gap and contact interaction between workpiece and rollers are the most prevailing factors in this context. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Variational sensitivity analysis of physical reaction forces and application to multiscale problems

Nowadays profitability and efficiency of practical and industrial applications and therefore of material design is becoming a more important issue. Due to different well-known and established approaches for analysis and simulation of complex heterogeneous materials on multiple scales based on numerical homogenisation techniques, development and production of high performance materials (using 3d printers for example) and as a consequence optimisation and design of materials is reality. The objective is to find optimal structures with optimal material distribution under given constraints related to posed problems and tailoring applications to their special requirements. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modelling and Simulation of Curing Processes of Epoxy Resin

During the curing reaction, the adhesive changes its thermomechanical material behaviour from a viscous fluid to a viscoelastic solid. This phase transition is an exothermal chemical reaction which is accompanied by thermal expansion, chemical shrinkage and changes in temperature. In this work the numerical simulation of the curing process will be presented. The material model for the implementation is presented in [1]. For the implementation of the material model the consistent tangent operator has been derived. In the presentation, experimental data and simulation are shown. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numerical investigation of the deformation characteristics and heat generation in pneumatic aircraft tires Part II. Thermal modeling

A numerical procedure to determine the temperature rise in aircraft tires under free rolling conditions is presented in this article. Energy dissipation from cyclic inelastic deformation is considered the main heat generation source. This modeling considers the deformation process of the tire to be a steady-state problem, where all concurrent cycles are assumed to be the same as the first. The inelastic energy is determined by imposing a phase lag between the strain and the stress fields. The phase lag is assumed to be frequency independent in the range of interest, in keeping with the experimental observations in aircraft tire materials. It is further assumed that the inelastic energy is completely converted into volumetric heat input for a transient thermal conduction analysis. A conduction model is described and results are compared against thermocouple data recorded by Clark and Dodge [1].     

On the h-adaptive coupling of FE and BE for viscoplastic and elasto-plastic interface problems

This paper presents a posteriori error estimates for the symmetric finite element and boundary element coupling for a nonlinear interface problem: A bounded body with a viscoplastic or plastic material behaviour is surrounded by an elastic body. The nonlinearity is treated by the finite element method while large parts of the linear elastic body are approximated using the boundary element method. Based on the a posteriori error estimates we derive an algorithm for the adaptive mesh refinement of the boundary elements and the finite elements. Its implementation is documented and numerical examples are included.     

Numerical multiphase modeling of bubbly flows

Bubbly flows appear in a large variety of engineering applications from the petroleum to the nuclear industry. A common model used in these contexts is the so-called drift–flux model where the slip velocity (the difference between the velocities of the gas and of the liquid) is expressed on the basis of empirical correlations. However, depending on these empirical correlations, these models are not always hyperbolic and this induces severe mathematical and numerical difficulties. Using asymptotic analysis in the limit of large drag terms, we propose an Eulerian mixture model where the slip velocity is expressed under the form of a Darcy-like law. We study the mathematical properties of this model and describe a Godunov type scheme for its approximation. Some numerical relevant test-cases are presented.      

Vehicle dynamics simulations with coupled multibody and finite element models

With the advent of multibody system simulations (MSS) programs, it has become common practice to use computer modeling to evaluate vehicle dynamics performance. This approach has proved to be very effective for predicting the handling performance of vehicles; however, it has proved less successful for predicting the vehicle response at frequencies that are of interest in ride harshness and durability applications. The lack of correlation between theory and experiment can be partially traced back to tire models that are inadequate for rough road simulation. This paper presents a comprehensive vehicle dynamics model for simulating the dynamic response of ground vehicles on rough surfaces. This approach uses a MSS program to simulate the vehicle and a nonlinear FE program for the tires. Parallel processing of the tire models improves the efficiency of the overall simulation. Applications for this technology include vehicle ride and harshness analysis and durability loads simulation. This paper describes the MSS vehicle model, the tire FE model, and the interface which transfers data between the two simulations. Simulation and experiment results for a single tire without a vehicle encountering an obstacle and for a vehicle with four tires driving across a pot hole are presented. Conclusions and opportunities for further research end the paper.     

用截面变形耦合有限元法分析复合材料梁

复合材料板和梁具有优良的特性, 从而获得了广泛的应用．然而由于材料的各向异性, 使得对这类材料构件作变形和应力分析时,即使应用如有限元法的数值分析手段仍是非常复杂费时的．为此提出了一个可应用常规有限单元法,分析等截面复合材料梁承受均匀拉弯扭载荷的一个简单精确分析的实施方法．由于巧妙地利用了变形的对称特性,使得分析只需建立在梁的一个切片构造的几何模型上,用常规三维实体有限单元进行结构离散．推导了精确的变形场模式,并借助结构平移自由度的耦合关系使得数值分析易于实施．并通过数值算例来阐明方法的实施过程．     

Identification of optimal material models and parameters in finite strain plasticity

The numerical simulation of the behaviour of a workpiece during manufacturing depends to a large extent on the quality of the applied material model. In this work, a method for the identification of constitutive models and material parameters in engineering applications is proposed. The presented method is used in the setting of optimal experimental design and is based on successive optimization of a set of finite strain plasticity models with kinematic and/or isotropic hardening. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Nonlinear analysis of residual stresses in a rail manufacturing process by FEM

The aim of this paper is to study the residual stresses in an UIC-60 rail and their reduction by means of roller straightening. Both experimental and numerical investigations have been carried out in the past to reveal the formation of dominant longitudinal residual stresses. However, the agreement between both investigations was not particularly good. The finite element method (FEM) has also been used to simulate one, two and three-dimensional analyses of a rail during roller straightening processes. The present model considers the longitudinal movement of a rail through the straightening machine, contact conditions between rail and rollers and kinematic hardening so as to take into account the plastic behaviour of the rail material (steel). These results were compared with the experimental investigations and good agreement was observed. In this respect, this paper presents a novel, more realistic numerical simulation by FEM for the roller straightening process. Finally, an improvement of the straightening process in order to obtain smaller residual stress in the rail section is proposed.     

Limiting Models for Josephson Junctions and Superconducting Weak Links

One of the broadest applications of superconductivity is the technology based on Josephson junction devices. These junction devices are formed by placing a thin layer of normal (nonsuperconducting) material between layers of superconducting material. We consider various limiting cases for models of the junction device based on the Ginzburg-Landau equations. Examples include a model for large values of the Ginzburg-Landau parameter, κ, in the high-field regime and a model for a thin normal layer. Convergence analysis for the simplified models is established and numerical simulations are presented.     

Homogenization of fibre composites using X-FEM

A successful material design process for novel textile reinforced composites requires an integrated simulation of the material behaviour and the estimation of the effective properties used in a macroscopic structural analysis. In this context the Extended Finite Element Method (X-FEM) is used to model the behavior of materials that show a complex structure on the mesoscale efficiently. A homogenization technique is applied to compute effective macroscopic stiffness parameters. This contribution gives an outline of the implementation of the X-FEM for complex multi-material structures. A modelling procedure is presented that allows for the automated generation of an extended finite element model for a specific representative volume element. Furthermore, the problem of branching material interfaces arising from complex textile reinforcement architectures in combination with high fibre volume fractions will be addressed and an appropriate solution is proposed. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Multiscale modeling of continuous fiber and fabric reinforced rubber components

Fabric or continuous fiber reinforced rubber components (e.g. tires, air springs, industrial hoses, conveyor belts or membranes) are underlying high deformations in application and show a complex, nonlinear material behavior. A particular challenge depicts the simulation of these composites. In this contribution we show the identification of the stress and strain distributions by using an uncoupled multiscale modeling method, see [1]. Within this method, two representation levels are described: One, the meso level, where all constituents of the composite are shown in a discrete manner by a representative volume element (RVE) and secondly, the macro level, where the structural behavior of the component is defined by a smeared anisotropic hyperelastic constitutive law. Uncoupled means that the RVE does not drive the macroscopic material behavior directly as in a coupled approach, where a RVE boundary value problem has to be solved at every integration point of the macro level. Thus an uncoupled approach leads to a tremendous reduction in numerical effort because the boundary value problem of a RVE just has to be solved at a point of interest, see [1]. However, the uncoupled scale transition has to fulfill the HILL–MANDEL condition of energetic equivalence of both scales. We show the calibration of material parameters for a given constitutive model for fiber reinforced rubber by fitting experimental data on the macro level. Additionally, we demonstrate the determination of effective properties of the yarns. Finally, we compare the energies of both scales in terms of compliance with the HILL–MANDEL condition by using the example of a biaxial loaded sample and discuss the consequences for the mesoscopic level. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)