Numerical Prediction of Macroscopic Material Failure

The aim of this contribution is the numerical determination of macroscopic material properties based on constitutive relationships characterising the microscale. A macroscopic failure criterion is computed using a three dimensional finite element formulation. The proposed finite element model implements the Strong Discontinuity Approach (SDA) in order to include the localised, fully nonlinear kinematics associated with the failure on the microscale. This numerical application exploits further the Enhanced–Assumed–Strain (EAS) concept to decompose additively the deformation gradient into a conforming part corresponding to a smooth deformation mapping and an enhanced part reflecting the final failure kinematics of the microscale. This finite element formulation is then used for the modelling of the microscale and for the discretisation of a representative volume element (RVE). The macroscopic material behaviour results from numerical computations of the RVE. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Finite element simulation of deformation behaviour of cellular rubber components

This paper presents a new prospect of investigating the mechanical behaviour of cellular rubber using porous hyperelastic material model. There are number of hyperelastic material models to describe the behaviour of homogeneous elastomer, but very few to characterise the complex properties of cellular rubber. The analysis of dependence of material behaviour on pore density using the new material model is supported with experiments to characterise the actual material behaviour. The new material model which is based on Danielsson et al [1] decouples the influence of porosity from the mechanical properties of the solid material by introducing volume fraction of the pores as an explicit scalar variable. The finite element simulations are then followed by experiments on complex model to validate the material model. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

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)     

Estimation of material properties of cancellous bone using multiscale FEM

Cancellous bone is a spongy type of bone with voids filled by blood marrow. Without much loss of generality it can be modeled as a material with periodic microstructure where overall parameters can be calculated using homogenization methods. Here the multiscale finite element method is applied and the assumed representative volume element (RVE) is a cube with solid frame and fluid core. From the point of view of the finite element method the RVE is a combination of solid and shell elements. As the acoustic excitation is considered, a complex stiffness matrix and complex displacements appear in the solution of the problem. Calculation of overall properties is repeated for different geometries of the solid frame. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Spatial Random Material Property Model for Vibration of Composites

Investigation of vibration and buckling of thin walled composite structures is very sensitive to parameters like uncertain material properties and thickness imperfections. Because of the manufacturing process and others, thin walled composite and other structures show uncertainties in material properties, and other parameters which cannot be reduced by refined discretization. These parameters are mostly spatial distributed in nature. Here I introduce a semivariogram type material property model to predict the spatial distributed material property (like young's modulus) over the structure. The computation of semivariogram parameters needs the local material properties over a prespecified gird. The material properties at each grid have been obtained by considering a statistically homogeneous representative volume element (RVE) at each gird. According to random nature of the spatial arrangement of fibers, the statistically homogeneous RVE is obtained using image processing. The effective material properties of the RVE have been obtained numerically with the help of periodic boundary condition. The methodology is applied to a composite panel model and modal analysis has been carried. The results of the modal analysis (eigen values and mode shapes) are compared with experimental modal analysis results which are in good agreement. Using the presented material property model we can better predict the vibration characteristics of the thin walled composite structures with the inherent uncertainties. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Homogenization of microstructures in dynamics using periodic boundary conditions

A homogenization method is used to calculate effective material properties of periodic microstructures subjected to small, time-harmonic strain fields. The method is based on the equivalence of averaged micro-field quantities in dispersive heterogeneous media and those in effective homogeneous media with frequency dependent elastic constants. Solutions to the elastodynamic boundary value problem (BVP) are obtained from a boundary element method where periodic boundary conditions on the unit-cell are incorporated using Lagrangian multipliers. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Comparison of different plasticity criteria for trabecular bone failure modelling

Different plasticity criteria applied to failure analysis of trabecular bone are compared. A cylindrical sample of bovine trabecular bone is mechanically tested in uniaxial compression/tension with 2% applied strain. Obtained response in compared to responses obtained using finite element model of trabecular bone inner structure subjected to the same loading conditions. FE model is reconstructed from micro–CT images. Elastic material properties at the level of trabecula are determined using nanoindentation. Compared plasticity criteria are based on these elastic material properties, i.e. on Young's modulus of elasticity from nanoindentation. The objective of the paper is to demonstrate the importance to reflect the anisotropic plasticity and to evaluate variation in obtained response when the anisotropy is neglected. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Inclusion of Manufacturing Induced Uncertainties into Linear Vibration of Structures

Owing to manufacturing, composite materials and others can show considerable uncertainties in wall-thickness, fluctuations in material properties and other parameters, which are spatially distributed over the structure. These uncertainties have a random character and they cannot be reduced by mesh refinement within the finite element (FE) model. So what we need is a suitable statistical approach to describe the parameter changing that holds for the statistics of the process and the correlation between the parameter spatially distributed over the structure. The paper presents a solution for a spatial correlated simulation of parameter distribution owing to the manufacturing process or other causes that is suitable to be included in the finite element analysis (FEA). The spatial variation of parameters is modelled using variogram approach and it has been applied into FEA. For example the effect of spatial variation of thickness and the effect of spatial variation of material properties has been studied in this part of work. The effect of thickness on buckling has been also studied. The results could be used to asses the robustness of the structure and to get limits for manufacturing induced uncertainties. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numerical simulations of spalling tests in order to investigate material properties of UHPC

In order to evaluate the material composition of Ultra High Performance Concrete (UHPC), material properties such as dynamic tensile strength or fracture strength and also the fracture energy under impact loading are of significant importance. The use of a modified Hopkinson Bar enables the determination of the required data. On the basis of experimental investigations our contribution deals with the numerical finite element simulation of the Hopkinson Bar test. The propagation of stress waves is reproduced by means of a special time-integration scheme. We simulate the propagation of cracks by using adaptive cohesive elements including a corresponding separation law. The critical energy release rate (Griffith-energy) is calculated and compared to the values determined by experimental results. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Experimental and numerical investigation of different types of articular cartilage replacement materials

The aim of the presented work is to characterize the mechanical properties of different types of articular cartilage replacement materials. For this propose an elastic-diffusion model is developed to identify the elastic and diffusion properties of the replacement materials. A set of unconfined compression tests were performed with several kinds of implants. By means of finite element simulation integrated with an user-defined material model, the material parameters were identified. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the Excitation of Rolling Tires from the Road Surface Texture

Rolling tires are excited from the contact with the rough road surface to vibrations, which cause rolling noise. A two scale approach is suggested, where at the macro–scale the vibration of the rolling tire structure is modeled by quite detailed finite element methods. The road surface is described using measured textures. A fine resolution finite element discretization of the tread rubber is performed in order to resolve the asperity contact. The material properties are described by a non–linear viscoelastic rubber model. The tread patch is enforced to approach the rough surface in a transient dynamics manner. From these investigations an enveloping surface profile is reconstructed to be used for the excitation. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Computation of the effective nonlinear material behaviour of composites using X-FEM - Analysis of the matrix material behaviour

For a consequent lightweight design the consideration of the nonlinear macroscopic material behaviour of composites, which is amongst others driven by damage and strain–rate effects on the mesoscale, is required. Therefore, the modelling approach using numerical homogenization techniques based on the simulation of representative volume elements which are modelled by the extended finite element method (X–FEM) is currently extended to nonlinear material behaviour. While the glass fibres are assumed to remain linear elastic, a viscoplastic constitutive law accounts for strain–rate dependence and inelastic deformation of the matrix material. This paper describes the process of finding suitable constitutive relations for the polymeric matrix material Polypropylene in the small–strain regime. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Determining Material Parameter of Solder Alloys by Nanoindentation

Environmental awareness motivates the replacement of traditional plumbiferous solder joints in microelectronic devices by new material alloys. In our group mechanical properties of some lead-free alloys are determined by nanoindentation experiments. We use a Microsystems-Nanoindenter Machine with Berkovich tip and apply standard techniques to extract the material properties from the measured load-displacement curves. To assess the quality of our experimental results we model and analyze the setup by finite element computations. By comparing the real (input) material data with the results determined from the load-displacement curves we analyze the obtained data in dependence of strength and stiffness of the materials under consideration. For low-strength material we point out deviations. By inverse analysis we adapt numerically elastic modulus and yield stress to experimentally measured load-displacement curves. To obtain information on the material's work hardening we suggest the use of a blunt indenter tip, e.g., a spherical indenter. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Linear and Nonlinear Finite Element Analysis of Active Composite Laminates

The paper presents a finite element concept for analysis of thin-walled active structures featuring fiber reinforced composite laminate as a passive structural material. The structure is rendered active by embedding piezoelectric material as a multifunctional material. A 9-node degenerated shell element based on the first order shear deformation theory is developed as a modelling tool capable of predicting the general behavior of the structure for controlling purposes. The von-Kármán type nonlinearities are considered. The solution strategy of the geometrical nonlinear analysis is based on the incremental approach using the updated Lagrangian formulation. Some numerical results are given to demonstrate the behavior of the element. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Transient response of sandwich viscoelastic beams, plates, and shells under impulse loading

The transient response of sandwich beams, plates, and shells with viscoelastic layers under impulse loading is studied using the finite element method. The viscoelastic material behavior is represented by a complex modulus model. An efficient method using the fast Fourier transform is proposed. This method is based on the trigonometric representation of the input signals and the matrix of the transfer functions. The present approach makes it possible to preserve exactly the frequency dependence of the storage and loss moduli of viscoelastic materials. The logarithmic decrements are determined using the steady state vibrations of sandwich structures to characterize their damping properties. Test problems and numerical examples are given to demonstrate the validity and application of the approach suggested in this paper. Submitted to the 11th International Conference on Mechanics of Composite Materials (Riga, June 11–15, 2000). Published in Mekhanika Kompozitnykh Materialov, Vol. 36, No. 3, pp. 367–378, March–April, 2000.     

Analysis of functionally graded plates using higher order shear deformation theory

This work addresses a static analysis of functionally graded material (FGM) plates using higher order shear deformation theory. In the theory the transverse shear stresses are represented as quadratic through the thickness and hence it requires no shear correction factor. The material property gradient is assumed to vary in the thickness direction. Mori and Tanaka theory (1973) [1] is used to represent the material property of FGM plate at any point. The thermal gradient across the plate thickness is represented accurately by utilizing the thermal properties of the constituent materials. Results have been obtained by employing a C° continuous isoparametric Lagrangian finite element with seven degrees of freedom for each node. The convergence and comparison studies are presented and effects of the different material composition and the plate geometry (side-thickness, side–side) on deflection and temperature are investigated. Effect of skew angle on deflection and axial stress of the plate is also studied. Effects of material constant n on deflection and the temperature distribution are also discussed in detail.     

Fracture Mechanical Investigation of Elastomeric Material

The increasing use of elastomeric components in advanced engineering applications requires a thorough understanding of the complex material properties and a reliable assessment of the quality and durability of the products. This contribution concentrates on the computational determination of fracture mechanical parameters for rubber material using the material force method. For dissipative, inelastic material, a distinction between two fracture mechanical parameters is presented. The time-dependent behaviour of these fracture mechanical parameters is illustrated by an application to the dwell-effect. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

An improved continuum skin and proximity effect model for hexagonally packed wires

This work presents approximate but closed-form expressions for “effective” complex-valued magnetic permeability and electric conductivity that represent the effects of proximity and skin effect losses in wound coil with hexagonally packed wires. Previous work is extended by providing improved accuracy versus finite element results for effective permeability and by providing an expression for effective conductivity, which was previously neglected. These material properties can then be used in 2D/axisymmetric finite element models in which the coil is modeled as a coarsely meshed, homogeneous region (i.e., removing the need for modeling each turn in the coil).