Micromechanical creep model for pure copper

A Unit Cell made of copper is simulated and investigated under creep conditions within the framework of micromechanics. Geometrical 3D model of the copper microstructure is represented as a Unit Cell with grains of random crystallographical orientation and geometry. Such simulation enables algorithm of Voronoi tessellation. The stress-strain behavior of grains in the general case is anisotropic due to the ordered crystalline structure. The anisotropic model for a material with a cubic symmetry is implemented in Abaqus and used to assign behavior of grain interior in elastic and creep regions. Material parameters for elastic model are taken from elastic tests of single crystal copper [1]. Power law material parameters for creep model are taken from creep test performed for single crystal copper [2]. The model parameter ξ is validated numerically. Creep results are presented for the case of proportional loading during the primary and secondary creep. Statistical analysis of creep curves received for 55 different realizations of Unit Cell geometry is carried out. As a result confident interval and mathematical expectation of creep data are calculated. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Effective Dynamic Material Properties of Foam-like Microstructures

The effective material parameters of a microstructured material can be found using homogenization procedures based on calculations of a Representative Volume Element (RVE) of the material. In our approach the RVE is calculated in frequency domain and inertia is taken into account, leading to a frequency dependent behavior of the RVE.With the frequency response of the RVE, effective dynamic properties of the material are calculated using an optimization procedure. Due to the frequency dependent material behavior on the microscale a viscoelastic constitutive equation is applied on the macroscale. An example calculation is presented for an auxetic 2-D foam-like microstructure which is modelled as a plane frame structure. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Creep damage modeling of a polycrystalline material

A polycrystalline material is investigated under creep conditions within the framework of continuum micromechanics. Geometrical 3D model of a polycrystalline microstructure is represented as a unit cell with grains of random crystallographical orientation and shape. Thickness of the plains, separating neighboring grains in the unit cell, can have non-zero value. Obtained geometry assigns a special zone in the vicinity of grain boundaries, possessing unordered crystalline structure. A mechanical behavior of this zone should allow sliding of the adjacent grains. Within the grain interior crystalline structure is ordered, what prescribes cubic symmetry of a material. The anisotropic material model with the orthotropic symmetry is implemented in ABAQUS and used to assign elastic and creep behavior of both the grain interior and grain boundary material. Appropriate parameters set allows transition from the orthotropy to the cubic symmetry for the grain interior. Material parameters for the grain interior are identified from creep tests for single crystal copper. Model parameters for the grain boundary are set from the physical considerations and numerical model validation according to the experimental data of the grain boundary sliding in a polycrystalline copper [2]. As the result of analysis representative number of grains and grain boundary thickness in the unit cell are recommended. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Designing Statistically Similar RVEs for 3D Dual Phase Steel Microstructures

This contribution presents a method for the construction of three-dimensional Statistically Similar Representative Volume Elements (SSRVEs) for dual phase steels (DP steels). From such kind of advanced high strength steels, enhanced material properties are observed, which originate in the interaction of the individual constituents of the material on the microscale. Our aim is to directly incorporate the microstructure in the material modeling, which can be accomplished by applying i. e. the FE² method. A RVE representing the real material is used in the microscopic boundary value problem, which is solved at each macroscopic integration point. Since such RVEs usually exhibit a high complexity due to the underlying real microstructure, high computational costs are a drawback of the approach. We replace this RVE with a SSRVE, which has a lower complexity but which is still able to represent the mechanical behavior of the RVE and thus of the real microstructure. Virtual experiments show the performance of the method. (© 2013 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)     

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)     

Study on statistically similar RVEs for real microstructures based on different statistical descriptors

A method for constructing statistically similar representative volume elements (SSRVEs) for a real dual-phase (DP) steel microstructure is presented in this contribution. The advantageous material properties of such kind of steels originate from the interaction of the microstructure constituents of the material on the microscale. In order to capture these effects directly in the material modeling, the FE² method is a suitable tool, where an RVE representing the microstructure of a material is used in the microscopic boundary value problem, which is solved at each Gauss-point of the macroscopic boundary value problem. However, RVEs based on real microstructures typically implicate high computational expenses due to the complexity of the underlying microstructure and its discretization. SSRVEs, which have a lower complexity than conventional RVEs but are still able to represent the material, can be used instead. Here, different statistical measures for the construction of SSRVEs and their comparison are the main focus. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A desktop computer model of the arc,weld pool and workpiece in metal inert gas welding

A sophisticated computational model of metal inert gas arc welding of aluminium alloys is presented. The arc plasma, the wire electrode and the workpiece are included in the computational domain self-consistently. The flow in the arc plasma and in the weld pool are calculated in three dimensions using equations of computational fluid dynamics, modified to take into account plasma effects and coupled to electromagnetic equations. The formation of metal vapour from the wire electrode and workpiece is considered, as is the mixing of the wire electrode alloy with the workpiece alloy in the weld pool. A graphical user interface (GUI) has been developed, and the model runs on standard desktop or laptop computers.The computational model is described, and results are presented for lap-fillet weld geometry. The importance of including the arc in the computational domain is shown. The predictions of the model show good agreement with measurements of weld geometry and weld composition. The GUI is introduced, and the application of the model to predicting the thermal history of the workpiece, which is the input information that is required for predicting important weld properties such as residual stress and distortion and weld microstructure, is discussed. Initial predictions of residual stress and distortion of the workpiece are presented.     

Multiscale Modeling for the Simulation of Damage Processes at Refractory Materials under Thermal Shock

A brittle damage model based on multiscale considerations and homogenisation procedures is presented. Cell models are developed as RVE including different microstructural features. The material laws themselves are formulated on the continuum level. Local failure occurs if the damage variable reaches a critical value. For simple configurations of the microstructure, the relation between stress, strain und temperature is derived from analytical considerations. In order to properly model the thermo-mechanical coupling, the temperature-dependence of material constants is taken into account. Fracture and damage mechanical approaches are combined using different techniques. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Determination of Effective Properties of MMC by Computational Homogenization

On the macrolevel Metal Matrix Composites (MMCs) resemble a homogeneous material. However, on the microlevel they show an inhomogeneous microstructure. This paper will have how heterogeneities affect the overall properties and the behaviour of a material (i. e. the effective properties). This is done using computational homogenization techniques. Finite element (FE) simulations were conducted in ABAQUS in connection with MATLAB, using material parameters for aluminium alloy AA2124 and SiC to develop a representative volume element (RVE) of the MMC AMC217xe. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A RVE-based micro mechanical model for short fiber reinforced plastic materials including matrix damage and fiber fracture

The representative volume element (RVE) method is applied to a fiber reinforced polymer material undergoing matrix damage and fiber fracture. Results of RVE computations are compared to uniaxial tensile tests performed with the composite material. It is shown that the macroscopic behavior of the composite material can accurately be predicted by RVE computations. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Multiscale Modelling of the Effective Viscoplastic Material Behaviour of Textile-Reinforced Polymers Using XFEM

In this contribution a modelling approach using numerical homogenisation techniques is applied to predict the effective nonlinear material behaviour of composites from simulations of a representative volume element (RVE). Numerical models of the heterogeneous material structure in the RVE are generated using the eXtended Finite Element Method (XFEM) which allows for a regular mesh. Suitable constitutive relations account for the material behaviour of the constituents. The influence of the nonlinear matrix material behaviour on the composite is studied in a physically nonlinear FE simulation of the local material behaviour in the RVE ­ effective stress-strain curves are computed and compared to experimental observations. The approach is currently augmented by a damage model for the fibre bundle. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

FE-implementation of plane strain gradient elasticity constitutive equations obtained by homogenization

This paper presents a plane strain gradient elasticity model together with a strength criterion based on the maximum hoop stress. It is developed by higher order homogenization based on a cylindrical RVE containing a void and is implemented as mixed–type finite element formulation into the FE–code Abaqus. Numerical simulations are performed in order to study the size effect related to the onset of failure of specimens of porous elastic material. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Micromechanical material models for polymer composites through advanced numerical simulation techniques

The paper deals with the determination of macroscopic material properties of polymer composites by meso-mechanical numerical modeling. Focus is laid on the methodology how to build up appropriate representative volume elements (RVE) to describe the microstructure of spherical-particles and fibers reinforced composites and how to apply appropriate 3D boundary conditions. The work includes the comparison of the effective material parameters calculated through numerical homogenization of our FE-models with existing analytical formulations as well as with experimental data. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Comparison of Statistical Descriptors for the Construction of Statistically Similar RVEs

A method for the construction of three-dimensional statistically similar representative volume elements (SSRVEs) is presented. Since the beneficial material properties of microheterogeneous materials originate in the microstructure, its incorporation in material modeling is desired. The FE₂ method is a suitable tool to accomplish this step. Applying this method, a microscopic boundary value problem, given by a representative volume element (RVE) is attached to every integration point of the macroscale. Such RVEs taken from real microstructures exhibit a high level of complexity, thus raise computational costs. The use of a SSRVE with lower complexity is able to decrease these costs. Here, different statistical measures are compared in view of the performance in the SSRVE construction procedure. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The equivalent inclusion technique and its convergence

This paper addresses the convergence characteristics of an iterative solution scheme of the Neumann‐type useful for obtaining homogenized mechanical material properties within an RVE. The analysis is based on the idea of “equivalent inclusions” and, within the context of stress/strain analysis, allows modeling of elastically highly heterogeneous bodies with the aid of discrete Fourier transforms. Within the iterative scheme the proof of convergence depends critically upon the choice of an appropriate, auxiliary stiffness matrix, which also determines the speed of convergence. Mathematically speaking it is based on Banach's fixpoint theorem and only results in necessary convergence conditions. However, for all cases of elastic heterogeneity that are of practical importance convergence can be demonstrated.     

Microstructural Model of a Closed-Cell Foam on the Basis of Image Analysis

The focus of this work is the identification of a unit cell that is able to represent the microstructure of a closed-cell solid foam to predict the effective behaviour of the foam numerically. For the investigation, a finite element model consisting of a repeating unit cell with periodical boundary conditions is implemented. A tetrakaidecahedral foam microstructure is considered as simplified cell geometry, and a strain-energy based homogenisation concept is utilized. On the basis of image analysis imperfections are applied to the cell. The obtained model is used as a representative volume element (RVE) for further investigations of the postbuckling behaviour of the foams. Different analyses are performed and the results are compared to literature and experimental data. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

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)     

A finite element model based on statistical two-scale analysis for equivalent heat transfer parameters of composite material with random grains

In this paper, a new finite element model based on statistical two-scale analysis for predicting the equivalent heat transfer parameters of the composite material with random grains is presented and its convergence, its error result and the symmetry, positive property of equivalent heat transfer parameters matrix are also proved. Firstly, some definitions of the probability space and the composite material with random grains are described and the STSA formulation predicting the equivalent heat transfer parameters of the composite material are briefly reviewed. Next, a finite element formulation and its corresponding procedure for the composite material with random grains is described. Then, the convergence, the error estimate and the symmetry, positive property of the equivalent heat transfer parameters matrix computed by FE based on STSA are proved. The numerical result shows the validity of the FE model based on STSA and the convergence and the symmetry, positive property of the equivalent heat transfer parameter matrix of the composite material with random grains by the FE model.