Parameteridentification of Hostun-Sand and Shear-Band Simulation of Landsliding

The simulation of deformation process of landsliding needs the knowledge of the very complex behaviour of granular materials, e. g., sand. The triax experiments on sand show a highly non-linear elasto-plastic material behaviour. Therefore, it is necessary to use a yield criteria, e. g., single-surface yield criteria with isotropic hardening and non-associated plastic potential, which satisfies adequately the requirements of the material properties. This kind of material behaviour can be described by an elasto-plastic material law in the frame of Theory of Porous Media, which is implemented in the FE tool PANDAS. By means of the data of Hostun-Sand, the material parameters of the singlesurface yield criteria are determined by use of a optimization algorithm, namely Sequential Quadratic Programming (SQP) a gradient based optimization method, which is coupled with PANDAS. Using this optimized material parameters, a simulation of a initial boundary-value problem of landsliding is presented. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the calculation of Topological Derivatives considering an exemplary nonlinear material model

In this contribution, a new approach for dealing with material nonlinearities in structural optimization is presented. The method combines the advantage of the calculation of the Topological Derivatives in elasticity problems with the use of meta-modelling for capturing complex correlations. For an exemplary nonlinear material model, the calculation of the Topological Derivative and the resulting difference to the linear elastic material model is shown. An academic example shows the difference between the linear and the nonlinear material model. © 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Vibration using for the longitudinal elasticity modulus determination

Longitudinal elasticity modulus, E, is a material specific feature, which,. in general, is establish on the pieces by longitudinal stress. This procedure is possible to apply to the compact material but not to the sintered power parts (or porous material test pieces). For sintered parts, the establishing of Young's modulus, in this paper, it is proposed by transmition of mechanical vibrations along to the test pieces. The test pieces of compact or porous material were strained at longitudinal vibrations. It was establish the linkage between vibration and density, respective between the density and the value of the longitudinal elasticity modulus. Using the test pieces of compact material we realized the methodology to obtain the longitudinal elasticity modulus regarding the compact material, and in this way can be establish the possibility to measure with a good result the longitudinal elasticity modulus for the pieces of sintered powders or of porous material. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

An Unified Computational Framework for Parameter Identification of Material Models in Finite Inelasticity

Parameter identification processes concern the determination of parameters in a material model in order to fit experimental data. We provide a distinct, unified algorithmic setting of a generic class of material models and discuss the associated gradient–based optimization problem. Gradient–based optimization algorithms need derivatives of the objective function with respect to the material parameter vector κ . In order to obtain the necessary derivatives, an analytical sensitivity analysis is pointed out for the unified class of algorithmic material models. The quality of the parameter identification is demonstrated for a representative example.     

Modelling the material behaviour of magnetorheological fluids under shear deformation

In recent years the interest in materials with specific adjustable properties has increased due to higher requirements on the material performance. Here a smart composite material is to be developed, whose stiffness can be varied subjected to a magnetic field. To realise this aim a magnetorheological fluid (MRF) embedded in a polymeric matrix material is considered. To model the material behaviour of the composite a homogenisation method will be applied. Amongst others this requires the knowledge of the multiaxial material behaviour of each constituent. The modelling of the material behaviour of MRF under shear deformation, which is the aim of this work, represents the first step in this process. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Material stability analysis of particle methods

Material instabilities are precursors to phenomena such as shear bands and fracture. Therefore, numerical methods that are intended for failure simulation need to reproduce the onset of material instabilities with reasonable fidelity. Here the effectiveness of particle discretizations in reproducing of the onset of material instabilities is analyzed in two dimensions. For this purpose, a simplified hyperelastic law and a Blatz–Ko material are used. It is shown that the Eulerian kernels used in smooth particle hydrodynamics severely distort the domain of material stability, so that material instabilities can occur in stress states that should be stable. In particular, for the uniaxial case, material instabilities occur at much lower stresses, which is often called the tensile instability. On the other hand, for Lagrangian kernels, the domain of material stability is reproduced very well. We also show that particle methods without stress points exhibit instabilities due to rank deficiency of the discrete equations. AMS subject classification 74S30     

An indifferent constitutive law in finite elasticity

The concepts of material frame-indifference and material symmetry group with respect to isotropic scalar functions, as represented by energy functions, are discussed. An energy function for a structured heterogeneous (transversal isotropic) medium in large elastic deformations, which is known to satisfy the Ponyting’s effect [1], is highlighted. It is shown that the constitutive relation due to this energy function is material frame-indifferent.     

Stresses in elastic conical tubes of transversely isotropic materials with spherical anisotropies under temperature and force loadings

Analytic solutions are proposed for a number of new problems on determining the state of stress of a transversely-isotropic hollow cone with spherical anisotropy. An exact solution of the problem of the axisymmetric deformation of a long conical tube (or continuous cone) from an elastic transversely-isotropic material with spherical anisotropy subjected to an axial force is obtained in a spherical coordinate system R, , θ, the material axis of symmetry is directed along the spherical radius R. A rigorous solution is given of the problem of the uniform heating of a conical tube of transversely-isotropic material with spherical anisotropy for particular values of Poisson's ratios; the material axis of symmetry is directed along the θ-axis. For arbitrary Poisson's ratios an asymptotic solution is found for the temperature problem for a tube with small conicity.     

Simulation of thick adhesive layers at finite strains utilizing an associated flow rule in a thermodynamically consistent framework

The application of elastoplastic material models is commonly used for the modelling of adhesive layers with high strength adhesives as realized with polyurethane or epoxy resin. To fulfill thermodynamic consistency often restrictions on the choice of material parameters are requested. One of them is the introduction of a non-associated flow rule, which always ensures positive dissipation. Nevertheless, this assumption is a non-essential criterion, which will be addressed in this work. Continuing along this argumentation, the constitutive relations for the material is modified based on an associated flow rule. The applied model for the simulation of the adhesives is based on a small strain theory. A yield surface including two stress invariants, the hydrostatic pressure as well as the deviator stress state, set the elastic limit of the material response. Linear as well as exponential hardening is incorporated and material softening that arises subsequently is also included by substituting effective invariants in the yield function. This material model as proposed from literature was extended to finite strain application with the concept of generalized stress-strain-measure, which was realized in a previous work. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Analysis of nanoindentation experiments by means of rheological models

The nanoindentation technique is established in the field of material characterization at small dimensions. It is daily practice to analyze nanoindentation data with an almost “classical” formula based on the publications by Oliver and Pharr and Fischer-Cripps. The procedure works well for elastic-time independent plastic material behavior, for example copper and the calibration material fused silica, even at higher test temperatures. However, low melting solder materials are susceptible to creep behavior. For this reason, additional analysis procedures are required to determine the material parameters more precisely. In this paper the authors want to give an introduction to an “enhanced” analysis of nanoindentation data based on rheological models, which are often used to describe the time-dependence of material response. Two examples of such models are the MAXWELL- and the KELVIN-body. The authors present a rheological model, published by Mencik in 2011 [1], in context with the corresponding equation which is used to extract the material properties from the recorded data. Results of the analysis at the calibration material fused silica are presented and discussed together with the material parameters published in the literature. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Rheology of polarizable non-piezoelectromagnetic material in relativity

Following the work of Carter on nonlinear perfectly elastic solid and perfect nonlinearly polarizable nonconducting solid, we have constructed models whose free gravitational field is of Petrov typeD: (i) in inertial reference frame (IRF), (ii) with pure expansion and (iii) with pure rotation with the assumption that the flow field is expressible in terms of two real null vectors of the Newman-Penrose (N-P) tetrad. By using the strain variation equation, the necessary and sufficient conditions on the dynamical variables are obtained in Newman-Penrose version. We observe that the initial pressure tensor depends on the polarizable and electromagnetic properties of the material. Further, we conclude that there does not exist such a material with pure expansion but there exists such a material moving rigidly with or without rotation. We obtain the Hawking energy conditions and invariants for this material in IRF.     

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)     

Material-Force-Based Refinement Indicators in Adaptive Strategies

A material-force-based refinement indicator for adaptive finite element strategies for finite elasto-plasticity is proposed. Starting from the local format of the spatial balance of linear momentum, a dual material counterpart in terms of Eshelby's energy-momentum tensor is derived. For inelastic problems, this material balance law depends on the material gradient of the internal variables. In a global format the material balance equation coincides with an equilibrium condition of material forces. For a homogeneous body, this condition corresponds to vanishing discrete material nodal forces. However, due to insufficient discretization, spurious material forces occur at the interior nodes of the finite element mesh. These nodal forces are used as an indicator for mesh refinement. Assigning the ideas of elasticity, where material forces have a clear energetic meaning, the magnitude of the discrete nodal forces is used to define a relative global criterion governing the decision on mesh refinement. Following the same reasoning, in a second step a criterion on the element level is computed which governs the local h-adaptive refinement procedure. The mesh refinement is documented for a representative numerical example of finite elasto-plasticity. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Identification of material behavior via a Finite Element Model Updating strategy

In this paper an inverse and iterative method for the identification of material behavior is presented, based on the Finite Element Model Updating (FEMU) strategy. The FE simulations are performed with a commercial FE software code, using a self-implemented elastic material model at finite strain. The iterative identification procedure is based on an experimental test (numerical) whose measured kinematic values are compared to the corresponding simulated ones. Through an optimization algorithm the material parameters are varied in a way that the least-squares sum of the kinematic values is minimized and the optimal material parameters yielding the material behavior are identified. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numerical simulation of Richtmyer-Meshkov instability

The compressible Navier-Stokes equations discretized with a fourth order accurate compact finite difference scheme with group velocity control are used to simulate the Richtmyer-Meshkov (R-M) instability problem produced by cylindrical shock-cylindrical material interface with shock Mach number Ms=1.2 and density ratio 1:20 (interior density/outer density). Effect of shock refraction, reflection, interaction of the reflected shock with the material interface, and effect of initial perturbation modes on R-M instability are investigated numerically. It is noted that the shock refraction is a main physical mechanism of the initial phase changing of the material surface. The multiple interactions of the reflected shock from the origin with the interface and the R-M instability near the material interface are the reason for formation of the spike-bubble structures. Different viscosities lead to different spike-bubble structure characteristics. The vortex pairing phenomenon is found in the initial double mode simulation. The mode interaction is the main factor of small structures production near the interface.

     

Damage identification in a concrete dam by fitting measured modal parameters

We propose a method, based on an inverse problem, to obtain numerically the material parameters that characterize the elasticity tensor of a body with linear elastic behavior, using accurate measurements of the first modal parameters, namely the natural frequencies and the modes of vibration (the eigenfrequencies and the eigenvectors). Appropriate functionals are defined, whose minimum points correspond to the unknown material parameters. To obtain these minimum points a highly nonlinear parametric optimization problem is solved. Its resolution involves specific mathematical tools like the derivative of the eigenvalues and eigenvectors with respect to the material parameters, the adjoint method, and gradient methods for the minimization of the functional. An application is presented, which considers a cracked dam in which is assumed the presence of transversely isotropic material in the cracked zone. The material parameters of the transversely isotropic material are obtained by minimizing the distance between the modal parameters (eigenfrequencies and eigenvectors) of a numerical model of the dam and the observed modal parameters physically measured in the dam. The algorithm is implemented in a C++ home made code with the aid of open-source libraries for scientific computation.     

An extended tube model for thermo-viscoelasticity of rubberlike materials: Parameter identification and examples

The extended tube-model was presented by KALISKE & HEINRICH (RCT 72, 602-632) in 1999 as a novel approach for isothermal hyperelasticity of rubberlike materials. This contribution is dedicated to its further development to finite non-linear thermo-viscoelasticity. A non-linear evolution law and a thermo-mechanical coupled free energy formulation are the kernel of the phenomenological approach where the elastic material response is inspired by statistical-mechanical theory. The representation of viscoelasticity is based on a multiplicative decomposition of the deformation gradient. The Helmholtz free energy of the material is formulated in terms of isothermal free energy functions multiplicatively coupled with non-linear temperature evolution functions. The non-linear evolution law for the viscous material branch is solved by applying a predictor-corrector algorithm with an exponential mapping scheme. In today's literature, several sophisticated thermo-mechanical material models are available. However, they are built upon a considerable number of material parameters governing the mechanical and thermal material response which need to be identified for practical application. Therefore, particular emphasis is given to an appropriate parameter identification technique for the thermal field. For the latter, a uniaxial extension test is carried out where the recorded data of the temperature field of the rubber specimen under cyclic loading is used for parameter identification. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)