H. Andrä

Programming Shape Morphing in Metamaterials

The internal structuring of materials on a mesoscale, e.g., µm-cm enables to design almost arbitr... more The internal structuring of materials on a mesoscale, e.g., µm-cm enables to design almost arbitrary effective physical properties into so called metamaterials. Moreover, programmable materials can be useful in application where conflicting conditions to the shape of the material exist (e.g., wings, personalized tools). They use a stimuli-excited change in the meso-structure to manipulate macroscopic properties in a controlled manner. The mesostructure is no longer static, but responsive to stimuli. The property changes can be either continuous, as a designed non-linear elastic behavior (processing a function), or abrupt (if-then-else condition). Such a logical behavior is implemented into unit cells to control the local Poisson's Ratio as well as the stiffness. These properties are related to geometrical parameters (angles, beam thicknesses) of unit cells that can be varied over a material's volume. The combination of the local unit cell logic and the global parameter distribution leads to a specific shape morphing behavior. Multiscale models and mathematical optimization methods enable us to compute optimal unit cell parameters for large cell arrays. Several unit cells created by different manufacturing methods (3D-printing, foil stacking) will be shown. The designed shape morphing behavior will be presented based on simulations as well as with physical demonstrators.

Download

Exploring Vae-Driven Implicit Parametric Unit Cells for Multiscale Topology Optimization

Data‐based prediction of the viscoelastic behavior of short fiber reinforced composites

PAMM

The viscoelastic behavior of short fiber reinforced polymers (SFRPs) partly depends on different ... more The viscoelastic behavior of short fiber reinforced polymers (SFRPs) partly depends on different microstructural parameters such as the local fiber orientation distribution. To account for this by simulation on component level, two‐scale methods couple simulations on the micro‐ and macroscale, which involve considerable computational costs. To circumvent this problem, the generation of a viscoelastic surrogate model is presented here. For that purpose, an adaptive sampling technique is investigated and data are obtained by creep simulations of representative volume elements (RVEs) using a fast Fourier transform (FFT) based homogenization method. Numerical tests confirm the high accuracy of the surrogate model. The possibility of using that model for efficient material optimization is shown.

Error indicators in the parallel finite element solver for linear elasticity DDFEM

This report discusses two approaches for a posteriori error indication in the linear elasticity s... more This report discusses two approaches for a posteriori error indication in the linear elasticity solver DDFEM: An indicator based on the Richardson extrapolation and Zienkiewicz-Zhu-type indicator. The solver handles 3D linear elasticity steady-state problems. It uses own input language to describe the mesh and the boundary conditions. Finite element discretization over tetrahedral meshes with first or second order shape functions (hierarchical basis) has been used to resolve the model. The parallelization of the numerical method is based on the domain decomposition approach. DDFEM is highly portable over a set of parallel computer architectures supporting the MPI-standard.

Download

Introduction to modern galerkin-type boundary element methods with an application from mechanical engineering

Forsch Ingenieurw, 1999

Estimation of fiber orientation and fiber bundles of MDF

Materials and Structures, 2015

This paper presents numerical methods for the characterization of fiber orientation and fiber bun... more This paper presents numerical methods for the characterization of fiber orientation and fiber bundles of medium density wood fiberboards (MDF). The strength and stiffness of MDF is significantly affected by the fiber orientation and fiber bundles. Proposed methods and results are necessary to virtually generate realistic fiber networks and optimize MDF by using computer simulations. Based on 3D $$\mu$$μCT images for laboratory manufactured MDF with oriented fibers, the fiber orientation is calculated in two ways. Firstly, we use an image processing method based on Hessian matrix directly on $$\mu$$μCT image. Secondly, we computed the effective heat conductivity by solving PDEs on a segmentation of the $$\mu$$μCT image to estimate the fiber orientation. A fiber bundle segmentation method based on local fiber orientations is introduced. Fiber bundles, which are segmented by this method show good agreement with manually segmented ones. It was observed that fiber bundles are oriented in MDF plane with log-normal distribution of bundle length. The proposed methods are general and can be used also to calculate fiber orientation and segment fiber bundles in fiber concrete, paper, glass and carbon fiber composites.

Multiscale Modeling of Progressive Damage in Elasto-Plastic Composite Materials

Abstract. Conventional macro mechanical models and closed form estimates are in many cases not su... more Abstract. Conventional macro mechanical models and closed form estimates are in many cases not sufficient to appropriately predict the mechanical material response of composite materials. Composite failure occurs as a result of complex microstructural damage mechanisms. In this contribution we propose an alternative approach, non-linear material effects caused by progressive damage behavior are captured directly on a finer scale and the microstructural constituents are modeled explicitly. In contrast to conventional methods, which resort to the Finite Element Method (FEM), the boundary value problem is reformulated into an integral equation of Lippmann-Schwinger type and solved more efficiently using Fast Fourier Transforms (FFT). In the work at hand, a ductile damage model and an equivalent microscopic boundary value problem are described. The numerical method is validated with experimental data for a thermoplastic composite material.

Download

Development of a User-Defined Material Model for Sheet Molding Compounds

The compression molding of Sheet Molding Compounds (SMCs) is typically thought of as a fluid mech... more The compression molding of Sheet Molding Compounds (SMCs) is typically thought of as a fluid mechanics problem. The simulation of such materials is at present based on the background of compression or injection molded short fiber reinforced materials. The usage of CF-SMC consisting of high fiber volume content (over 50%) and long fiber reinforcement structures (up to 50 mm) challenges the feasibility of this point of view. The goal of this work is the development of a user-defined material model based on a solid mechanics formulation for SMC materials in LS-DYNA®. To allow for large deformations in the simulation an Arbitrary Lagrangian-Eulerian (ALE) approach is used. As a first step, a material characterization is carried out in a so-called press rheometer test where the mechanical behavior of the SMC material is analyzed during the compression molding process. The resulting stress response of the material then serves as input information for the material model. The material model...

Download

Structural simulation of a bone-prosthesis system of the knee joint

Sensors, Sep 24, 2008

Abstract: In surgical knee replacement, the damaged knee joint is replaced with artificial prosth... more Abstract: In surgical knee replacement, the damaged knee joint is replaced with artificial prostheses. An accurate clinical evaluation must be carried out before applying knee prostheses to ensure optimal outcome from surgical operations and to reduce the probability of having long-term problems. Useful information can be inferred from estimates of the stress acting onto the bone-prosthesis system of the knee joint. This information can be exploited to tailor the prosthesis to the patient's anatomy. We present a compound system for pre- ...

Download

Fluid‐structure interaction in porous media for loaded filter pleats

PAMM, 2011

Download

Highly Shrinkable Objects as Obtained from 4D Printing

Macromolecular Materials and Engineering

Designing Shape Morphing Behavior through Local Programming of Mechanical Metamaterials

Advanced Materials

Digital Rock Physics Benchmarks–Part II: Computing effective properties Proposed paper for Computers & Geoscience special issue

This is the second and final part of our digital rock physics (DRP) benchmarking study. We use se... more This is the second and final part of our digital rock physics (DRP) benchmarking study. We use segmented 3-D images (one for Fontainebleau, three for Berea, three for a carbonate, and one for a sphere pack) to directly compute the absolute permeability, the electrical resistivity, and elastic moduli. The numerical methods tested include a finite-element solver (elastic moduli and electrical conductivity), two finite-difference solvers (elastic moduli and electrical conductivity), a Fourier-based Lippmann-Schwinger solver (elastic moduli), a lattice-Boltzmann solver (hydraulic permeability), and the explicit-jump method (hydraulic permeability and electrical conductivity). The setups for these numerical experiments, including the boundary conditions and the total model size, varied as well. The results thus produced vary from each other. For example, the highest computed permeability value may differ from the lowest one by a factor of 1.5. Nevertheless, all these results fall within the ranges consistent with the relevant laboratory data. Our analysis provides the DRP community with a range of possible outcomes which can be expected depending on the solver and its setup.

Download

Micromechanical network model for the evaluation of quality controls of paper

ABSTRACT In this paper, we discuss the challenges in modelling and simulating infinitesimal and l... more ABSTRACT In this paper, we discuss the challenges in modelling and simulating infinitesimal and large deformations of cellulose fiber networks, mainly in the context of the prediction of quality controls for paper. Understanding the influence and sensitivity of macroscopic production parameters like grammage and thickness of paperboard and understanding the influence of the fiber suspension on the quality of paper is important for the development of better papers and for preserving raw materials and energy. The new simulation framework consists of the virtual stochastic paper structure generator PaperGeo, that was integrated in the GeoDict 1 software suite, and the finite element solver FeelMath (Finite Elements for Elastic Materials and Homogenization) for solving the equations of elasticity. The fibers and the contacts are modelled by using geometrically exact beams of Simo-type [1]. The microstructural model and the fiber network model are validated against standard measurements of existing papers in the following way: At first we perform tensile and bending tests to measure the macroscopic stress-strain relations. In the next step we apply a representative macroscopic stress or strain onto the boundaries of realizations of the stochastic fiber network model and compute by homogenization the effective (stiffness) coefficients. Finally we compare the numerical results with the measurements. This procedure can also be used for an identification of elastic parameters on the microscale and to study the sensitivity of the effective (macroscopic) stiffness with regard to the parameters of the microstructure

Micromechanical network model for the evaluation of quality controls of paper

ABSTRACT In this paper, we discuss the challenges in modelling and simulating infinitesimal and l... more ABSTRACT In this paper, we discuss the challenges in modelling and simulating infinitesimal and large deformations of cellulose fiber networks, mainly in the context of the prediction of quality controls for paper. Understanding the influence and sensitivity of macroscopic production parameters like grammage and thickness of paperboard and understanding the influence of the fiber suspension on the quality of paper is important for the development of better papers and for preserving raw materials and energy. The new simulation framework consists of the virtual stochastic paper structure generator PaperGeo, that was integrated in the GeoDict 1 software suite, and the finite element solver FeelMath (Finite Elements for Elastic Materials and Homogenization) for solving the equations of elasticity. The fibers and the contacts are modelled by using geometrically exact beams of Simo-type [1]. The microstructural model and the fiber network model are validated against standard measurements of existing papers in the following way: At first we perform tensile and bending tests to measure the macroscopic stress-strain relations. In the next step we apply a representative macroscopic stress or strain onto the boundaries of realizations of the stochastic fiber network model and compute by homogenization the effective (stiffness) coefficients. Finally we compare the numerical results with the measurements. This procedure can also be used for an identification of elastic parameters on the microscale and to study the sensitivity of the effective (macroscopic) stiffness with regard to the parameters of the microstructure

Micromechanical network model for the evaluation of quality controls of paper

ABSTRACT In this paper, we discuss the challenges in modelling and simulating infinitesimal and l... more ABSTRACT In this paper, we discuss the challenges in modelling and simulating infinitesimal and large deformations of cellulose fiber networks, mainly in the context of the prediction of quality controls for paper. Understanding the influence and sensitivity of macroscopic production parameters like grammage and thickness of paperboard and understanding the influence of the fiber suspension on the quality of paper is important for the development of better papers and for preserving raw materials and energy. The new simulation framework consists of the virtual stochastic paper structure generator PaperGeo, that was integrated in the GeoDict 1 software suite, and the finite element solver FeelMath (Finite Elements for Elastic Materials and Homogenization) for solving the equations of elasticity. The fibers and the contacts are modelled by using geometrically exact beams of Simo-type [1]. The microstructural model and the fiber network model are validated against standard measurements of existing papers in the following way: At first we perform tensile and bending tests to measure the macroscopic stress-strain relations. In the next step we apply a representative macroscopic stress or strain onto the boundaries of realizations of the stochastic fiber network model and compute by homogenization the effective (stiffness) coefficients. Finally we compare the numerical results with the measurements. This procedure can also be used for an identification of elastic parameters on the microscale and to study the sensitivity of the effective (macroscopic) stiffness with regard to the parameters of the microstructure

Micromechanical network model for the evaluation of quality controls of paper

ABSTRACT In this paper, we discuss the challenges in modelling and simulating infinitesimal and l... more ABSTRACT In this paper, we discuss the challenges in modelling and simulating infinitesimal and large deformations of cellulose fiber networks, mainly in the context of the prediction of quality controls for paper. Understanding the influence and sensitivity of macroscopic production parameters like grammage and thickness of paperboard and understanding the influence of the fiber suspension on the quality of paper is important for the development of better papers and for preserving raw materials and energy. The new simulation framework consists of the virtual stochastic paper structure generator PaperGeo, that was integrated in the GeoDict 1 software suite, and the finite element solver FeelMath (Finite Elements for Elastic Materials and Homogenization) for solving the equations of elasticity. The fibers and the contacts are modelled by using geometrically exact beams of Simo-type [1]. The microstructural model and the fiber network model are validated against standard measurements of existing papers in the following way: At first we perform tensile and bending tests to measure the macroscopic stress-strain relations. In the next step we apply a representative macroscopic stress or strain onto the boundaries of realizations of the stochastic fiber network model and compute by homogenization the effective (stiffness) coefficients. Finally we compare the numerical results with the measurements. This procedure can also be used for an identification of elastic parameters on the microscale and to study the sensitivity of the effective (macroscopic) stiffness with regard to the parameters of the microstructure

Multi-scale modeling of the macroscopic, elastic mismatch and thermal misfit stresses in metal matrix composites

Composite Structures

ABSTRACT A 3D multiscale method is proposed to model the residual stresses in multiphase material... more ABSTRACT A 3D multiscale method is proposed to model the residual stresses in multiphase materials under the hybrid-semiconcurrent multiscale framework. As an illustration, the quenching residual stresses in SiCp/2124Al composite are modeled. The total residual stresses are separated into the macro, elastic misfit and thermal misfit residual stresses by means of the present multiscale model. In this multiscale model, one macroscale model is connected to two microscale models via scale transition boundary conditions. The predicted total residual strains in the metal matrix and the reinforcing particles coincide with reported experimental data very well. The predicted total, macro, elastic misfit and thermal misfit residual stresses agree reasonably well with the reported experimental ones. The present model provides a new tool to gain a deep insight into the residual stresses in multiphase materials.

Integrationsverfahren zur Galerkin-Randeiementmethode für dreidimensionale Elastizitätsprobleme

Forschung im Ingenieurwesen

Zusammenfassung Für die dreidimensionalen Elastizitätsgleichungen wird eine Lösungsmethode über ... more Zusammenfassung Für die dreidimensionalen Elastizitätsgleichungen wird eine Lösungsmethode über ein System von singulären Integralgleichungen behandelt. Diese Vorgehensweise stellt eine Alternative zur Methode der Finiten Elemente (FE) dar und hat für dreidimensionale Probleme den Hauptvorteil, daß kein FE-Volumennetz, sondern nur ein Oberflächennetz generiert werden muß. Die Integralgleichungen werden mit der Galerkin-Randeiementmethode, die gegenüber der weitverbreiteten Kollokationsmethode mehrere wesentliche Vorteile besitzt, diskretisiert, Gegenwärtig

Einführung in moderne Galerkin-Randeiementmethoden mit einer Anwendung aus dem Maschinenbau

Forschung im Ingenieurwesen

... Die mathematische Theorie ist nicht einfach fbertragbar, so daft beispiels-weise i. allg. die... more

Uploads

Papers by H. Andrä

Log In