Microscale modeling and homogenization of rope-like textiles

This contribution deals with rope-like textiles. On the macroscopic level rope-like textiles are characterized by a large length-to-thickness ratio, such that a discretization with beam elements is numerically efficient. To capture the contact behavior the representative volume element is explicitly modeled by means of a volumetric micro sample. A suitable, beam-specific FE₂ method is developed, which connects the homogeneous macro level to a fiber structured micro sample. This contribution investigates the determination of the nonlinear constitutive behavior of rope-like textiles. Selected examples for the macroscopic behavior of microscopic heterogeneous fiber structured materials are presented. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Homogenization of random elastic networks with non-affine kinematics

This contribution concerns the mechanics of materials with random network microstructures. It develops a general homogenization approach that allows to link the microscopic deformation of fibers in the disordered network with the macroscopic response of the continuous solid. This link is established by a novel micro-macro relation based on the kinematics of maximal advance paths that constrains the unknown microscopic stretch of fibers with respect to the macroscopic strain. This relation accounts for the topology of the network, in particular, its connectivity and takes for the tetrafunctional networks a clearly interpretable tensorial form. In line with the principle of the minimum averaged free energy the elastic response of the network is obtained by the relaxation of the variable fiber stretch subjected to the kinematic constraint. (© 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)     

On the simulation of textile reinforced composites and structures

This paper presents experimental and numerical methods to perform simulations of the mechanical behavior of textile reinforced composites and structures. The first aspect considered refers to the meso-to-macro transition in the framework of the finite element (FE) method. Regarding an effective modelling strategy the Binary Model is used to represent the discretized complex architecture of the composite. To simulate the local response and to compute the macroscopic stress and stiffness undergoing small strain a user routine is developed. The results are transfered to the macroscopic model during the solution process. The second aspect concerns the configuration of the fiber orientation and textile shear deformation in complex structural components. To take these deformations which affect the macroscopic material properties into account they are regarded in a macroscopic FE model. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Theoretical study and numerical simulation of textiles

We propose a new approach for developing continuum models fit to describe the mechanical behavior of textiles. We develop a physically motivated model, based on the properties of the yarns, which can predict and simulate the textile behavior. The approach relies on the selection of a suitable topological model for the patch of the textile, coupled with constitutive models for the yarn behavior. The textile structural configuration is related to the deformation through an energy functional, which depends on both the macroscopic deformation and the distribution of internal nodes. We determine the equilibrium positions of these latter, constrained to an assigned macroscopic deformation. As a result, we derive a macroscopic strain energy function, which reflects the possibly nonlinear character of the yarns as well as the anisotropy induced by the microscopic topological pattern. By means of both analytical estimates and numerical experiments, we show that our model is well suited for both academic test cases and real industrial textiles, with particular emphasis on the tricot textile.     

Some Basic Ideas for the Simulation of Wave Propagation in Microstructures using Proper Orthogonal Decomposition

For the modeling of micro-heterogeneous materials, models are required that take into account the microstructure. More and more, computational homogenization is used to quantify the effective macroscopic response. The large number of resulting microscopic boundary value problems need to be solved efficiently. To reduce the computational effort and simulation time, model reduction methods may be applied. In this contribution the performance of the proper orthogonal decomposition is analyzed for the wave propagation in fiber reinforced materials. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modeling of the effective viscoelastic material behavior of textile reinforced composites using a multi-scale approach

The increasing importance of constructive lightweight in modern engineering science involves the use of advanced materials like textile reinforced composites. In order to reduce development costs, efficient numerical simulations are needed to model the macroscopic behavior of the final product. Focussing on long term phenomena, which are important when parts made of composites with rate-dependent material behavior are assembled by bolted or screwed joints, a two-step homogenization procedure is used to obtain an effective homogeneous equivalent material at the macroscopic scale. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Homogenization for contact problems with friction on rough interface

We consider a contact problem between a macroscopic solid with a smooth boundary and a technical textile, while the textile has a periodic microscopic structure and microscopically rough surface. Two–scale homogenization approach is applied to the problem. The microscopic solution is approximated in terms of macroscopic solution and some concentration factor, given as a solution of auxiliary boundary value or contact problems of elasticity on the periodicity cell. Local friction condition is represented as a continuous non–linear functional over the stress field. Two–scale convergence is used to prove the convergence of friction functional. The macroscopic initial frictional limit is found. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the simulation of textile reinforced concrete using a multi scale approach

Textile reinforced concrete (TRC) is a composite of textile structures made of multi-filament yarns (rovings) within a cementitious matrix. Experimental investigations of textile reinforced concrete specimen show very complex failure mechanisms on different length scales. Therefore mechanical models on the micro, meso and macro scale are introduced. The paper presents a hierarchical material model of TRC on three scales. While on the micro scale the individual filaments of the fiber bundles are distinguished to determine an effective roving behavior, models on the meso scale are used to predict the macroscopic response of the composite material. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A Microscopic model for a cell-seeded material

The aim of the present paper is to account for the growth of fiber which is observed in a cell-seeded material stimulated in a bioreactor. For this purpose, the change of mass is considered in the balance laws, and the deformation energy is assumed to be a function of varying mass and the Helmholtz free-energy. Fiber growth at the microscopic level causes a macroscopic change of the material's mechanical properties. The study is a first approach towards a micromechanical model accounting for remodelling in cartilage replacement materials. In so doing, constitutive equations for renewable soft tissues are proposed. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numerical homogenization of foam-like structures based on the FE2-approach

The computation of foam–like structures is still a topic of research. There are two basic approaches: the microscopic model where the foam–like structure is entirely resolved by a discretization (e.g. with Timoshenko beams) on a micro level, and the macroscopic approach which is based on a higher order continuum theory. A combination of both of them is the FE²-approach where the mechanical parameters of the macroscopic scale are obtained by solving a Dirichlet boundary value problem for a representative microstructure at each integration point. In this contribution, we present a two–dimensional geometrically nonlinear FE²-framework of first order (classical continuum theories on both scales) where the microstructures are discretized by continuum finite elements based on the p-version. The p-version elements have turned out to be highly efficient for many problems in structural mechanics. Further, a continuum–based approach affords two additional advantages: the formulation of geometrical and material nonlinearities is easier, and there is no problem when dealing with thicker beam–like structures. In our numerical example we will investigate a simple macroscopic shear test. Both the macroscopic load displacement behavior and the evolving anisotropy of the microstructures will be discussed. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Computational Multi-Scale Stability Analysis of Periodic Electroactive Polymer Composites at Finite Strains

This work is dedicated to multi-scale stability analysis, especially macroscopic and microscopic stability analysis of periodic electroactive polymer (EAP) composites with embedded fibers. Computational homogenization is considered to determine the response of materials at macro-scale depending on the selected representative volume element (RVE) at micro-scale [4, 5]. The quasi-incompressibility condition is considered by implementing a four-field variational formulation on the RVE, see [7]. Based on the works [1–3, 6, 8] the macroscopic instabilities are determined by the loss of strong ellipticity of homogenized moduli. On the other hand, the bifurcation type microscopic instabilities are treated exploiting the Bloch-Floquet wave analysis in context of finite element discretization, which allows to detect the changed critical size of periodicity of the microstructure and critical macroscopic loading points. Finally, representative numerical examples are given which demonstrate the onset of instability surfaces, the stable macroscopic loading ranges, and further a periodic buckling mode at a microscopic instability point is presented. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Finite element (FE) simulation of textile-reinforced composites using a COSSERAT Element

The efficient simulation of textile reinforced composites requires reliable material parameters describing the macroscopic material behavior. Due to the micro–structure, decoupled tensile and bending stiffnesses are observed in experimental investigations. This motivates the use of higher order continuum theories. For numerical simulation of this material behavior, the formulation and application of a volume element based on the Cosserat continuum theory is presented. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Cross-linked actin networks: Micro- and macroscopic effects

Actin plays a crucial role in the mechanical response of cells. Together with other proteins, it also drives protrusion, motility and cell division. Two important aspects of the mechanical modeling of this kind of protein are considered: its microscopic and macroscopic behavior. At the microscopic level, we start with a model proposed by Holzapfel and Ogden [1] providing a relationship between the stretch of a single polymer chain and the applied tension force. The model is advantageous as it simulates the so-called ‘exceptional normal stresses’. This effect is typical for biopolymers and contradicts with the Poynting effect typically observed in rubber-like polymers. The multiscale finite element method (FEM) is applied to simulate the effective mechanical behavior of cell cytoplasm. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Optimization of piezoelectric fiber distribution in composite smart materials

A new approach to obtain macroscopic properties of fiber‐matrix composite materials is given by the optimization of the fiber distribution for a given pair of materials. The optimization was carried out by Evolution Strategies using an interface to the finite‐element‐software ANSYS. To cover the effects of varied micro level parameters, a homogenization algorithm was included in the optimization process. Two applications verify the correct implementation of the software. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Linking macroscopic deformation processes to microstructure evolution using an FE-FFT-based micro-macro transition and non-conserved phase-fields

The purpose of this work is the multiscale FE-FFT-based prediction of macroscopic material behavior, micromechanical fields and bulk microstructure evolution in polycrystalline materials subjected to macroscopic mechanical loading. The macroscopic boundary value problem (BVP) is solved using implicit finite element (FE) methods. In each macroscopic integration point, the microscopic BVP is embedded, the solution of which is found employing fast Fourier transform (FFT), fixed-point and Green's function methods. The mean material response is determined by the stress-strain relation at the micro scale or rather the volume average of the micromechanical fields. The evolution of the microstructure is modeled by means of non-conserved phase-fields. As an example, the proposed methodology is applied to the modeling of stress-induced martensitic phase transformations in metal alloys. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)