Opportunities and challenges for textile reinforced composites

For several decades researchers have been interested in textile processes for the production of composite reinforcement. These technologies have offered several promises: reduced fabrication costs, 3-D multiaxial reinforcement, and damage tolerance. Despite these advantages, textile composites have not reached the level of implementation of laminated composites. In this paper, the opportunities provided by textile reinforced composites and the challenges that limit their implementation will be discussed in detail. Textile composites refer to a family of processes: weaving, braiding, knitting, and hybrids thereof. The various families of textiles will be defined and the basics of fabric formation for each family will be detailed. In particular, the strengths and weaknesses of each manufacturing technique will be addressed to provide a view of the applicability of each technology. This will include some guidance on shape formation capability, property ranges, size limitations, and estimates of cost to produce. Potential applications for these materials will be presented. Among the limitations on the application of textile reinforced composites is the lack of adequate modeling capabilities for these materials. Textile composites have rather large unit cell structures and are highly inhomogeneous throughout their volumes. These features provide benefits in manufacturing, but require novel modeling techniques to correctly understand the mechanical behavior. A review of analytical techniques applied to textile composites will be presented along with a discussion of the benefits and weaknesses of each of these methods. The enabling technologies needed to further the implementation of textile composites in structural applications will be discussed. Submitted to the 11th International Conference on Mechanics of Composite Materials (Riga, June 11–15, 2000). Published in Mekhanika Kompozitnykh Materialov, Vol. 36, No. 2, pp. 165–194, March–April, 2000.     

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)     

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)     

Two-scale computational homogenization of magneto-electric composites

This contribution presents a two-scale computational homogenization framework for the micro-macro simulation of magneto-electro-mechanically coupled materials. Energetically consistent micro-macro transition conditions will be derived from a generalized form of the classical Hill-Mandel condition. A focus of the work is on the computation of effective magneto-electric moduli which are derived on the basis of an algorithmically consistent linearization of the macroscopic field equations. The method will be applied to the homogenization of magneto-electric composites which are composed of piezomagnetic and piezoelectric phases. The effective magneto-electric moduli of two-phase composites will be computed. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numerical aspects on computational homogenization of epoxy/glass composites

Numerical aspects of two-scale modeling of epoxy/glass composites are presented. The homogenization process is carried out under consideration of periodic boundary constraints (PBC) of the representative volume element (RVE) due to the periodic structure of glassfiber reinforced epoxy systems. The introduction of artificial constraints for computing macro-stresses and macro-moduli is presented by giving the modified algorithmic treatment of a two-scale approach using PBC. The proposed algorithm is applied to an ISO 527 epoxy/glass test specimen. The results of computations considering or not considering interphases and interfaces within the composite are compared. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Nonlinear homogenization of metal-ceramic composites with lamellar microstructure

Using nonlinear homogenization methods for the computation of the material response of metal-ceramic composites with lamellar microstructure is a power approach to do computation less costly in comparison to finite elements modeling. A modified secant homogenization method is utilized in this study for simulation of inelastic behaviors of the composite micro-constituents. A nonlinear homogenization method is based on a linear homogenization scheme for multilayer composites. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the spectrum of stiffness matrices arising from isogeometric analysis

We study the spectral properties of stiffness matrices that arise in the context of isogeometric analysis for the numerical solution of classical second order elliptic problems. Motivated by the applicative interest in the fast solution of the related linear systems, we are looking for a spectral characterization of the involved matrices. In particular, we investigate non-singularity, conditioning (extremal behavior), spectral distribution in the Weyl sense, as well as clustering of the eigenvalues to a certain (compact) subset of \(\mathbb C\) . All the analysis is related to the notion of symbol in the Toeplitz setting and is carried out both for the cases of 1D and 2D problems.     

Long-term strength of reinforced composites

Conclusion A criterion of long-term strength was proposed for composite materials. The criterion can be used to calculate time to failure for arbitrary loading programs. It was shown that the criterion provides for good agreement with the experimental data not only in the cases of instantaneous and long-term static loadings, but also for fatigue loading in tension, in compression, and in mixed regimes with different asymmetry coefficients.Translated from Mekhanika Kompozitnykh Materialov, No. 1, pp. 16–22, January–February, 1989.     

Application of domain decomposition methods to isogeometric analysis

During the past decade various new spatial discretization techniques have been developed. In particular, the usage of NURBS based shape functions, well known to the CAD community, has been adapted to finite element technology. In the present work we use the mortar finite element method for the coupling of nonconforming discretized sub-domains in the framework of nonlinear elasticity. We show that the method can be applied to isogeometric analysis with little effort, once the framework of NURBS based shape functions has been implemented. Furthermore, a specific coordinate augmentation technique allows the design of an energy-momentum scheme for the constrained mechanical system under consideration. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the macroscopic material behaviour of textile reinforced concrete undertensile loading

This paper concerns with the development of the macroscopic material behaviour of textile reinforced concrete (TRC) using an analytical approach. Therefore the heterogeneous structure of TRC is modelled on the mesoscopic level. The overall material behaviour on the macroscopic level is obtained by means of the homogenisation technique. The analytical approach is based on the micro mechanical solution for a single inclusion according to Eshelby . In extension of this solution for multidirectional reinforced concrete an effective field approximation is used. This approach considers the interactions between the different orientated rovings and the micro cracks in an average sense. For the mechanical modelling of the bond behaviour between roving and matrix after initiating of the macro cracking a slip based bond model with a multiple linear shear stress-slip relation is used. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Fiber waviness in textile composites and its stochastic modeling

A generic stochastic theory of composite materials with continuous, randomly curved (imperfect) fiber reinforcements, recently developed by the present authors, enables one to quantify the effect of fiber deviations from the assumed perfect paths. The theory of random functions and stochastic extension of the orientational averaging approach are utilized to evaluate the mean values and standard deviations of the full set of anisotropic stiffness characteristics. The major advantage of this novel stochastic approach is its applicability to practically any fiber reinforcement architecture, from unidirectional to multidirectional, 3-D woven, and braided composites. Importantly, the approach does not ask for exact quantification of the reinforcement imperfections, but needs only a limited knowledge of the mean path of the reinforcement and standard deviation of the local tangent. Numerical examples illustrating applications of the stochastic theory developed consider three types of composites having (i) unidirectional, (ii) biaxial, 2-D braided, and (iii) 3-D orthogonally woven reinforcements. The first example concerns validation of the model. The second example is selected due to the commonly observed significant randomness of the fiber architecture in biaxially braided composite shell elements. The third example illustrates the effect of Z-yarn waviness (illustrated by optical microscopy) in orthogonally woven composites on their elastic characteristics.     

Mean and full field homogenization of artificial long fiber reinforced thermoset polymers

Based on two artificial microstructures representing a long fiber reinforced thermoset material, the effective linear elastic material properties are calculated by both a mean and a full field homogenization method. Concerning the mean field method, the effective elastic material properties are approximated using the homogenization scheme by Mori and Tanaka, formulated explicitly in terms of orientation averages. This allows to use orienation tensors of 2nd and 4th order describing the orientation information on the micro level. The full field method is based on the fast Fourier transformation (FFT), for which the effective material properties are determined by volume averaging. The comparison between both methods show good agreements, the deviations are in the range between 2% and 12%. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Creep of orthogonally reinforced spherofibrous composites

Models of composites with three-dimensional structure, a proposed problem solving method, and Rabotnov's creep operators were used assuming purely elastic deformation of the composite along the orientation of the fibers to determine the viscoelastic properties of composites on inclined surfaces in a three-dimensional stressed state. The formulas used in viscoelasticity theory in the elastic region of component deformation lead to results in satisfactory accord with the reported experimental elastic properties of composites with three-dimensional structure.A. A. Blagonravov Mechanical Engineering Institute, Russian Academy of Sciences, Moscow. Translated from Mekhanika Kompozitnykh Materialov, Vol. 32, No. 6, pp. 780–786, November–December, 1996.