Influence of the nonlinear matrix material behaviour on the effective properties of textile-reinforced thermoplastics

For a consistent lightweight design the consideration of the nonlinear macroscopic material behaviour of composites, which is amongst others driven by damage and strain-rate effects on the mesoscale, is required. Therefore, a modelling approach using numerical homogenization techniques is applied to predict the effective nonlinear material behaviour of the composite based on the finite element simulation of a representative volume element (RVE). In this RVE suitable constitutive relations account for the material behaviour of each constituents. While the reinforcing glass fibres are assumed to remain linear elastic, a viscoplastic constitutive law is applied to represent the strain-rate dependent, inelastic deformation of the matrix material. In order to analyse the influence of the nonlinear matrix material behaviour on the global mechanical response of the composite, effective stress-strain-curves are computed for different load cases and compared to experimental observations. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Microstructural behaviour of transversal isotropic material

We discuss and simulate transversal isotropic material under tension loading. The preferential direction of the material is inclined under 45 degrees to the direction of the tensile resultant. In this configuration the deformation of a rectangular test specimen differ from the behaviour of isotropic material in the way, that beside Poissons effect additional displacement appear perpendicular to the tension direction. In classical continuum theories, this transverse deformations describe a typical S–shape. By using a non–local continuum theory, the effect of microstructural orientation is incorporated into the numerical model. Then, it depends on a phenomenological parameter of inner structure whether the energetically favoured configuration is classical or contains microstructural behaviour. In the second case, the transverse deformation is not described by the typical S–shape, but with higher forms of it. A simple experimental model will show the connection between the inner structure of the material and the rotational parameters within the non–local continuum theory. It is evident, that these parameters are responsible for the non–classical behaviour and give the possibility to find energetically favoured solutions. The results of the finite–element–analyses can help to understand constitutive parameters for the non–local continuum theory and to apply it to other specimens. (© 2008 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)     

A material model of nonlinear fractional viscoelasticity

Multiscale methods are frequently used in the design process of textile reinforced composites. In addition to the models for the local material structure it is necessary to formulate appropriate material models for the constituents. While experiments have shown that the reinforcing fibers can be assumed as linear elastic, the material behavior of the polymer matrix shows certain nonlinearities. These effects are mainly due to strain rate dependent material behavior. Fractional order models have been found to be appropriate to model this behavior. Based on experimental observations of Polypropylene a one-dimensional nonlinear fractional viscoelastic material model has been formulated. Its parameters can be determined from uniaxial, monotonic tensile tests at different strain rates, relaxation experiments and deformation controlled processes with intermediate holding times at different load levels. The presence of a process dependent function for the viscosity leads to constitutive equations which form nonlinear fractional differential equations. Since no analytical solution can be derived for these equations, a numerical handling has been developed. After all, the stress-strain curves obtained from a numerical analysis are compared to experimental results. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Nonlinear,finite deformation,finite element analysis

The roles of the consistent Jacobian matrix and the material tangent moduli, which are used in nonlinear incremental finite deformation mechanics problems solved using the finite element method, are emphasized in this paper, and demonstrated using the commercial software ABAQUS standard. In doing so, the necessity for correctly employing user material subroutines to solve nonlinear problems involving large deformation and/or large rotation is clarified. Starting with the rate form of the principle of virtual work, the derivations of the material tangent moduli, the consistent Jacobian matrix, the stress/strain measures, and the objective stress rates are discussed and clarified. The difference between the consistent Jacobian matrix (which, in the ABAQUS UMAT user material subroutine is referred to as DDSDDE) and the material tangent moduli (C^e) needed for the stress update is pointed out and emphasized in this paper. While the former is derived based on the Jaumann rate of the Kirchhoff stress, the latter is derived using the Jaumann rate of the Cauchy stress. Understanding the difference between these two objective stress rates is crucial for correctly implementing a constitutive model, especially a rate form constitutive relation, and for ensuring fast convergence. Specifically, the implementation requires the stresses to be updated correctly. For this, the strains must be computed directly from the deformation gradient and corresponding strain measure (for a total form model). Alternatively, the material tangent moduli derived from the corresponding Jaumann rate of the Cauchy stress of the constitutive relation (for a rate form model) should be used. Given that this requirement is satisfied, the consistent Jacobian matrix only influences the rate of convergence. Its derivation should be based on the Jaumann rate of the Kirchhoff stress to ensure fast convergence; however, the use of a different objective stress rate may also be possible. The error associated with energy conservation and work-conjugacy due to the use of the Jaumann objective stress rate in ABAQUS nonlinear incremental analysis is viewed as a consequence of the implementation of a constitutive model that violates these requirements.     

Modelling of predeformation- and frequency-dependent material behaviour of filled rubber under large predeformations superimposed with harmonic deformations of small amplitudes

Viscoelastic materials show a significant frequency and predeformation dependent behaviour under loadings consisting of large predeformations superimposed by small harmonic deformations. Based on further material models of Haupt & Lion [1] and Lion, Retka & Rendek [2] we introduce a recently developed constitutive approach of finite viscoelasticity in the frequency domain that is able to describe the frequency and predeformation dependent material behaviour with respect to storage and loss modulus. The constitutive equations are geometrically linearised in the neighbourhood of the predeformation and will be evaluated in the frequency domain. Furthermore a formulation for incompressible material behaviour is introduced and the corresponding dynamic modulus tensors are derived. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

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)     

Nonlinear electro-dynamic analysis of micro-actuators: Effect of material nonlinearity

This paper presents a nonlinear dynamic analysis of a micro-actuator made of nonlinear elasticity materials. The theoretical formulations are based on Bernoulli–Euler beam theory and include the effects of mid-plane stretching due to large deformation and material nonlinearity. By employing Linstedt–Poincaré perturbation method, the nonlinear governing equation is transformed into a set of linear differential equations which are then solved using Galerkin’s method. Numerical results show that the linear constitutive relationship used in previous studies is valid for small deformation only whereas for large deformation, the nonlinear elasticity constitutive relationship must be used for accurate analysis. The effects of initial gap and beam length on the nonlinear electro-dynamic behavior of the micro-actuator are also discussed.     

Magnetostrictive actuation of a smart beam with hysteretic material behaviour

Magnetostrictive materials can be used as actuators in smart structures technology. The relation between induced strain and the applied magnetic field is nonlinear and shows hysteretic behaviour. Thus the magnetomechanical coupling coefficient is not constant and should be defined as a function of strain or magnetic field in computations. In this study the hysteresis of a mechanically unconstrained actuator is determined using the Michelson interferometry. The hysteretic behaviour is modelled phenomenologically by a Preisach model. Using these experimental data for the modelling of an active structure with embedded magnetostrictive actuators, the actual coupling coefficient can be determined utilising the Preisach model. With this procedure the actuation strain of an embedded actuator, including the physical nonlinearities, can be calculated using the material characteristics obtained with an unconstrained actuator. For the determination of the actual coupling coefficient a strain- and field-dependent approach is used. For an experimental validation of the method outlined above, a magnetostrictive actuator is characterised experimentally and then applied to a cantilever aluminium beam. Then, the tip displacement of the actuated beam is measured with a laser triangulation sensor and compared with the numerical results. (© 2008 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)     

Molecular static simulations of ferroelectric material hysteresis behaviour

The present contribution deals with molecular static modelling and the simulation of ferroelectric material hysteresis behaviour. Therefore the core-shell model is implemented in a molecular static algorithm. Moreover the algorithm is implemented as a finite element method for nonlinear trusses. Thereby the computational costs are reduced significantly compared to molecular dynamics. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Constitutive modelling of thermo-viscoelastic-plastic behaviour of adhesively bonded joints

For ductile structural adhesives under thermal and mechanical loading, a thermo-viscoelastic-plastic interfacial constitutive model is introduced using a generalised MAXWELL solid in series with a thermal strain element and a ST.-VENANT body with isotropic hardening for plasticity. The temperature dependency of the viscosity is taken into account on assuming thermorheologically simple material behaviour, while the yield threshold and the hardening parameters depend on empirical functions of temperature. Numerical examples for the model verification and validation are discussed. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Computational modeling of shape memory fibers in conforming and non-conforming compound structures

In this work a material model for shape memory alloy (SMA) fibers is presented. A constitutive model is provided which aims for computational use. The presented model incorporates all relevant material nonlinear phenomena. It takes pseudoplasticity into account as well as pseudoelasticity and further the shape memory effect (SME). The constrained SME (CSME) and the two-way SME are covered by the presented material model. The constitutive model is implemented in a one-dimensional truss formulation and in a 3D-rebar element. Both formulations are used to model fiber composite structures. Those are described by the use of a non-conforming and a conforming mesh on the mesoscale. The numerical examples show the capability of the formulation. Different meshing strategies for the fiber–matrix compound are discussed. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Finite Element Models of Hyperelastic Materials Based on a New Strain Measure

To construct constitutive equations for hyperelastic materials, one increasingly often proposes new strain measures, which result in significant simplifications and error reduction in experimental data processing. One such strain measure is based on the upper triangular (QR) decomposition of the deformation gradient. We describe a finite element method for solving nonlinear elasticity problems in the framework of finite strains for the case in which the constitutive equations are written with the use of the QR-decomposition of the deformation gradient. The method permits developing an efficient, easy-to-implement tool for modeling the stress–strain state of any hyperelastic material.     

Identification of optimal material models and parameters in finite strain plasticity

The numerical simulation of the behaviour of a workpiece during manufacturing depends to a large extent on the quality of the applied material model. In this work, a method for the identification of constitutive models and material parameters in engineering applications is proposed. The presented method is used in the setting of optimal experimental design and is based on successive optimization of a set of finite strain plasticity models with kinematic and/or isotropic hardening. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

An energetic material model for time‐dependent ferroelectric behaviour: existence and uniqueness

We discuss rate‐independent engineering models for the multi‐dimensional behaviour of ferroelectric materials. These models capture the non‐linear and hysteretic behaviour of such materials. We show that these models can be formulated in an energetic framework which is based on the elastic and the electric displacements as reversible variables and on interior, irreversible variables like the remanent polarization. We provide quite general conditions on the constitutive laws which guarantee the existence of a solution. Under more restrictive assumptions we are also able to establish uniqueness results. Copyright © 2006 John Wiley & Sons, Ltd.     

Application of a viscoplastic material model on a combined quasi-static-electromagnetic forming process

The prediction and simulation of material behavior by finite element methods has become indispensable. Furthermore, various phenomena in forming processes lead to highly differing results. In this work, we have investigated the process chain on a cross-shaped cup in cooperation between the Institute of Applied Mechanics (IFAM) of the RWTH Aachen and the Institute of Forming Technology and Lightweight Construction (IUL) of the TU Dortmund. A viscoplastic material model based on the multiplicative decomposition of the deformation gradient in the context of hyperelasticity has been used [1,2]. The finite strain constitutive model combines nonlinear kinematic and isotropic hardening and is derived in a thermodynamically consistent setting. This anisotropic viscoplastic model is based on the multiplicative decomposition of the deformation gradient in the context of hyperelasticity. The kinematic hardening component represents a continuum extension of the classical rheological model of Armstrong-Frederick kinematic hardening. The constitutive equations of the material model are integrated in an explicit manner and implemented as a user material subroutine in the commercial finite element package LS-DYNA with the electromagnetical module. The aim of the work is to show the increasing formability of the sheet by combining quasi-static deep drawing processes with high speed electromagnetic forming. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Representation of the linear viscoelastic behaviour of wood with a constitutive theory based on fractional time derivatives

Like many other materials used in mechanical and civil engineering, wood shows a pronounced history-dependent mechanical material behaviour. Due to its anisotropy its rheological behaviour is strongly dependent on the direction. In this research project, the material behaviour is represented with a phenomenological theory of anisotropic fractional viscoelasticity. In order to identify the material functions and parameters, the time-dependent creep compliances are measured in three orthogonal directions under tension and shear. As a result of the developed constitutive approach, the experimentally observed creep data is described by several power functions. In the second part of the presentation, some differences between classical models of viscoelasticity which are based on Kelvin-Voigt or Maxwell elements and the fractional approach are presented. The assets and drawbacks with respect to wood are discussed. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The influence of the filler volume fraction on the mechanical behaviour of thermoplastic materials

Uniaxial experiments clarify that the mechanical behaviour of PTFE compounds depends strongly on the amount of filler particles. In order to describe these dependencies, a finite endochronic viscoplastic material model based on material isomorphisms has been applied to various glass fibre filled PTFE compounds. The model allows to characterize viscoplastic material behaviour with equilibrium hysteresis using a rate‐independent endochronic elastoplastic model in parallel connection with a nonlinear Maxwell model. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)