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)     

Direct connection of rheological elements at large strains: Application to multiplicative viscoplasticity

In the field of nonlinear continuum mechanics, rheological models are often used to exemplify the structure of complex material models at large strains. For this purpose, different rheological elements are combined in series and parallel connections. Ihlemann [1] developed an innovative concept, which enables the direct connection of rheological elements within the framework of multiplicative decomposition of the deformation gradient. In the contribution at hand, this approach is applied to multiplicative viscoplasticity. Towards this end, the relations for parallel and series connections are introduced and several individual material models, i.e. the rheological elements, are defined. By analytical and numerical evaluation of the connection relations, a viscoplastic material model from the literature is reproduced. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

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)     

Modelling of composite plates including damage

The paper is concerned with the modelling and numerical simulation of fibre-composite plates in the nonlinear range due to large strains and damage. The layer-wise approach is applied. Each layer is treated as elastic-brittle and assumed to be orthotropic in the local material coordinate system. The appearance of damage is controlled according to the failure criteria [1,2,3,4]. When the failure condition is satisfied, the mechanical properties of the material are modified appropriately, depending on the type of damage (fibre breakage, matrix crack, fibre-matrix shear). We have programmed the model as a user subroutine within the ABAQUS environment and carried out a number of numerical simulations. The obtained numerical results are compared with the experimental data available in the literature [3]. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Simulation of micro-cutting considering finite deformation crystal plasticity

Micro-machining processes on metalic microstructures are influenced by the crystal structure, i. e. the grain orientation. Furthermore, the chip formation underlies large deformations. To perform finite element simulations of micro-cutting processes, a large deformation material model is necessary in order to model the hyperelastic and finite plastic material behaviour. In the case of cp-titanium material with hcp-crystal structure the anisotropic behaviour must be considered by an appropriate set of slip planes and slip directions. In the present work the impact of the grain orientation on the plastic deformation is demonstrated by means of finite element simulations of a finite deformation single slip crystal plasticity model. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the direct connection of rheological elements in nonlinear continuum mechanics

The structure of complicated phenomenological material models at finite strains is often exemplified with the help of rheological elements. Thereby, simple material behaviour, i.e. elasticity or viscous and plastic flow, are composes by components. In our approach, we directly apply this concept to obtain material models at finite strains. Towards this end, the thermodynamically consistent material behaviour of single elements is defined first. Subsequently, the elements are connected by evaluation of stress equilibria equations formulated on interconnecting configurations. The basic equations of this concept are presented using the example of nonlinear viscoelasticity of Maxwell type. The model results from a series connection of an elastic and a viscous element, whereas both are formulated in a thermodynamically consistent way within the framework on nonlinear continuum mechanics. Furthermore, an approach of numerical implementation using the stress equilibria is suggested. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Evaluation of self-activating temperature influence on cracks initiation in GRP laminates

The paper deals with problems of fatigue processes of GRP laminates under the influence of cyclic loads. An important aspect which takes place in laminate fatigue with polymer matrix is self-activating temperature generated by friction. As it has been shown in previous authors' research, the phenomenon has significant influence on laminate behavior, also, when self-activating temperature comes to glass-transition temperature, which begins transition from elastic to viscoelastic material model. After passing over of this temperature the stiffness decreasing is supervised, that can lead to more quick propagation of faults (especially delaminations) and decreasing of life cycle of composite laminate element. The aim of the presented paper is simulation research of fatigue processes with taking into consideration self-activating temperature and rheology of material. In the research four cases are analyzed, in which layers rotation, self-activating temperature increasing and changes of rheological model were taken into consideration. As the research shows, the self-activating temperature has significant influence on fatigue processes, because it can cause transition of the rheological model of the material. In the future research an experimental verification of the model is planned. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The effect of interphase on residual thermal stresses. 2. Unidirectional fiber composite materials

In real composite materials an additional phase may exist between the fiber and the matrix. This phase, commonly known as the interphase, is a local region that results from the matrix bonds with the fiber surface or the fiber sizing. The differing thermal expansions or contractions of the fiber and matrix cause thermally induced stresses in composite materials. In the present study, a four-cylinder model is proposed for the determination of residual thermal stresses in unidirectional composite materials. The elastic modulus of the interphase is a function of the interphase radius and thickness. The governing equations in terms of displacements are solved in the form of expansion into a series [1]. The effective elastic characteristics are obtained using the finite element approach. The effect of the interphase thickness and different distributions of the interphase Young's modulus on the thermal residual stress field in unidirectional composite materials is investigated.For Pt. 1, see [1].Published in Mekhanika Kompozitnykh Materialov, Vol. 33, No. 2, pp. 200–214, March–April, 1997.     

Deep drawing of a layered composite: material characterization and finite-element simulation

Composite materials are widely used in different industrial fields, because of their good formability and their high strength to weight ratio. In the present work a triple-layered sandwich composite is investigated. Experimental tests at room temperature are carried out for the materials constituting the composite. A finite element model of a deep-drawing process of the composite is performed, where a finite strain constitutive model for the metal part, with material parameters calibrated to uniaxial tensile tests, has been implemented. Experimental results are compared to the numerical simulations in view of validation purposes. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the h-adaptive coupling of FE and BE for viscoplastic and elasto-plastic interface problems

This paper presents a posteriori error estimates for the symmetric finite element and boundary element coupling for a nonlinear interface problem: A bounded body with a viscoplastic or plastic material behaviour is surrounded by an elastic body. The nonlinearity is treated by the finite element method while large parts of the linear elastic body are approximated using the boundary element method. Based on the a posteriori error estimates we derive an algorithm for the adaptive mesh refinement of the boundary elements and the finite elements. Its implementation is documented and numerical examples are included.     

On dynamic finite element analysis of viscoplastic thin-walled structures with non-local damage

In this article we propose a non-local damage model for dynamic finite element computation of viscoplastic thin-shell structures. To take void nucleation and growth into account, the free energy function is enhanced phenomenologically in terms of a non-local damage variable and its gradient on the mid-surface of shell structures. The dynamic thin-shell elastic theory including large rotations proposed by Simo and Tarnow (1994) is used to capture finite deformation. Local constitutive laws considering viscoplastic behaviour, isotropic hardening and isotropic ductile damage leading to softening in Velde et al. (2009) are employed. The performance of the proposed approach is demonstrated through the preliminary numerical simulations of shock-wave loaded structures, which are validated by comparision with the experimental results. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A finite element model based on statistical two-scale analysis for equivalent heat transfer parameters of composite material with random grains

In this paper, a new finite element model based on statistical two-scale analysis for predicting the equivalent heat transfer parameters of the composite material with random grains is presented and its convergence, its error result and the symmetry, positive property of equivalent heat transfer parameters matrix are also proved. Firstly, some definitions of the probability space and the composite material with random grains are described and the STSA formulation predicting the equivalent heat transfer parameters of the composite material are briefly reviewed. Next, a finite element formulation and its corresponding procedure for the composite material with random grains is described. Then, the convergence, the error estimate and the symmetry, positive property of the equivalent heat transfer parameters matrix computed by FE based on STSA are proved. The numerical result shows the validity of the FE model based on STSA and the convergence and the symmetry, positive property of the equivalent heat transfer parameter matrix of the composite material with random grains by the FE model.     

A Finite Deformation Microsphere Model for Magneto-Visco-Elastic Response in Magnetorheological Elastomers

In this work we present a novel approach to the modeling of magnetorheological elastomers (MREs) for finite deformations. Keeping in mind the composite nature at the microscale, we employ the microsphere model as an effective tool to capture the constitutive response of the material. The microsphere model has been successfully applied to the modelling of rubber-like materials. Here, we extend this approach by taking into account the effect of the magnetic dipole-dipole interactions on the orientation of the polymer chains. Thus, the presented microsphere model is directly motivated by considering the underlying phenomena at the microscale level. Finally the material model is embedded in a finite element framework and the results of a boundary value problems is presented. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Influence of structural hypotheses on the elastic-viscoplastic response of shock wave-loaded plates

If circular metal plates are subjected repeatedly to impulsive loadings, damage and failure of the structures can occur. In order to predict the damage evolution in finite element simulations, a structural theory combined with viscoplastic constitutive equations acounting for damage is used. However, different structural hypotheses, used in the theoretical model, can lead to variations in the numerical result. Therefore, first- and third-order shear deformations theories are applied in a finite element code. Moreover, local and non-local damage approaches are used. The aim is to determine the numerical model, which leads to the most accurate results compared to experiments. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On three-dimensional fibrous flaws in unidirectional fibre reinforced elastic composites

This paper examines the problem of the stress concentration at a flaw in a unidirectional fibre reinforced composite. The geometry of the flaw corresponds to a spheroidal region in which the reinforcing fibres exhibit continuity across the flaw surface. The composite containing the flaw is subjected to a uniaxial stress field which acts along the fibre direction. An exact solution is devoloped for the stress concentration factor at the reinforced flaw boundary. Typical numerical results presented in the paper illustrate the manner in which the stress concentration at the bridged flaw is influenced by the fibre volume fraction, the fibre-matrix modular ratio and the flaw geometry.     

Computation of the effective nonlinear material behaviour of composites using X-FEM - Analysis of the matrix material behaviour

For a consequent 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, the modelling approach using numerical homogenization techniques based on the simulation of representative volume elements which are modelled by the extended finite element method (X–FEM) is currently extended to nonlinear material behaviour. While the glass fibres are assumed to remain linear elastic, a viscoplastic constitutive law accounts for strain–rate dependence and inelastic deformation of the matrix material. This paper describes the process of finding suitable constitutive relations for the polymeric matrix material Polypropylene in the small–strain regime. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modeling of thermal response and ablation in laminated glass fiber reinforced polymer matrix composites due to lightning strike

Thermal response and ablation of laminated glass fiber reinforced polymer matrix composites subjected to lightning strike are studied. The associated nonlinear time-dependent heat transfer model includes specific features of lightning arcs observed in physical measurements such as lightning channel radius expansion, non-uniform lightning current density, and associated heat flux. Moving spatially and temporally non-uniform lightning-current-induced heat flux boundary and moving boundary due to material phase transition caused by rapid surface ablation are also included. To predict moving phase boundary in the laminated anisotropic composites, an element deletion method is developed and embedded into finite element analysis (FEA), which is performed using ABAQUS. The Umeshmotion + ALE method based on the user subroutine Umeshmotion and arbitrary Lagrangian–Eulerian (ALE) adaptive mesh technique is also used, when applicable (i.e., moving phase boundary is confined within a top layer of the composite laminate). Heat transfer analysis is performed for a non-conductive laminated glass fiber reinforced polymer matrix composite panel representing the SNL 100-00 wind turbine tip. Thermal response of the panel subjected to pulsed and continuing lightning currents at three different lightning protection levels, LPL I, LPL II, and LPL III, is studied. Temperature-dependent anisotropic thermal properties of the composite panel are included in the analysis. The FEA results include temperature distributions and ablation zone profiles. The results show the Umeshmotion + ALE method is sufficient for the pulsed lightning current at all three LPL levels since the moving phase boundary, i.e. the ablation front, is found to be confined within the top layer of the laminate. For the continuing lightning currents at all three LPL levels, the Umeshmotion + ALE method is not applicable since the moving phase boundary comes to rest at depths exceeding the thickness of the top layer of the composite laminate.     

Experimental and Numerical Study of Polypropylene/Polyethylene Thin Foil in Biaxial Tension

The material under consideration is a thermoplastic copolymer blend of polypropylene and polyethylene (PP/PE), constituting the core layer of a steel/polymer/steel composite material. A biaxial loading machine was developed for studying the behavior of the copolymer subjected to in-plane complex stress states. A study on the shape of the specimen by means of numerical finite element simulations and preliminary experimental tests are carried out, in order to obtain a maximization of the strain distribution in the middle region of the cruciform specimen. Afterwards, the sensitivity of the mechanical response under both equibiaxial and non-equibiaxial conditions is addressed. All the experiments are monitored by means of a digital image correlation (DIC) system, providing full-field measurements of the displacements, and, consequently, of the strain distribution. The presented experimental results will be used for validating the material model developed for the PP/PE layer material. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Estimation of the macroscopic stress-strain curve of a particulate composite with a crosslinked polymer matrix

The main focus of the present paper is the estimation of the macroscopic stress–strain behavior of a particulate composite. A composite with a cross-linked polymer matrix in a rubbery state filled with an alumina-based mineral filler is investigated by means of the finite-element method. The hyperelastic material behavior of the matrix is described by the Mooney–Rivlin material model. Numerical models on the basis of unit cells are developed. The existence of a discontinuity (breaking) in the matrix at higher loading levels is taken into account to obtain a more accurate estimate for the stress–strain behavior of the particulate composite investigated. The numerical results obtained are compared with an experimental stress–strain curve, and a good agreement is found to exist. The paper can contribute to a better understanding of the behavior and failure of particulate composites with a polymer matrix.     

Dynamic analysis of functionally graded nanocomposite beams reinforced by randomly oriented carbon nanotube under the action of moving load

This work deals with a study of the vibrational properties of functionally graded nanocomposite beams reinforced by randomly oriented straight single-walled carbon nanotubes (SWCNTs) under the actions of moving load. Timoshenko and Euler-Bernoulli beam theories are used to evaluate dynamic characteristics of the beam. The Eshelby-Mori-Tanaka approach based on an equivalent fiber is used to investigate the material properties of the beam. An embedded carbon nanotube in a polymer matrix and its surrounding inter-phase is replaced with an equivalent fiber for predicting the mechanical properties of the carbon nanotube/polymer composite. The primary contribution of the present work deals with the global elastic properties of nano-structured composite beams. The system of equations of motion is derived by using Hamilton’s principle under the assumptions of the Timoshenko beam theory. The finite element method is employed to discretize the model and obtain a numerical approximation of the motion equation. In order to evaluate time response of the system, Newmark method is also used. Numerical results are presented in both tabular and graphical forms to figure out the effects of various material distributions, carbon nanotube orientations, velocity of the moving load, shear deformation, slenderness ratios and boundary conditions on the dynamic characteristics of the beam. The results show that the above mentioned effects play very important role on the dynamic behavior of the beam and it is believed that new results are presented for dynamics of FG nano-structure beams under moving loads which are of interest to the scientific and engineering community in the area of FGM nano-structures.