Complex Material Behavior Research Articles

Investigation on the Elastic Modulus of Rubber-Like Materials by Straight Blade Indentation Using Numerical Analysis

The indentation technique has been proven to be useful in determining mechanical properties of materials, but it is rarely applied to rubber-like materials (elastomers). It is difficult to describe accurately the mechanical properties of an elastomer by theoretical formulation due to its complex material behaviour. Indentation of a Styrene Butadiene Rubber (SBR-0) material by a rigid straight blade with a tip angle of 45 and 60 degrees was performed to estimate the elastic modulus. Indentation was carried out numerically by finite element analysis (FEA) and for the elastomer the hyper-elastic material model of Mooney-Rivlin is used. The estimated elastic modulus was calculated based on the contact depth. The predicted result was also verified by tensile test results. It was found that the predicted elastic modulus of the elastomer agrees with the tensile test result.

Understanding Ionomer in Fuel-Cell Catalyst Layers

One of the keys to optimizing polymer-electrolyte-fuel-cell performance is understanding it’s transport phenomena. This is especially critical in the polymer electrolyte in both the bulk and in particular the catalyst layers, where it exists as thin, nanometer-thick film covering the catalyst agglomerates. In these structures, it is known to perhaps inhibit performance, especially as the total platinum content is reduced. Interactions of the membrane with the local environment and as a thin film within the CL result in highly complex material behavior that is highly dependent on the environmental conditions, ionomer thickness, and the material interactions, e.g., carbon, platinum, etc. Thus, characterization of the role of ionomer in fuel-cell catalyst layers requires understanding the transport properties and water-uptake behavior throughout a wide thickness range. In this talk, the role of the ionomer and its underlying structure/function relationships will be elucidated. Ex-situ testing of the catalyst-layer ionomer demonstrates reduced water content for both Nafion and the short-side-chain, lower equivalent weight 3M ionomer. These studies are complemented by thin-film structural and swelling measurements using x-ray scattering and ellipsometry, respectively, which likewise show reduced water content and phase separation as the film thickness decreases. This decrease is caused by an increase in the packing of the polymer chains resulting in increases in mechanical modulus. In addition, direct measurement of the permeability of thin-films is accomplished, again showing that the thin films may result in substantial mass transport limitations. Acknowledgement The authors thank Steve Hamrock and Mike Yandrasits from 3M for helpful discussion and ionomer samples as well as Kunal Karan, Kirt Page, Chris Stafford, and Mike Hickner for discussions. This work made use of facilities at the Advanced Light Source (ALS), supported by the Office of Science, Office of Basic Energy Sciences, of the U.S. Department of Energy. This work was funded by the Assistant Secretary for Energy Efficiency and Renewable Energy, Fuel Cell Technologies Office, of the U. S. Department of Energy under contract number DE-AC02—05CH11231 and a CRADA with Toyota Motor Company.

A Study of Forming Tool Profile Effect in Single Point Incremental Forming by Finite Element Analysis

The Single Point Incremental Forming Process, SPIF, is a forming technique of sheet material based on layered manufacturing principles. The forming tool is moved along the tool path while the edges of sheet material are clamped on fixture by holder. The finished part is performed by the CNC milling machine. The description of the process is more complicated by highly nonlinear boundary conditions, namely contact and frictional effects have been accomplished. Due to the fact that the mathematical analysis of SPIF is complex, numerical approaches dominated by the FEA are now in widespread use. The paper presents the data and main results of a study concerning the effect of forming tool profile on SPIF through FEA, that permits the modeling of complex geometries, material behavior and boundary conditions. SPIF has been studied under certain process conditions referring to the test workpiece, tool, etc., using ANSYS 11.0. The results showed that the model of simulation can predict an ideal profile of processing track, spring back error of SPIF, the behavior of contact tool - workpiece, the accuracy of product by evaluation the strain and the stress distributions between forming tool and workpiece surface interface, and sample of results have been demonstrated.

Real‐Time Subspace Integration for Example‐Based Elastic Material

AbstractExample‐based material allows simulating complex material behaviors in an art‐directed way. This paper presents a method for fast subspace integration for example‐based elastic material, which is suitable for real‐time simulation in computer graphics. At the core of the method is the formulation of a new potential using example‐based Green strain tensors. By using this potential, the deformation can be attracted towards the example‐based deformation feature space, the example weights can be explicitly obtained and the internal force can be decomposed into the conventional one and an additional one induced by the examples. The real‐time subspace integration is then developed with subspace integration costs independent of geometric complexity, and both the reduced conventional internal force and additional one being cubic polynomials in reduced coordinates. Experiments demonstrate that our method can achieve real‐time simulation while providing comparable quality with the prior art.

Modeling the arterial wall mechanics using a novel high-order viscoelastic fractional element

The fractional viscoelastic models (FVMs) have provided promising results for modeling the behavior of complex materials such as polymers and living tissues. These viscoelastic models are composed by springs, dashpots and the fractional element called spring-pot. In this paper we prove that the accuracy of these models can be improved through the use of a modified version of the spring-pot element, called high-order spring-pot (HOSP).We describe and implement a numerical method for characterization of mechanical properties of FVMs. The method consists of minimizing the misfit among experimental measures of strains or stresses and the respective values predicted by the model. The method is validated by solving four numerical examples. In the first three examples the data is artificially generated using different models such as the Double Maxwell-arm Wiechert one. The characterization is performed using FVMs models including the traditional spring-pot element and the new HOSP element proposed in this article. In these examples we assume small strains and homogeneous material properties. In a final example the method is applied to the characterization of the mechanical properties of FVMs using stress–strain data obtained from in vitro ovine arterial wall measurements reported in the literature.The results obtained show that the proposed method properly determines the mechanical parameters even in presence of noise in the data. In addition, it is evident from the results that the proposed modification of the spring-pot element increases the accuracy of the FVMs models. The results obtained allow us to conclude that the FVMs can model better the behavior of complex materials when a HOSP element is included. In particular, it was shown that these models are appropriate for modeling the arterial wall mechanics with higher accuracy, as well as other materials with complex behavior.

Artificial neural network modeling (ANN) for predicting rutting performance of nano-modified hot-mix asphalt mixtures containing steel slag aggregates

Due to the complex behavior of asphalt pavement materials under various loading conditions, pavement structure, and environmental conditions, accurately predicting the permanent deformation of asphalt pavement is difficult. To predict, it is required to find the mathematical relation between the input and output data by an accurate and simple method. In recent years, artificial neural networks (ANNs) have been used to model the properties and behavior of materials, and to find complex relations between different properties in many fields of civil engineering applications, because of their ability to learn and to adapt. This study discusses the application of ANN in predicting permanent deformation of asphalt concrete mixtures modified by Nano-additives. A total number of 270 asphalt mixtures were constructed from two different aggregate sources (natural and steel slag) and were modified by micro silica and Nano TiO2/SiO2. All samples were tested at three different testing temperatures of 40, 50, and 60°C and five stresses of 100–500kPa. An ANN model developed using five input parameters including: aggregate source, additive type, additive content, temperature, and stress. An ANN with 10 neurons in hidden layer was considered as the appropriate architecture for predicting final strain of asphalt mixtures, and an excellent conformity was observed between the predicted and the test data. The result indicates that the proposed model can be applied in predicting final strain of asphalt mixtures. The model is further applied to evaluate the effect of different percentages of Nano-additive on permanent asphalt deformation. Results show that an increase in percentage of Nano-additives is very effective in reducing the final strain of asphalt mixtures. However, an increase in percentage of additives over 8.5% does not help to reduce permanent deformation under dynamic loading in the asphalt mixtures.

On the Solid Bonding Phenomena in Linear Friction Welding and Accumulative Roll Bonding Processes: Numerical Simulation Insights

Solid Bonding based welding processes allow to obtain defect free joints with low residual stress and low distortion. However, the engineering and optimization of solid bonding processes is difficult and requires a large number of time and cost consuming test trials. In this way, proper numerical models are essential tools permitting effective process design. The aim of this research was the comparison of the material process conditions during two different manufacturing processes taking advantage of the same metallurgical phenomenon, namely solid bonding. Linear Friction Welding, used to weld non-axisymmetric components and Accumulative Roll Bonding, used to increase the mechanical properties of sheet metals, were considered. Numerical models were set up, validated and used to design the process by studying the complex material behavior during the solid bonding of different aluminum alloys. An implicit approach was used for the Linear Friction Welding and Accumulative Roll Bonding processes, leading to the understanding of the main process variables influence on the field variables distribution and the occurrence of actual bonding.

Evaluation of Ductile Fracture Using Micro-samples

The FEM simulations in the field of design and safety assessment represent very powerful tools. Because of the growing demands on safety, reliability and longer lifetime period of structural facilities it is neccesary to use precise material data in a numerical simulation that considers ductile damage. Ductile fracture occurs after all the material plasticity is consumed. The plastic strain represents one of the most crucial parts in the process of ductile damage. If the damage additionally affects plastic behavior of the material then we can talk about the so called coupledcontinual damage model.The FEM simulations are strongly limited by material input data and available material models. Many of the current calculations are still performed on the basis of standard tensile tests, if not only on database data or data from literature. Such a material description is not sufficient for accurate design assessment and detailed material behaviour description has to be used for a reliable results.Standard tensile test is mainly based on uniaxial sample loading and small strains. Gained standard tensile test results are useful for elastic solutions or elastic-plastic solution for small plastic strains. If states near to fracture are to be considered, more complex material description taking into account multiaxial loading conditions should be applied. Thus samples of various geometries tested under various loading modes have to be used. On the basis of these tests a complex material behavior model covering elastic and plastic material behavior for various triaxiality states can be obtained. This kind of material behaviour description allows a wide range of applications from calculation of the component limit loading conditions to material properties conversion for samples of different sizes.The current paper is dealing with ductile damage parameters determination based on small samples for the structural ferriticsteel 15Ch2NMFA widelly used in the nuclear industry. The newly proposed specimen size is very small in comparison to standard size specimens. Different shapes of these test samples were tested and evaluatedin order to cover the whole range of the Stress Triaxiality.The obtained material plastic damage parameters are subsequently applied to FEM simulation and to the performed experimental tests. The comparison of the experimental and simulation results exhibits very good agreement and thus confirms applicability of the material models considered for reliable simulation of the material investigated.

Mathematical Description and Algorithmization of Expert Knowledge for the Support of the Topology Optimization of Crashworthiness Structures

AbstractThis contribution deals with the mathematical description and algorithmization of expert knowledge so that this expert knowledge can be used within automatic optimization procedures with a focus on the topology optimization of crashworthiness structures. Up to now, a purely mathematical topology optimization of crashworthiness structures is not possible. The reasons for that are the nonlinearities coming from the large displacements and rotations, contact phenomena and complex material behaviour (e.g. plasticity, failure and strain rate dependency). One approach to overcome these problems by using heuristics based on expert knowledge and an application example are shown in this contribution. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Modeling advanced high‐strength steels based on direct micro‐macro calculations

AbstractAdvanced high strength steels have immense commercial applicability today owing to the good combination of strength and ductility they offer. These properties mainly result from interactions of micro‐heterogeneities leading to a complex macroscopic material behavior. One of these steels is the Dual Phase (DP) steel which has a microstructure consisting of two phases: ferrite (matrix material) and martensite (inclusion material). This paper proposes a technique to model the post‐production situation of these steels, which is characterized by distributed material properties as well as eigenstresses. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Modeling Slump of Ready Mix Concrete Using Genetically Evolved Artificial Neural Networks

Artificial neural networks (ANNs) have been the preferred choice for modeling the complex and nonlinear material behavior where conventional mathematical approaches do not yield the desired accuracy and predictability. Despite their popularity as a universal function approximator and wide range of applications, no specific rules for deciding the architecture of neural networks catering to a specific modeling task have been formulated. The research paper presents a methodology for automated design of neural network architecture, replacing the conventional trial and error technique of finding the optimal neural network. The genetic algorithms (GA) stochastic search has been harnessed for evolving the optimum number of hidden layer neurons, transfer function, learning rate, and momentum coefficient for backpropagation ANN. The methodology has been applied for modeling slump of ready mix concrete based on its design mix constituents, namely, cement, fly ash, sand, coarse aggregates, admixture, and water-binder ratio. Six different statistical performance measures have been used for evaluating the performance of the trained neural networks. The study showed that, in comparison to conventional trial and error technique of deciding the neural network architecture and training parameters, the neural network architecture evolved through GA was of reduced complexity and provided better prediction performance.

Assessment of the fundamentals of failure theories for composite materials

Abstract Failure theories for composite materials have been a subject of concern for almost half a century. Numerous theories have been proposed over the years, but none of them has successfully predicted the full range of observed behavior. This paper critically reviews some of the main theories in an effort to understand their deficiencies. Rather than seek their validity by comparison with test data, the assumptions and analyses underlying the proposed theories are examined. Certain remedies are proposed to the current approaches to achieve a failure analysis procedure with a potential to succeed in predicting the complex failure behavior of composite materials.

A numerical study of the influence from pre‐existing cracks on granite rock fragmentation at percussive drilling

SummaryThe aim of this study is to investigate the effect of pre‐existing, or structural, cracks on dynamic fragmentation of granite. Because of the complex behavior of rock materials, a continuum approach is employed relying upon a plasticity model with yield surface locus as a quadratic function of the mean pressure in the principal stress space coupled with an anisotropic damage model. In particular, Bohus granite rock is investigated, and the material parameters are chosen based on previous experiments. The equation of motion is discretized using a finite element approach, and the explicit time integration method is employed. The pre‐existing cracks are introduced in the model by considering sets of elements with negligible tensile strength that leads to their immediate failure when loaded in tension even though they still carry compressive loads as crack closure occurs because of compressive stresses. Previously performed edge‐on impact tests are reconsidered here to validate the numerical model. Percussive drilling is simulated, and the influence of the presence of pre‐existing cracks is studied. The results from the analysis with different crack lengths and orientations are compared in terms of penetration stiffness and fracture pattern. It is shown that pre‐existing cracks in all investigated cases facilitate the drilling process. Copyright © 2014 John Wiley & Sons, Ltd.

A Study of Single Point Incremental Forming by Finite Element Analysis

The Single Point Incremental Forming Process (SPIF) involves extensive plastic deformation. The description of the process is more complicated by highly nonlinear boundary conditions, namely contact and frictional effects have been accomplished. The SPIF analysis is mathematically complex. However, due to the complex nature of these models, numerical approaches dominated by the FEA are now in widespread use. The paper presents the data and main results of a study on SPIF through FEA, that permits the modeling of complex geometries, boundary conditions and material behavior. SPIF have been studied under certain process conditions referring to the test workpiece, tool, etc., using ANSYS 11.0. An important result is showing that the model of simulation can give as clearly the behavior of contact tool - workpiece and the effect it on strain and stress distributions, also on the accuracy of product. Relevant dependences between tool and workpiece surface interface and sample of results have been demonstrated.

A reverse updated Lagrangian finite element formulation for determining material properties from measured force and displacement data

The mechanical response of solids exhibiting complex material behavior has traditionally been determined by fitting constitutive models of specified functional form to experimentally derived force-displacement (stress-strain) data. However, characterizing the nonlinear mechanical behavior of complex materials requires a method of quantifying material behavior that is not restricted by a specific constitutive relation. To this end, a new method, termed the reverse updated Lagrangian finite element method (RULFEM), which is based on the three-dimensional displacement field of the deformed solid and the finite element method, is developed for incrementally linear materials. Using the RULEFM, the body is discretized by finite elements and its material properties are determined element-wise, i.e., the properties are assumed to be uniform at the element level and may vary from one element to another. The validity of RULFEM is demonstrated by three noise-free numerical examples and three numerical examples with various input noise levels. Two methods to assess the global and local errors of the results due to error in the measured input data (noisy data) are also discussed.

A fractional K-BKZ constitutive formulation for describing the nonlinear rheology of multiscale complex fluids

The relaxation processes of a wide variety of soft materials frequently contain one or more broad regions of power-law like or stretched exponential relaxation in time and frequency. Fractional constitutive equations have been shown to be excellent models for capturing the linear viscoelastic behavior of such materials, and their relaxation modulus can be quantitatively described very generally in terms of a Mittag–Leffler function. However, these fractional constitutive models cannot describe the nonlinear behavior of such power-law materials. We use the example of Xanthan gum to show how predictions of nonlinear viscometric properties, such as shear-thinning in the viscosity and in the first normal stress coefficient, can be quantitatively described in terms a nonlinear fractional constitutive model. We adopt an integral K-BKZ framework and suitably modify it for power-law materials exhibiting Mittag–Leffler type relaxation dynamics at small strains. Only one additional parameter is needed to predict nonlinear rheology, which is introduced through an experimentally measured damping function. Empirical rules such as the Cox–Merz rule and Gleissle mirror relations are frequently used to estimate the nonlinear response of complex fluids from linear rheological data. We use the fractional model framework to assess the performance of such heuristic rules and quantify the systematic offsets, or shift factors, that can be observed between experimental data and the predicted nonlinear response. We also demonstrate how an appropriate choice of fractional constitutive model and damping function results in a nonlinear viscoelastic constitutive model that predicts a flow curve identical to the elastic Herschel-Bulkley model. This new constitutive equation satisfies the Rutgers-Delaware rule, which is appropriate for yielding materials. This K-BKZ framework can be used to generate canonical three-element mechanical models that provide nonlinear viscoelastic generalizations of other empirical inelastic models such as the Cross model. In addition to describing nonlinear viscometric responses, we are also able to provide accurate expressions for the linear viscoelastic behavior of complex materials that exhibit strongly shear-thinning Cross-type or Carreau-type flow curves. The findings in this work provide a coherent and quantitative way of translating between the linear and nonlinear rheology of multiscale materials, using a constitutive modeling approach that involves only a few material parameters.

Lateral load bearing capacity modelling of piles in cohesive soils in undrained conditions: An intelligent evolutionary approach

The complex behaviour of fine-grained materials in relation with structural elements has received noticeable attention from geotechnical engineers and designers in recent decades. In this research work an evolutionary approach is presented to create a structured polynomial model for predicting the undrained lateral load bearing capacity of piles. The proposed evolutionary polynomial regression (EPR) technique is an evolutionary data mining methodology that generates a transparent and structured representation of the behaviour of a system directly from raw data. It can operate on large quantities of data in order to capture nonlinear and complex relationships between contributing variables. The developed model allows the user to gain a clear insight into the behaviour of the system. Field measurement data from literature was used to develop the proposed EPR model. Comparison of the proposed model predictions with the results from two empirical models currently being implemented in design works, a neural network-based model from literature and also the field data shows that the EPR model is capable of capturing, predicting and generalizing predictions to unseen data cases, for lateral load bearing capacity of piles with very high accuracy. A sensitivity analysis was conducted to evaluate the effect of individual contributing parameters and their contribution to the predictions made by the proposed model. The merits and advantages of the proposed methodology are also discussed.

On the influence of frequency-dependent elastic properties in vibro-acoustic modelling of porous materials under structural excitation

The aspects related to modelling the frequency dependence of the elastic properties of air-saturated porous materials have been largely neglected in the past for several reasons. For acoustic excitation of porous materials, the material behaviour can be quite well represented by models where the properties of the solid frame have little influence. Only recently has the importance of the dynamic moduli of the frame come into focus. This is related to a growing interest in the material behaviour due to structural excitation. Two aspects stand out in connection with the elastic-dynamic behaviour. The first is related to methods for the characterisation of the dynamic moduli of porous materials. The second is a perceived lack of numerical methods able to model the complex material behaviour under structural excitation, in particular at higher frequencies. In the current paper, experimental data from a panel under structural excitation, coated with a porous material, are presented. In an attempt to correlate the experimental data to numerical predictions, it is found that the measured quasi-static material parameters do not suffice for an accurate prediction of the measured results. The elastic material parameters are then estimated by correlating the numerical prediction to the experimental data, following the physical behaviour predicted by the augmented Hooke׳s law. The change in material behaviour due to the frequency-dependent properties is illustrated in terms of the propagation of the slow wave and the shear wave in the porous material.

Numerical Simulation of Membrane of LNG Insulation System using User Defined Material Subroutine

304L stainless steel sheets are used as a primary barrier for the insulation of membrane-type liquefied natural gas(LNG) carrier cargo containment system. 304L stainless steel is a transformation-induced-plasticity(TRIP) steel that exhibits complex material behavior, because it undergoes phase transformation during plastic deformation. Since the TRIP behavior is very important mechanical characteristics in a low-temperature environment, significant amounts of data are available in the literature. In the present study, a uniaxial tensile test for 304L stainless steel was performed to investigate nonlinear mechanical characteristics. In addition, a viscoplastic model and damage model is proposed to predict material fractures under arbitrary loads. The verification was conducted not only by a material-based comparative study involving experimental investigations, but also by a structural application to the LNG membrane of a Mark-III-type cargo containment system.

Thermomechanical finite element simulations of selective electron beam melting processes: performance considerations

The present contribution is concerned with the macroscopic modelling of the selective electron beam melting process by using the finite element method. The modelling and simulation of the selective electron beam melting process involves various challenges: complex material behaviour, phase changes, thermomechanical coupling, high temperature gradients, different time and length scales etc. The present contribution focuses on performance considerations of solution approaches for thermomechanically coupled problems, i.e. the monolithic and the adiabatic split approach. The material model is restricted to nonlinear thermoelasticity with temperature-dependent material parameters. As a numerical example a straight scanning path is simulated, the predicted temperatures and stresses are analysed and the performance of the two algorithms is compared. The adiabatic split approach turned out to be much more efficient for linear thermomechanical problems, i.e. the solution time is three times less than with the monolithic approach. For nonlinear problems, stability issues necessitated the use of the Euler backward integration scheme, and therefore, the adiabatic split approach required small time steps for reasonable accuracy. Thus, for nonlinear problems and in combination with the Euler backward integration scheme, the monolithic solver turned out to be more efficient.