scholarly journals Finite Element Model Updating Combined with Multi-Response Optimization for Hyper-Elastic Materials Characterization

Materials ◽  
2019 ◽  
Vol 12 (7) ◽  
pp. 1019 ◽  
Author(s):  
Saúl Íñiguez-Macedo ◽  
Rubén Lostado-Lorza ◽  
Rubén Escribano-García ◽  
María Martínez-Calvo
Keyword(s):  
Finite Element ◽  
Standardized Tests ◽  
Model Updating ◽  
Computational Cost ◽  
Styrene Butadiene Rubber ◽  
Butadiene Rubber ◽  
Stress Strain ◽  
Desirability Functions ◽  
Hyper Elastic ◽  
Force Displacement

The experimental stress-strain curves from the standardized tests of Tensile, Plane Stress, Compression, Volumetric Compression, and Shear, are normally used to obtain the invariant λi and constants of material Ci that will define the behavior elastomers. Obtaining these experimental curves requires the use of expensive and complex experimental equipment. For years, a direct method called model updating, which is based on the combination of parameterized finite element (FE) models and experimental force-displacement curves, which are simpler and more economical than stress-strain curves, has been used to obtain the Ci constants. Model updating has the disadvantage of requiring a high computational cost when it is used without the support of any known optimization method or when the number of standardized tests and required Ci constants is high. This paper proposes a methodology that combines the model updating method, the mentioned standardized tests and the multi-response surface method (MRS) with desirability functions to automatically determine the most appropriate Ci constants for modeling the behavior of a group of elastomers. For each standardized test, quadratic regression models were generated for modeling the error functions (ER), which represent the distance between the force-displacement curves that were obtained experimentally and those that were obtained by means of the parameterized FE models. The process of adjusting each Ci constant was carried out with desirability functions, considering the same value of importance for all of the standardized tests. As a practical example, the proposed methodology was validated with the following elastomers: nitrile butadiene rubber (NBR), ethylene-vinyl acetate (EVA), styrene butadiene rubber (SBR) and polyurethane (PUR). Mooney–Rivlin, Ogden, Arruda–Boyce and Gent were considered as the hyper-elastic models for modeling the mechanical behavior of the mentioned elastomers. The validation results, after the Ci parameters were adjusted, showed that the Mooney–Rivlin model was the hyper-elastic model that has the least error of all materials studied (MAEnorm = 0.054 for NBR, MAEnorm = 0.127 for NBR, MAEnorm = 0.116 for EVA and MAEnorm = 0.061 for NBR). The small error obtained in the adjustment of the Ci constants, as well as the computational cost of new materials, suggests that the methodology that this paper proposes could be a simpler and more economical alternative to use to obtain the optimal Ci constants of any type of elastomer than other more sophisticated methods.

scholarly journals Model Updating Method Based on Kriging Model for Structural Dynamics

2019 ◽  
Vol 2019 ◽  
pp. 1-12 ◽  
Author(s):  
Hong Yin ◽  
Jingjing Ma ◽  
Kangli Dong ◽  
Zhenrui Peng ◽  
Pan Cui ◽  
...  
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Frequency Response ◽  
Structural Dynamics ◽  
Model Updating ◽  
Computational Cost ◽  
Element Model ◽  
Kriging Model ◽  
Surface Model ◽  
Sample Points

Model updating in structural dynamics has attracted much attention in recent decades. And high computational cost is frequently encountered during model updating. Surrogate model has attracted considerable attention for saving computational cost in finite element model updating (FEMU). In this study, a model updating method using frequency response function (FRF) based on Kriging model is proposed. The optimal excitation point is selected by using modal participation criterion. Initial sample points are chosen via design of experiment (DOE), and Kriging model is built using the corresponding acceleration frequency response functions. Then, Kriging model is improved via new sample points using mean square error (MSE) criterion and is used to replace the finite element model to participate in optimization. Cuckoo algorithm is used to obtain the updating parameters, where the objective function with the minimum frequency response deviation is constructed. And the proposed method is applied to a plane truss model FEMU, and the results are compared with those by the second-order response surface model (RSM) and the radial basis function model (RBF). The analysis results showed that the proposed method has good accuracy and high computational efficiency; errors of updating parameters are less than 0.2%; damage identification is with high precision. After updating, the curves of real and imaginary parts of acceleration FRF are in good agreement with the real ones.

Effect of Finite Extensibility on the Viscoelastic Properties of a Styrene-Butadiene Rubber Vulcanizate in Simple Tensile Deformations up to Rupture

1970 ◽  
Vol 43 (4) ◽  
pp. 714-734
Author(s):  
T. L. Smith ◽  
R. A. Dickie
Keyword(s):  
Strain Rate ◽  
Constant Strain Rate ◽  
Shift Factor ◽  
Styrene Butadiene Rubber ◽  
Butadiene Rubber ◽  
Stress Strain ◽  
Temperature Function ◽  
Extension Ratio ◽  
Styrene Butadiene ◽  
Maximum Extensibility

Abstract Stress-strain and rupture data were determined on an unfilled styrene-butadiene vulcanizate at temperatures from −45 to 35° C and at extension rates from 0.0096 to 9.6 min−1. The data were represented by four functions: (1) the well-known temperature function (shift factor) aT; (2) the constant-strain-rate modulus, F (t, T) reduced to temperature T0 and time t/aT, i.e., T0F (t/aT)/T (3) the time-dependent maximum extensibility λm (t/aT); and (4) a function Ω(χ) where χ=(λ−1)λm0/λm, in which λ is the extension ratio and λm0 is the maximum extensibility under equilibrium conditions. The constant-strain-rate modulus characterizes the stress-time response to a constant extension rate at small strains, within the range of linear response; λm is a material parameter needed to represent the response at large λ; and Ω(χ) represents the stress-strain curve of the material in a reference state of unit modulus and λm=λm0. The shift factor aT was found to be sensibly independent of extension. At all values of t/aT for which the maximum extensibility is time-independent, the relaxation rate was also found to be independent of λ. These observations indicate that the monomeric friction coefficient is strain-independent over the ranges of T and λ covered in the present study. It was found that λm0=8.6 and that the largest extension ratio at break (λb)max is 7.3. Thus, rupture always occurs before the network is fully extended.

scholarly journals Modeling and Stochastic Model Updating of Bolt-Jointed Structure

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Ming Zhan ◽  
Qintao Guo ◽  
Lin Yue ◽  
Baoqiang Zhang
Keyword(s):  
Finite Element ◽  
High Resolution ◽  
Material Properties ◽  
Model Updating ◽  
Computational Cost ◽  
Three Dimensional ◽  
Element Model ◽  
Joint Interface ◽  
Unknown Parameters ◽  
Updating Procedure

Bolt-jointed structure is widely used in engineering fields. The dynamic characteristics of bolt-jointed structure are complex, and there is a variety of uncertainties in the jointed structure. In this study, modeling and updating of a typical bolt-jointed structure are investigated. In modeling terms, three-dimensional brick elements are used to represent the substructures, and thin-layer elements with virtual material properties are employed to represent the joint interface. Modal tests and experimental modal analysis of substructures and built-up structure are performed. A hierarchical model updating strategy based on Bayesian inference is applied to identify the unknown parameters in the substructures model and those in the overall model. Radial basis function (RBF) models are used as surrogates of time-consuming finite element model with high resolution to avoid the enormous computational cost. The results indicate that the updated model can reproduce modal frequencies used in updating and can predict those not used in the updating procedure.

Highly Efficient Probabilistic Finite Element Model Updating Using Intelligent Inference With Incomplete Modal Information

2016 ◽  
Vol 138 (5) ◽  
Author(s):  
K. Zhou ◽  
J. Tang
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Model Updating ◽  
Computational Cost ◽  
Sampling Technique ◽  
Element Model ◽  
Measurement Information ◽  
Model Parameters ◽  
Finite Element Model Updating ◽  
Highly Efficient

A highly efficient probabilistic framework of finite element model updating in the presence of measurement noise/uncertainty using intelligent inference is presented. This framework uses incomplete modal measurement information as input and is built upon the Bayesian inference approach. To alleviate the computational cost, Metropolis–Hastings Markov chain Monte Carlo (MH MCMC) is adopted to reduce the size of samples required for repeated finite element modal analyses. Since adopting such a sampling technique in Bayesian model updating usually yields a sparse posterior probability density function (PDF) over the reduced parametric space, Gaussian process (GP) is then incorporated in order to enrich analysis results that can lead to a comprehensive posterior PDF. The PDF obtained with densely distributed data points allows us to find the most optimal model parameters with high fidelity. To facilitate the entire model updating process with automation, the algorithm is implemented under ansys Parametric Design Language (apdl) in ansys environment. The effectiveness of the new framework is demonstrated via systematic case studies.

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

2015 ◽  
Vol 1123 ◽  
pp. 55-58 ◽  
Author(s):  
Budi Setiyana ◽  
F.D. Wicahyo ◽  
Rifky Ismail ◽  
J. Jamari ◽  
D.J. Schipper
Keyword(s):  
Mechanical Properties ◽  
Elastic Modulus ◽  
Tensile Test ◽  
Material Model ◽  
Styrene Butadiene Rubber ◽  
Butadiene Rubber ◽  
Element Analysis ◽  
Theoretical Formulation ◽  
Straight Blade ◽  
Hyper Elastic

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.

Evaluation of Crosslink Density Using Material Constants of Ethylene-Propylene-Diene Monomer/Styrene-Butadiene Rubber with Different Nanoclay Loading: Finite Element Analysis-Simulation and Experimental

2020 ◽  
Vol 12 (5) ◽  
pp. 632-642 ◽  
Author(s):  
S. Vishvanathperumal ◽  
V. Navaneethakrishnan ◽  
G. Anand ◽  
S. Gopalakannan
Keyword(s):  
Experimental Data ◽  
Finite Element Analysis ◽  
Finite Element ◽  
Strain Energy ◽  
Tension Test ◽  
Styrene Butadiene Rubber ◽  
Butadiene Rubber ◽  
Element Analysis ◽  
Strain Behavior ◽  
Styrene Butadiene

Nanoclay is used to enhance the mechanical properties of ethylene-propylene-diene rubber (EPDM)/styrene-butadiene rubber (SBR) blends. Sulphur (S), dicumyl peroxide (P), and mixed systems (S + P) were used as crosslinking or vulcanizing agents for the EPDM/SBR nanocomposites. The experimental data of the stress–strain behavior of EPDM/SBR blends with different nanoclay loading have been determined through a tension test. Nonlinear mechanical behaviors of the rubbers are described by strain energy functions in order to assurance that rigid body motions play no role in the constitutive law. The mathematical model such as the Mooney-Rivlin model based on the existence of strain energy density functions depends on the right Cauchy-Green's deformation tensor or Green's strain tensor. The experimental data are fitted to the Mooney-Rivlin model in order to find the rubber material constants. These constants are used to find the crosslinking density. A comparison between the experimental stress–strain behavior and finite element analysis of a uniaxial tension test at different nanoclay loading is presented.

scholarly journals Determining the Compression-Equivalent Deformation of SBR-Based Rubber Material Measured in Tensile Mode Using the Finite Element Method

2021 ◽  
Vol 2 (1) ◽  
pp. 195-208
Author(s):  
Sahbi Aloui ◽  
Mohammed El Yaagoubi
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Styrene Butadiene Rubber ◽  
Butadiene Rubber ◽  
Compression Tests ◽  
The Finite Element Method ◽  
Rubber Material ◽  
Styrene Butadiene ◽  
Element Method

A timesaving characterization approach of rubber materials in compression using the finite element method (FEM) is presented. Rubber materials based on styrene butadiene rubber (SBR) are subjected to tensile and compression tests. Using the neo–Hooke, Mooney–Rivlin and Yeoh material models, a compression-equivalent deformation of the SBR samples is derived from the tensile testing. The simulated state is then compared with the experimental results obtained from compression measurement. The deviation in the strain energy density between the measurements and the simulations depends on the quality of the fitting.

Finite Element Modeling and Critical Plane Analysis of a Cut-and-Chip Experiment for Rubber

2020 ◽  
Author(s):  
Christopher G. Robertson ◽  
Jesse D. Suter ◽  
Mark A. Bauman ◽  
Radek Stoček ◽  
William V. Mars
Keyword(s):  
Finite Element ◽  
Impact Force ◽  
Styrene Butadiene Rubber ◽  
Butadiene Rubber ◽  
Critical Plane ◽  
Element Analysis ◽  
Rate Laws ◽  
Plane Analysis ◽  
Chip Experiment ◽  
The Impact

ABSTRACT Rubber surfaces exposed to concentrated, sliding impacts carry large normal and shearing stresses that can cause damage and the eventual removal of material from the surface. Understanding this cut-and-chip (CC) effect in rubber is key to developing improved tread compounds for tires used in off-road or poor road conditions. To better understand the mechanics involved in the CC process, an analysis was performed of an experiment conducted on a recently introduced device, the Coesfeld Instrumented Chip and Cut Analyser (ICCA), which repetitively impacts a rigid indenter against a rotating solid rubber wheel. The impact process is carefully controlled and measured on this lab instrument, so that the contact time, normal force, and shear force are all known. The numerical evaluation includes Abaqus finite element analysis (FEA) to determine the stress and strain fields during impact. The FEA results are combined with rubber fracture mechanics characteristics of the material as inputs to the Endurica CL elastomer fatigue solver, which employs critical plane analysis to determine the fatigue response of the specimen surface. The modeling inputs are experimentally determined hyperelastic stress-strain parameters, crack growth rate laws, and crack precursor sizes for carbon black–filled compounds wherein the type of elastomer is varied in order to compare natural rubber (NR), butadiene rubber (BR), and styrene-butadiene rubber (SBR). At the lower impact force, the simulation results were consistent with the relative CC resistances of NR, BR, and SBR measured using the ICCA, which followed the order BR > NR > SBR. Impact-induced temperature increases need to be considered in the fatigue analysis of the higher impact force to provide lifetime predictions that match the experimental CC resistance ranking of NR > SBR > BR.

scholarly journals Substructure Interface Reduction Techniques to Capture Nonlinearities in Bolted Structures

2020 ◽  
Author(s):  
Aabhas Singh ◽  
Matthew S. Allen ◽  
Robert J. Kuether
Keyword(s):  
Finite Element ◽  
Degrees Of Freedom ◽  
Model Updating ◽  
Computational Cost ◽  
Nonlinear Behavior ◽  
Element Model ◽  
System Level ◽  
Contact Interface ◽  
Single Node ◽  
Structural Dynamic

Abstract Structural dynamic finite element models typically use multipoint constraints (MPC) to condense the degrees of freedom (DOF) near bolted joints down to a single node, which can then be joined to neighboring structures with linear springs or nonlinear elements. Scalability becomes an issue when multiple joints are present in a system, because each requires its own model to capture the nonlinear behavior. While this increases the computational cost, the larger problem is that the parameters of the joint models are not known, and so one must solve a nonlinear model updating problem with potentially hundreds of unknown variables to fit the model to measurements. Furthermore, traditional MPC approaches are limited in how the flexibility of the interface is treated (i.e. with rigid bar elements the interface has no flexibility). To resolve this shortcoming, this work presents an alternative approach where the contact interface is reduced to a set of modal DOF which retain the flexibility of the interface and are capable of modeling multiple joints simultaneously. Specifically, system-level characteristic constraint (S-CC) reduction is used to reduce the motion at the contact interface to a small number of shapes. To capture the hysteresis and energy dissipation that is present during microslip of joints, a hysteretic element is applied to a small number of the S-CC Shapes. This method is compared against a traditional MPC method (using rigid bar elements) on a two-dimensional finite element model of a cantilever beam with a single joint near the free end. For all methods, a four-parameter Iwan element is applied to the interface DOF to capture how the amplitude dependent modal frequency and damping change with vibration amplitude.

Statistical Mechanics Material Model for the Constitutive Modelling of Elastomeric Compounds

1996 ◽  
Vol 210 (6) ◽  
pp. 575-585 ◽  
Author(s):  
J M Allport ◽  
A J Day
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Statistical Mechanics ◽  
Constitutive Modelling ◽  
Three Dimensions ◽  
Styrene Butadiene Rubber ◽  
Butadiene Rubber ◽  
Element Analysis ◽  
Material Modelling ◽  
Modelling Approach

Material models for the finite element analysis (FEA) of polymeric and elastomeric compounds are only available in limited form in most commercial finite element (FE) packages. The most common are the phenomenological Mooney-Rivlin and the Ogden models, for which the constants bear no relationship to the physical or chemical characteristics of the rubber and their derivation is difficult. Both models are limited in their accuracy for filled rubbers used in combined states of tensile and compressive deformation, and since these are common operational conditions for engineering components such as drive couplings, engine mounts and torsional vibration dampers, their use in engineering analyses is restricted. In this paper a statistical mechanics material modelling approach for synthetic, filled elastomeric compounds in FEA is presented. Using styrene-butadiene rubber (SBR) as an example, the theory and its application in the commercially available ABAQUS finite element analysis program is explained. FE models of tensile and compressive specimens in two and three dimensions are used to demonstrate the use of the model, and results are presented, discussed and compared with measured data. Good correlation in both tension and compression is demonstrated. A practical application of the model to the SBR blocks in a Holset torsional drive coupling is presented; this analysis involves complex issues of mesh design and contact modelling. The results show good agreement with measured performance, and clearly demonstrate how this type of material modelling approach can be effectively used in the computer aided engineering and design of engineering rubber components.

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