Hyperelasticity Primer Robert M
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Application of Visco-Hyperelastic Devices in Structural Response Control
Application of visco-hyperelastic devices in structural response control Anantha Narayan Chittur Krishna Murthy Thesis submitted to the faculty of the Virginia Polytechnic Institute and State University in partial fulfillment of the requirements for the degree of Master of Science In Civil Engineering Dr. Finley A. Charney Dr. Raymond H. Plaut Dr. Carin L. Roberts Wollmann 11 May 2005 Blacksburg, Virginia Keywords: Visco-hyperelastic, Viscoelastic, dampers, Passive energy systems, Earthquakes, Seismic, Tires Application of visco-hyperelastic devices in structural response control (Anantha Narayan Chittur Krishna Murthy) Abstract Structural engineering has progressed from design for life safety limit states to performance based engineering, in which energy dissipation systems in structural frameworks assume prime importance. A visco-hyperelastic device is a completely new type of passive energy dissipation system that not only combines the energy dissipation properties of velocity and displacement dependent devices but also provides additional stability to the structure precluding overall collapse. The device consists of a viscoelastic material placed between two steel rings. The energy dissipation in the device is due to a combination of viscoelastic dissipation from rubber and plastic dissipation due to inelastic behavior of the steel elements. The device performs well under various levels of excitation, providing an excellent means of energy dissipation. The device properties are fully controlled through modifiable parameters. An initial study was conducted on motorcycle tires to evaluate the hyperelastic behavior and energy dissipation potential of circular rubber elements, which was preceded by preliminary finite element modeling. The rubber tires provided considerable energy dissipation while displaying a nonlinear stiffening behavior. The proposed device was then developed to provide additional stiffness that was found lacking in rubber tires. -
Method for the Unique Identification of Hyperelastic Material Properties Using Full-Field Measures
UCLA UCLA Previously Published Works Title Method for the unique identification of hyperelastic material properties using full-field measures. Application to the passive myocardium material response. Permalink https://escholarship.org/uc/item/1vs1s3jk Journal International journal for numerical methods in biomedical engineering, 33(11) ISSN 2040-7939 Authors Perotti, Luigi E Ponnaluri, Aditya VS Krishnamoorthi, Shankarjee et al. Publication Date 2017-11-01 DOI 10.1002/cnm.2866 Peer reviewed eScholarship.org Powered by the California Digital Library University of California Method for the unique identification of hyperelastic material properties using full field measures. Application to the passive myocardium material response Luigi E. Perotti1∗, Aditya V. Ponnaluri2, Shankarjee Krishnamoorthi2, Daniel Balzani3, Daniel B. Ennis1, William S. Klug2 1 Department of Radiological Sciences and Department of Bioengineering, University of California, Los Angeles 2 Department of Mechanical and Aerospace Engineering, University of California, Los Angeles 3 Institute of Mechanics and Shell Structures, TU Dresden, Germany, and Dresden Center of Computational Material Science SUMMARY Quantitative measurement of the material properties (e.g., stiffness) of biological tissues is poised to become a powerful diagnostic tool. There are currently several methods in the literature to estimating material stiffness and we extend this work by formulating a framework that leads to uniquely identified material properties. We design an approach to work with full field displacement data — i.e., we assume the displacement field due to the applied forces is known both on the boundaries and also within the interior of the body of interest — and seek stiffness parameters that lead to balanced internal and external forces in a model. -
Learning Corrections for Hyperelastic Models from Data David González, Francisco Chinesta, Elías Cueto
Learning corrections for hyperelastic models from data David González, Francisco Chinesta, Elías Cueto To cite this version: David González, Francisco Chinesta, Elías Cueto. Learning corrections for hyperelastic models from data. Frontiers in Materials. Computational Materials Science section, Frontiers, 2019, 6, 10.3389/fmats.2019.00014. hal-02165295v1 HAL Id: hal-02165295 https://hal.archives-ouvertes.fr/hal-02165295v1 Submitted on 25 Jun 2019 (v1), last revised 3 Jul 2019 (v2) HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Learning Corrections for Hyperelastic Models From Data David González 1, Francisco Chinesta 2 and Elías Cueto 1* 1 Aragon Institute of Engineering Research, Universidad de Zaragoza, Zaragoza, Spain, 2 ESI Group Chair and PIMM Lab, ENSAM ParisTech, Paris, France Unveiling physical laws from data is seen as the ultimate sign of human intelligence. While there is a growing interest in this sense around the machine learning community, some recent works have attempted to simply substitute physical laws by data. We believe that getting rid of centuries of scientific knowledge is simply nonsense. There are models whose validity and usefulness is out of any doubt, so try to substitute them by data seems to be a waste of knowledge. -
Gent Models for the Inflation of Spherical Balloons
International Journal of Non-Linear Mechanics 68 (2015) 52–58 Contents lists available at ScienceDirect International Journal of Non-Linear Mechanics journal homepage: www.elsevier.com/locate/nlm Gent models for the inflation of spherical balloons$ Robert Mangan a,n, Michel Destrade a,b a School of Mathematics, Statistics and Applied Mathematics, National University of Ireland Galway, University Road, Galway, Ireland b School of Mechanical and Materials Engineering, University College Dublin, Belfield, Dublin 4, Ireland article info abstract Article history: We revisit an iconic deformation of non-linear elasticity: the inflation of a rubber spherical thin shell. We Received 19 April 2014 use the 3-parameter Mooney and Gent-Gent (GG) phenomenological models to explain the stretch– Received in revised form strain curve of a typical inflation, as these two models cover a wide spectrum of known models for 26 May 2014 rubber, including the Varga, Mooney–Rivlin, one-term Ogden, Gent-Thomas and Gent models. We find Accepted 26 May 2014 that the basic physics of inflation exclude the Varga, one-term Ogden and Gent-Thomas models. We find Available online 25 June 2014 the link between the exact solution of non-linear elasticity and the membrane and Young–Laplace Keywords: theories often used a priori in the literature. We compare the performance of both models on fitting the Spherical shells data for experiments on rubber balloons and animal bladder. We conclude that the GG model is the most Membrane theory accurate and versatile model on offer for the modelling of rubber balloon inflation. Rubber modelling & 2014 Elsevier Ltd. -
Coupled Hydro-Mechanical Effects in a Poro-Hyperelastic Material
Journal of the Mechanics and Physics of Solids 91 (2016) 311–333 Contents lists available at ScienceDirect Journal of the Mechanics and Physics of Solids journal homepage: www.elsevier.com/locate/jmps Coupled hydro-mechanical effects in a poro-hyperelastic material A.P.S. Selvadurai n, A.P. Suvorov Department of Civil Engineering and Applied Mechanics, McGill University, 817 Sherbrooke Street West, Montréal, QC, Canada H3A 0C3 article info abstract Article history: Fluid-saturated materials are encountered in several areas of engineering and biological Received 17 December 2015 applications. Geologic media saturated with water, oil and gas and biological materials Received in revised form such as bone saturated with synovial fluid, soft tissues containing blood and plasma and 7 March 2016 synthetic materials impregnated with energy absorbing fluids are some examples. In Accepted 9 March 2016 many instances such materials can be examined quite successfully by appeal to classical Available online 15 March 2016 theories of poroelasticity where the skeletal deformations can be modelled as linear Keywords: elastic. In the case of soft biological tissues and even highly compressible organic geolo- Poro-hyperelasticity gical materials, the porous skeleton can experience large strains and, unlike rubberlike Fluid-saturated media materials, the fluid plays an important role in maintaining the large strain capability of the Canonical analytical solutions material. In some instances, the removal of the fluid can render the geological or biological Large deformations Time-dependent phenomena material void of any hyperelastic effects. While the fluid component can be present at Calibration of computational results various scales and forms, a useful first approximation would be to treat the material as hyperelastic where the fabric can experience large strains consistent with a hyperelastic material and an independent scalar pressure describes the pore fluid response. -
Averaged Strain Energy Density Criterion for Rupture
Averaged strain energy density criterion for rupture assessment of cracked rubbers: A novel method for determination of critical SED M.Heydari-MeybodiaM.R.AyatollahiaF.Bertob Abstract In the present study, the application of averaged strain energy density (ASED) criterion has been extended to hyperelastic materials. Because of the material and geometry nonlinearities, commonly known for rubber-like materials, the use of conventional relations for determining the criterion parameters is no longer allowable. Therefore, by taking the advantage of a simple uniaxial state of stress field ahead of the crack tip in hyperelastic materials, a novel method has been proposed for determining the critical value of strain energy density. The sound agreement between the theoretical estimates based on the employed ASED criterion and the experimental data, taken from the literature, confirms the suitability of the proposed method. Previous article in issue Next article in issue Keywords Fracture mechanics Failure assessment Crack growth Finite element analysis Rubber Nomenclature a Crack length C10,C01 Material parameters of the Mooney hyperelastic material model E Elastic modulus Ik(k=1,2,3) The invariants of the right Cauchy–Green deformation tensor Ijc(j=1,2) Critical value of the invariants of the right Cauchy–Green deformation tensor KIc Fracture toughness r Radial distance from the crack tip R‾ Radius of control volume Rc Critical radius of control volume W‾ SED value averaged over control volume Wc Critical value of SED σt Ultimate tensile strength ν Poisson’s ratio λj(j=1,2,3) Principal stretches λjc(j=1,2,3) Critical principal stretches λten Rupture stretch obtained in a uniaxial tensile test λU Loading direction stretch μ0,λm Material constants of the Arruda–Boyce material model ASED Averaged strain energy density CTR Crack tip radius DEC Double edge crack sample FEA Finite element analysis SBR Styrene butadiene rubber SED Strain energy density 1. -
Finite Element Based Improved Characterization of Viscoelastic Materials
1 Finite Element Based Improved Characterization of Viscoelastic Materials Xianfeng Song1*, Stefan Dircks1, Daniil Mirosnikov1, and Benny Lassen2 1Mads Clausen Institute, SDU, Sønderborg, Denmark 2DONG Energy, Fredericia, Denmark *SDU, Alsion 2, 6400, Sønderborg, Denmark, [email protected] Abstract: The objective of this study is to acquire II. Theory a full characterization of a hyperelastic material. The For the given material, linear elastic models (e.g. Neo- process is realized by performing a Dynamic Mechanical Hookean model) can not accurately describe the observed Analysis (DMA) while simultaneously extending it by behavior, so in order to overcome this problem hyperelastic advanced image processing algorithms in order to measure material models are introduced. Hyperelasticity provides the changing distance in the contracting direction. Using a means of modeling the stress-strain behavior of such COMSOL’s weak form PDE physics interface, three materials [4]. mathematical models are developed, where the strain- In this section a derivation of the governing equation is energy density function depends on different hyperelastic given. This theoretical part is required in order to perform constitutive equations. The chosen constitutive equations a finite element analysis. are Mooney-Rivlin, Yeoh and Arruda-Boyce. The results of the numerical study demonstrate that the all three models exhibit the correct trend of the non-linear behavior of the material, while the Arruda-Boyce model shows the best fitting performance. x3 B Keywords: finite element method, COMSOL, vis- −→ z3 u Bt coelastic material, image processing, dynamic mechanical −→ −→ analysis r R i3 I. Introduction z2 x2 i1 i2 z1 Viscoelastic materials have been used in many different applications, for example isolating vibration, dampening x1 noise and absorbing shock. -
Advancing the Modeling of Hyperelastic and Viscoelastic Materials
Case Study #2: Advancing the Modeling of Hyperelastic and Viscoelastic Materials Summary Challenges: • Accurately model To determine what the stress and strain limits are for deformation states of elastomers, MindMesh Inc. performed several calibration hyperelastic and tests for hyperelastic material models. This analysis was very viscoelastic materials crucial in calibrating rubber material which is used daily in • Calibrate hyperelastic and multiple industries and by consumers worldwide. There were viscoelastic materials for several types of tests used during this analysis. The tests modeling applications include simple tension strain (Fig. 1), simple compression strain, equal biaxial strain (Fig. 2), pure shear strain (Fig. 3), Results: and volumetric compression. With this we were able to understand how the material deforms, evaluate and calibrate • Developed calibration tests material properties and utilize them for nonlinear FEA for hyperelastic and analysis (Fig. 4 and 5). Understanding material properties viscoelastic materials allows us to interpret the deformation and modes of failure • Validated material models for parts or components developed with rubber-like under constant states of materials. There is a lot of research in this realm, however it stress and strain is not yet mainstream and therefore the results need to be interpreted from an engineering perspective especially for damage and failure. Fig. 1: Tension Experiment Fig. 2: Biaxial Extension Experiment Fig. 3: Pure Shear Experiment (Top images courtesy of Axel Products, Inc.) Fig. 4: Our results(Tension) Fig. 5: Our results (Biaxial) About the Client(s) Challenge This material property calibration methods was The purpose of calibrating hyperelastic material was to developed and addressed for several clients. -
Download-D638.Pdf>.Access In: 08/14/2014
Materials Research. 2015; 18(5): 918-924 © 2015 DOI: http://dx.doi.org/10.1590/1516-1439.320414 Mechanical Characterization and FE Modelling of a Hyperelastic Material Majid Shahzada*, Ali Kamranb, Muhammad Zeeshan Siddiquia, Muhammad Farhana aAdvance Materials Research Directorate, Space and Upper Atmosphere Research Commission – SUPARCO, Karachi, Sindh, Pakistan bInstitute of Space Technology – IST, Islamabad Highway, Islamabad, Pakistan Received: August 25, 2014; Revised: July 29, 2015 The aim of research work is to characterize hyperelastic material and to determine a suitable strain energy function (SEF) for an indigenously developed rubber to be used in flexible joint use for thrust vectoring of solid rocket motor. In order to evaluate appropriate SEF uniaxial and volumetric tests along with equi-biaxial and planar shear tests were conducted. Digital image correlation (DIC) technique was utilized to have strain measurements for biaxial and planar specimens to input stress-strain data in Abaqus. Yeoh model seems to be right choice, among the available material models, because of its ability to match experimental stress-strain data at small and large strain values. Quadlap specimen test was performed to validate material model fitted from test data. FE simulations were carried out to verify the behavior as predicted by Yeoh model and results are found to be in good agreement with the experimental data. Keywords: hyperelastic material, DIC, Yeoh model, FEA, quadlap shear test 1. Introduction Hyperelastic materials such as rubber are widely used The selection of suitable SEF depends on its application, for diverse structural applications in variety of industries corresponding variables and available data for material ranging from tire to aerospace. -
Determination of Material Properties of Basketball. Finite Element Modeling of the Basketball Bounce Height
Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 13 January 2021 Article Determination of Material Properties of Basketball. Finite Element Modeling of the Basketball Bounce Height Andrzej Makowski 1, 1 Faculty of Forestry and Wood Technology, Poznan University of Life Sciences, Poland * Correspondence: [email protected] Abstract: This paper presents a method to determine material constants of a standard basketball shell together with the development of a virtual numerical model of a basketball. Material constants were used as the basis for the hyperelastic material model in the strain energy function (SEF). Material properties were determined experimentally by strength testing in uniaxial tensile tests. Additionally, the digital image correlation technique (DIC) was applied to measure strain in axial planar specimens, thus providing input stress-strain data for the Autodesk software. Analysis of testing results facilitated the construction of a hyperelastic material model. The optimal Ogden material model was selected. Two computer programmes by Autodesk were used to construct the geometry of the virtual basketball model and to conduct simulation experiments. Geometry was designed using Autodesk Inventor Professional 2017, while Autodesk Simulation Mechanical 2017 was applied in simulation experiments. Simulation calculations of the model basketball bounce values were verified according to the FIBA recommendations. These recommendations refer to the conditions and parameters which should be met by an actual basketball. A comparison of experimental testing and digital calculation results provided insight into the application of numerical calculations, designing of structural and material solutions for sports floors. Keywords: hyperelastic materials; FEM; basketball; sports floors; Ogden model; FIBA 1. Introduction In the production of sports balls, particularly basketballs, the shelling is typically manufactured from rubber and rubber-based materials reinforced with synthetic fibres. -
Mechanics of Compliant Structures
CHAPTER 5 Mechanics of compliant structures C. H. M. Jenkins1, W. W. Schur2 & G. Greshchik3 1Compliant Structures Laboratory, Mechanical Engineering Department South Dakota School of Mines and Technology, Rapid City, USA. 2Balloon Projects Branch Code 842, NASA Wallops Flight Facility, Wallops Island, USA. 3Center for Aerospace Structures, University of Colorado, Boulder, USA. Abstract Biological organisms must be structurally efficient. Hence it is not surprising that nature has embraced the compliant membrane structure as a central element in higher biological forms. This chapter discusses the unique challenges of modeling the mechanical behavior of compliant membrane structures. In particular, we focus on several special characteristics, such as large deformation, lack of bending rigidity, material nonlinearity, and computational schemes. 1 Introduction 1.1 Motivation Biological organisms must be structurally efficient. They have benefited from millions of years of evolution to achieve, for example, high load carrying capacity per unit weight. It is not surprising then to find that compliant membrane structures play a significant role in nature, for membranes are among the most efficient of structural elements. Long ago, engineers adopted membrane structures for solutions where structural efficiency was critical. As an example, consider the working balloon. For a given balloon volume, the total lift available is fixed, implying a zero-sum trade between structure and payload. Modern high-altitude scientific balloons (Fig. 1), made of thin polymer film fractions of a millimeter thick with areal densities of a few grams per square meter, support payloads of a few tons! WIT Transactions on State of the Art in Science and Eng ineering, Vol 20, © 2005 WIT Press www.witpress.com, ISSN 1755-8336 (on-line) doi:10.2495/978-1-85312-941-4/05 86 Compliant Structures in Nature and Engineering Figure 1: Preparing to launch a high-altitude scientific balloon in Antarctica (courtesy NASA). -
Notes on Rate Equations in Nonlinear Continuum Mechanics
Notes on rate equations in nonlinear continuum mechanics∗ Daniel Aubram† September 29, 2017 Abstract: The paper gives an introduction to rate equations in nonlinear continuum mechanics which should obey specific transformation rules. Emphasis is placed on the geometrical nature of the operations involved in order to clarify the different concepts. The paper is particularly concerned with common classes of constitutive equations based on corotational stress rates and their proper implementation in time for solving initial boundary value problems. Hypoelastic simple shear is considered as an example application for the derived theory and algorithms. Contents 1 Introduction 2 2 Continuum Mechanics 2 2.1 MotionofaBody................................... ........ 2 2.2 DeformationGradientandStrain . .............. 4 2.3 StressandBalanceofMomentum. ............ 6 2.4 Constitutive Theory and Frame Invariance . ................. 8 3 Rates of Tensor Fields 10 3.1 Fundamentals.................................... ......... 10 3.2 CorotationalRates ............................... ........... 12 4 Rate Constitutive Equations 15 4.1 Hypoelasticity.................................. ........... 16 4.2 Hypoelasto-Plasticity. .............. 17 4.3 Hypoplasticity .................................. .......... 19 5 Objective Time Integration 20 5.1 Fundamentals and Geometrical Setup . .............. 20 5.2 AlgorithmofHughesandWinget . ............ 24 5.3 Algorithms Using a Corotated Configuration . ................ 25 6 Hypoelastic Simple Shear 28 6.1 AnalyticalSolution.