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  • Open Access


    Bubble-Enriched Smoothed Finite Element Methods for Nearly-Incompressible Solids

    Changkye Lee1, Sundararajan Natarajan2, Jack S. Hale3, Zeike A. Taylor4, Jurng-Jae Yee1,*, Stéphane P. A. Bordas3,*

    CMES-Computer Modeling in Engineering & Sciences, Vol.127, No.2, pp. 411-436, 2021, DOI:10.32604/cmes.2021.014947

    Abstract This work presents a locking-free smoothed finite element method (S-FEM) for the simulation of soft matter modelled by the equations of quasi-incompressible hyperelasticity. The proposed method overcomes well-known issues of standard finite element methods (FEM) in the incompressible limit: the over-estimation of stiffness and sensitivity to severely distorted meshes. The concepts of cell-based, edge-based and node-based S-FEMs are extended in this paper to three-dimensions. Additionally, a cubic bubble function is utilized to improve accuracy and stability. For the bubble function, an additional displacement degree of freedom is added at the centroid of the element. Several numerical studies are performed demonstrating… More >

  • Open Access


    T-Splines for Isogeometric Analysis of Two-Dimensional Nonlinear Problems

    Mayi Guo, Gang Zhao, Wei Wang*, Xiaoxiao Du, Ran Zhang, Jiaming Yang

    CMES-Computer Modeling in Engineering & Sciences, Vol.123, No.2, pp. 821-843, 2020, DOI:10.32604/cmes.2020.09898

    Abstract Nonlinear behaviors are commonplace in many complex engineering applications, e.g., metal forming, vehicle crash test and so on. This paper focuses on the T-spline based isogeometric analysis of two-dimensional nonlinear problems including general large deformation hyperelastic problems and small deformation elastoplastic problems, to reveal the advantages of local refinement property of T-splines in describing nonlinear behavior of materials. By applying the adaptive refinement capability of T-splines during the iteration process of analysis, the numerical simulation accuracy of the nonlinear model could be increased dramatically. The Bézier extraction of the T-splines provides an element structure for isogeometric analysis that can be… More >

  • Open Access


    Experimental and Analytical Studies of Tumor Growth

    Hao Sun1, Timothy Eswothy1, Kerlin P. Robert1, Jiaoyan Li2, L. G. Zhang1, James D. Lee1,*

    Molecular & Cellular Biomechanics, Vol.16, Suppl.2, pp. 75-75, 2019, DOI:10.32604/mcb.2019.07090

    Abstract Most biological phenomena commonly involve with mechanics. In this work, we proposed an innovative model that tumor is considered as a pyroelastic medium consisting of two parts: solid and fluid. The variation of solid part depends on whether the drug has been effectively delivered to the tumor site. We derived the governing equations of the tumor, in which large deformation is incorporated. Meanwhile, the finite element equations for coupled displacement field and pressure field are formulated. We proposed two sets of porosity and growth tensor. In both cases the continuum theory and FEM are accompanied by accurate numerical simulations. To… More >

  • Open Access


    Finite Element Analysis of 4D Printing

    Kerlin P. Robert1, Jiaoyan Li2, James D. Lee1,*

    Molecular & Cellular Biomechanics, Vol.16, Suppl.2, pp. 74-74, 2019, DOI:10.32604/mcb.2019.07125

    Abstract This presentation focuses on the new and upcoming concept of 4D printing and its vast scope and importance in the research and development in industry. The 3D printing object is considered as a layered structure. Each layer may have different orientation. Therefore each layer may behave differently under the change of its environment. We formulate the theoretical shape changing process of 4D printing resulted from (I) the biological growth or swelling, (II) the change of temperature, and (III) the effect of electric field on piezoelectric material of the 3D printing product. Then we illustrate this theory visually through finite element… More >

  • Open Access


    On the Indentation of a Chemically-treated Polymeric Membrane

    A. P. S. Selvadurai1, Q. Yu2

    CMES-Computer Modeling in Engineering & Sciences, Vol.9, No.1, pp. 85-110, 2005, DOI:10.3970/cmes.2005.009.085

    Abstract A characteristic feature of a polymeric material such as PVC is its hyperelasticity or the ability to experience large strains prior to failure. The exposure of PVC to chemicals such as acetone and ethanol results in embrittlement or the loss of the hyperelasticity property. In this paper, we examine the mechanical behaviour of a PVC membrane that has been exposed to ethanol. Due to leaching of the plasticizer, the constitutive response of the PVC changes from a hyperelastic material to a hardened material that displays dominant yield behaviour and particularly one that is capable of experiencing post-yield large strains and… More >

  • Open Access


    Compressibility of Arterial Wall in Ring-cutting Experiments

    K.Y. Volokh1

    Molecular & Cellular Biomechanics, Vol.3, No.1, pp. 35-42, 2006, DOI:10.3970/mcb.2006.003.035

    Abstract It is common practice in the arterial wall modeling to assume material incompressibility. This assumption is driven by the observation of the global volume preservation of the artery specimens in some mechanical loading experiments. The global volume preservation, however, does not necessarily imply the local volume preservation -- incompressibility. In this work, we suggest to use the arterial ring- cutting experiments for the assessment of the local incompressibility assumption. The idea is to track the local stretches of the marked segments of the arterial ring after the stress-relieving cut. In the particular case of the rabbit thoracic artery, considered in… More >

  • Open Access


    Estimation of Isotropic Hyperelasticity Constitutive Models to Approximate the Atomistic Simulation Data for Aluminium and Tungsten Monocrystals

    Marcin Maździarz1, Marcin Gajewski2

    CMES-Computer Modeling in Engineering & Sciences, Vol.105, No.2, pp. 123-150, 2015, DOI:10.3970/cmes.2015.105.123

    Abstract In this paper, the choice and parametrisation of finite deformation polyconvex isotropic hyperelastic models to describe the behaviour of a class of defect-free monocrystalline metal materials at the molecular level is examined. The article discusses some physical, mathematical and numerical demands which in our opinion should be fulfilled by elasticity models to be useful. A set of molecular numerical tests for aluminium and tungsten providing data for the fitting of a hyperelastic model was performed, and an algorithm for parametrisation is discussed. The proposed models with optimised parameters are superior to those used in non-linear mechanics of crystals. More >

  • Open Access


    A 3-D Visco-Hyperelastic Constitutive Model for Rubber with Damage for Finite Element Simulation

    Ala Tabiei1, Suraush Khambati2

    CMES-Computer Modeling in Engineering & Sciences, Vol.105, No.1, pp. 25-45, 2015, DOI:10.3970/cmes.2015.105.025

    Abstract A constitutive model to describe the behavior of rubber from low to high strain rates is presented. For loading, the primary hyperelastic behavior is characterized by the six parameter Ogden’s strain-energy potential of the third order. The rate-dependence is captured by the nonlinear second order BKZ model using another five parameters, having two relaxation times. For unloading, a single parameter model has been presented to define Hysteresis or continuous damage, while Ogden’s two term model has been used to capture Mullin’s effect or discontinuous damage. Lastly, the Feng-Hallquist failure surface dictates the ultimate failure for element deletion. The proposed model… More >

  • Open Access


    The Analytical and Numerical Study on the Nanoindentation of Nonlinear Elastic Materials

    Qiang Zhang, Qing-Sheng Yang1

    CMC-Computers, Materials & Continua, Vol.37, No.2, pp. 123-134, 2013, DOI:10.3970/cmc.2013.037.123

    Abstract In nanoindentation testing of materials, the analytical/numerical models to connect the indentation load, indentation depth and material properties are crucial for the extraction of mechanical properties. This paper studied the methods of extracting the mechanical properties of nonlinear elastic materials and built general relationships of the indentation load and depth of hyperelastic materials combined with the dimensional analysis and finite element method (FEM). Compared with the elastic contact models and other nonlinear elastic contact models, the proposed models can extract the mechanical properties of nonlinear elastic materials under large deformation simply and effectively. More >

  • Open Access


    Elastic Instability of Pseudo-Elastic Rubber Balloons

    Ren Jiusheng1

    CMC-Computers, Materials & Continua, Vol.7, No.1, pp. 25-32, 2008, DOI:10.3970/cmc.2008.007.025

    Abstract Elastic instability for the inflation and deflation of a thin-walled spherical rubber balloon is examined within the framework of finite pseudo-elasticity. When a spherical rubber balloon is inflated, it is subject to a complex deformation after a pressure maximum has been obtained. One part of the balloon is lightly stretched while the remainder becomes highly stretched. So an aspherical deformation is observed after the initial spherical inflation. A pseudo-elastic strain energy function including a damage variable which may model the loading, unloading and reloading of rubber is used. The balloon is idealized as an elastic membrane and the inflation, deflation… More >

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