Changkye Lee¹, Sundararajan Natarajan², Jack S. Hale³, Zeike A. Taylor⁴, Jurng-Jae Yee^1,*, Stéphane P. A. Bordas^3,*

CMES-Computer Modeling in Engineering & Sciences, Vol.127, No.2, pp. 411-436, 2021, DOI:10.32604/cmes.2021.014947 - 19 April 2021

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 More >

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 - 01 May 2020

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 More >

Hao Sun¹, Timothy Eswothy¹, Kerlin P. Robert¹, Jiaoyan Li², L. G. Zhang¹, James D. Lee^1,*

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 More >

Kerlin P. Robert¹, Jiaoyan Li², James D. Lee^1,*

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 More >

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 More >

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 More >

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 >

Jan Heczko¹, Radek Kottner², Tomáš Kroupa²

CMC-Computers, Materials & Continua, Vol.33, No.3, pp. 257-273, 2013, DOI:10.3970/cmc.2013.033.257

Abstract This work deals with mechanical properties of a rubber material that is used in modern tram wheels as a damping element. Nonlinear static response as well as strain softening and hysteresis are captured in the material model that is selected. Method of identification of the model's parameters is developed. The identification method relies on successive minimizations with respect to different sets of parameters. Tests in tension, compression and simple shear are performed. Parameters of the material model are identified based on the tension and compression data, while the shear data are used for validation only. More >

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 More >

M. Timmel¹, M. Kaliske¹, S. Kolling², R. Mueller³

CMC-Computers, Materials & Continua, Vol.5, No.3, pp. 161-172, 2007, DOI:10.3970/cmc.2007.005.161

Abstract A damage approach based on a material model with microstructural evolution is presented. In contrast to phenomenological constitutive laws, the material response is given by mechanisms at the microscale. At first, a micromechanical substructure is chosen, which represents the overall material behaviour. Then the system is described using a micromechanical model. A geometrical modification of the microstructure is allowed to minimize the total energy. Consequently, the global stiffness is reduced. In this context, thermodynamical considerations are based on configurational forces. With the help of the discussed approach, void growth phenomena of materials, which lead to More >