Abstract
This paper has a twofold objective: to present (a) a computational model for the finite deformation analysis of shell structures and (b) the development of mathematical model of biological cells based on homogenization techniques. In the first part, we present a finite element formulation which describes a refined shell theory in a natural and simple way using curvilinear coordinates. The first-order shell theory with seven parameters is derived with exact nonlinear deformations and under the framework of the Lagrangian description. This approach takes in-to account thickness changes and, therefore, 3D constitutive equations are utilized. In addition, we utilize the equal order, spectral/hp approximations for all variables in the finite element model to avoid membrane and shear. Numerical simulations and comparisons of the present results with those found in the literature for typical benchmark problems involving isotropic, laminated composites, as well as functionally graded shells are presented. In the second part, we present a mechanical model for a generalized biological cell, which includes the features of major cell types. The properties of biological materials are closely related to their internal molecular structure, and therefore require a micro-constituent based mathematical model to determine its macroscopic properties. In this work, the mathematical model is based on the actin fiber concentration, which could be used for the determination of mechanical properties of normal and diseased cells. Numerical results obtained with the present continuum model are compared with experimental results and a very good agreement is found.
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Acknowledgments
The authors gratefully acknowledge the support of this research through Oscar S. Wyatt Endowed Chair funds at Texas A&M University.
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Reddy, J., Arciniega, R., Unnikrishnan, G., Unnikrishnan, V. (2010). Numerical Modeling of Complex Structures: Shells and Biological Cells. In: Öchsner, A., da Silva, L., Altenbach, H. (eds) Materials with Complex Behaviour. Advanced Structured Materials, vol 3. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12667-3_8
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