Kuzmin V.V. Calculation of 3D Shape of a Hyperelastic Body for Nonlinear Elasticity Models Using the Newton Method
- Details
- Hits: 28
https://doi.org/10.15688/mpcm.jvolsu.2024.2.7
Vladislav V. Kuzmin
Postgraduate Student, Department of Computer Sciences and Experimental Mathematics,
Volgograd State University
This email address is being protected from spambots. You need JavaScript enabled to view it.
,
https://orcid.org/0009-0004-2788-9396
Prosp. Universitetsky, 100, 400062 Volgograd, Russian Federation
Abstract. This article discusses methods for calculating the deformations of objects with hyperelastic materials within the framework of the nonlinear elasticity theory. This topic is relevant due to the use of new technological materials in industry, and as a result, the emerging task of preliminary numerical calculations for operational reliability, research and modeling of deformation behavior. The first part provides a brief overview of the main provisions and formulas of the nonlinear elasticity theory. Then the spatial discretization of 3-dimensional objects and the calculation of the deformation gradient using the finite element method are considered. The article provides an algorithm for solving this problem, such as minimizing the functional of stored energy, and also considers the class of permissible deformations. Afterwards, a detailed description is given, along with pseudocode, of the method of implementing and calculating the minimization by Newton’s method. The last part demonstrates an example of the calculations performed, based on the developed software that allows for numerical experiments and computer modeling of deformations of hyperelastic bodies, and one of the capabilities of which is to perform these calculations using Newton’s method.
Key words: nonlinear elasticity theory, stored energy functional, deformation gradient, Newton’s method, hyperelastic body.
Calculation of 3D Shape of a Hyperelastic Body for Nonlinear Elasticity Models Using the Newton Method by Kuzmin V.V. is licensed under a Creative Commons Attribution 4.0 International License.
Citation in English: Mathematical Physics and Computer Simulation. Vol. 27 No. 2 2024, pp. 80-91
 kuzmin.pdfURL: https://mp.jvolsu.com/index.php/en/component/attachments/download/1161 | 42 Downloads |