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Keywords: energy-based models, hyperelastic materials, rubber-like materials, compressibility, genetic algorithms, evolutionary algorithms.

Summary

This paper shows the approximation of the values of material constants referring to energy-based models of hyperelastic materials by means of pseudorandom methods. As opposed to conventional approaches to these issues, this paper introduces the application of evolutionary algorithms for this purpose. The attention is focused particularly on genetic algorithms. The whole process of validation described in the paper was based on the Mooney model [1,2,3] modified by Wegner [1]. The chosen measure of adjustment is the mean square error value (MSE) of the stress, referring to the positions of the points on the theoretical curve, compared with corresponding experimental values obtained by Treloar [1]. The energy-based modelling, as a method of complex mechanical problem solving is based on fulfiling the conditions of the law of conservation of energy and material compressibility, which leads to a proper material description. Accordingly, five models fulfilling these assumptions have been taken into consideration [1,4].

The numerical compilation of parameters describing the material constants of the chosen material model is made in order to find the values for which an energy-based model approximates to experimentally obtained material characteristics the most precise way possible.

The optimisation algorithm consists of two parts. The operation of each of them is related to using different methods. The first part is founded on an enumerative method which is the binary searching method. The second part uses the simplicity of genetic algorithms that subject the population of possible results to processes of replication, crossing-over and mutation.

The genetic processing begins by determining individuals which will be included in a mating pool. This generation consists of two populations the conditioning of which satisfies the adjustment of the theoretical curve to the experimental one, in one of the two strain ranges: from small to medium and from medium to large. All the sets of material constants are submitted to binary coding and included in separate chromosomes. The individuals are then joined in pairs and the genetic material is exchanged between them. At the end of the whole process the binary codes obtained are decoded and for newly obtained sets of material constants MSE values are estimated. Next, the comparison is made of a generation created in this way with the initial one. As a result of the implemented method of validation, very promissing outcomes have been obtained and the values of mean squared errors characterising the best sets of material constants and the values of C₁, C₂ and K obtained by the algorithm are tabulated.

References

1: T. Wegner, "Energy-based method of modeling and charts determination of dynamic behavior for strong dumping mechanical elements, followed by an example of rotational-symmetric high amplitude vibrations of a ring made of nearly incompressible material", Polish edition, Associate Professors' Dissertation Series, 323, Academic Press, Poznan University of Technology, 1997.
2: T. Wegner, A. Peczak, "Implementation of a strain energy-based nonlinear finite element in the object-oriented environment", Computer Physics Communication, 181, 520-531, 2010. doi:10.1016/j.cpc.2009.10.027
3: M. Mooney, "A theory of large elastic deformation", Journal of Applied Physics, 11(9), 582-592, 1940. doi:10.1063/1.1712836
4: S. Hartmann, P. Neff, "Polyconvexity of generalized polynomial - type hyperelastic strain energy functions for near-incompressibility", International Journal of Solids and Structures, 40, 2767-2791, 2003. doi:10.1016/S0020-7683(03)00086-6

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Front Page Browse CCP CSETS CTR IJRT Other Authors Search Purchase Guide FAQ Contact us	Civil-Comp Proceedings ISSN 1759-3433 CCP: 99 PROCEEDINGS OF THE ELEVENTH INTERNATIONAL CONFERENCE ON COMPUTATIONAL STRUCTURES TECHNOLOGY Edited by: B.H.V. Topping Paper 61 Application of Genetic Algorithms for Approximation with Energy-Based Models W.B. Bonczyk Institute of Applied Mechanics, Poznan University of Technology, Poland doi:10.4203/ccp.99.61 purchase the full-text of this paper Full Bibliographic Reference for this paper W.B. Bonczyk, "Application of Genetic Algorithms for Approximation with Energy-Based Models", in B.H.V. Topping, (Editor), "Proceedings of the Eleventh International Conference on Computational Structures Technology", Civil-Comp Press, Stirlingshire, UK, Paper 61, 2012. doi:10.4203/ccp.99.61 Keywords: energy-based models, hyperelastic materials, rubber-like materials, compressibility, genetic algorithms, evolutionary algorithms. Summary This paper shows the approximation of the values of material constants referring to energy-based models of hyperelastic materials by means of pseudorandom methods. As opposed to conventional approaches to these issues, this paper introduces the application of evolutionary algorithms for this purpose. The attention is focused particularly on genetic algorithms. The whole process of validation described in the paper was based on the Mooney model [1,2,3] modified by Wegner [1]. The chosen measure of adjustment is the mean square error value (MSE) of the stress, referring to the positions of the points on the theoretical curve, compared with corresponding experimental values obtained by Treloar [1]. The energy-based modelling, as a method of complex mechanical problem solving is based on fulfiling the conditions of the law of conservation of energy and material compressibility, which leads to a proper material description. Accordingly, five models fulfilling these assumptions have been taken into consideration [1,4]. The numerical compilation of parameters describing the material constants of the chosen material model is made in order to find the values for which an energy-based model approximates to experimentally obtained material characteristics the most precise way possible. The optimisation algorithm consists of two parts. The operation of each of them is related to using different methods. The first part is founded on an enumerative method which is the binary searching method. The second part uses the simplicity of genetic algorithms that subject the population of possible results to processes of replication, crossing-over and mutation. The genetic processing begins by determining individuals which will be included in a mating pool. This generation consists of two populations the conditioning of which satisfies the adjustment of the theoretical curve to the experimental one, in one of the two strain ranges: from small to medium and from medium to large. All the sets of material constants are submitted to binary coding and included in separate chromosomes. The individuals are then joined in pairs and the genetic material is exchanged between them. At the end of the whole process the binary codes obtained are decoded and for newly obtained sets of material constants MSE values are estimated. Next, the comparison is made of a generation created in this way with the initial one. As a result of the implemented method of validation, very promissing outcomes have been obtained and the values of mean squared errors characterising the best sets of material constants and the values of C₁, C₂ and K obtained by the algorithm are tabulated. References 1 T. Wegner, "Energy-based method of modeling and charts determination of dynamic behavior for strong dumping mechanical elements, followed by an example of rotational-symmetric high amplitude vibrations of a ring made of nearly incompressible material", Polish edition, Associate Professors' Dissertation Series, 323, Academic Press, Poznan University of Technology, 1997. 2 T. Wegner, A. Peczak, "Implementation of a strain energy-based nonlinear finite element in the object-oriented environment", Computer Physics Communication, 181, 520-531, 2010. doi:10.1016/j.cpc.2009.10.027 3 M. Mooney, "A theory of large elastic deformation", Journal of Applied Physics, 11(9), 582-592, 1940. doi:10.1063/1.1712836 4 S. Hartmann, P. Neff, "Polyconvexity of generalized polynomial - type hyperelastic strain energy functions for near-incompressibility", International Journal of Solids and Structures, 40, 2767-2791, 2003. doi:10.1016/S0020-7683(03)00086-6 purchase the full-text of this paper (price £20) go to the previous paper go to the next paper return to the table of contents return to the book description purchase this book (price £65 +P&P)
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