SCALAR DAMAGE BASED ON MICROPOLAR CONTINUA ”“ MESH-FREE APPROXIMATION
DOI:
https://doi.org/10.26512/ripe.v2i7.21714Keywords:
Micropolar continua. Scalar damage. Strain localization. Mesh-free methods. Element Free Galerkin.Abstract
Recently, scalar damage models based on the micropolar continuum theory have been proposed, in order to represent the physically non-linear behaviour of quasi-brittle materials. Due to its regularization properties, widely investigated in elasto-plasticity, the micropolar theory represents a valid alternative for mitigating pathological phenomena that arise in the numerical simulations. In the last years, also the class of mesh-free methods have been shown to be capable to regularize the response of problems where localization occours. This paper investigates the coupling of micropolar damage models with mesh-free methods, with specific attention on the Element Free Galerkin (EFG) method. The micropolar theory is presented in a tensorial generalized form, and different scalar damage models are derived in a theoretical and computational unified framework for constitutive models. The computational aspects of the coupling between micropolar damage and mesh-free approach are also discussed, with specific attention on the implementation in the INSANE (INteractive Structural ANalysis Enviroment) system. Numerical simulations are presented in order to illustrate the proposed models.
Downloads
References
Andrade, M. P. & Silva, R. P., 2015. Implementac¸ao de bibliotecas de ˜ Algebra linear numérica via interface nativa no INSANE. In Proceedings of the XXXVI Ibero-Latin American Congress on Computational Methods in Engineering, Rio de Janeiro, Brazil. ABMEC - Brazilian Association of Computational Methods in Engineering. (in portuguese).
Bauer, S., Dettmer, W., Peric, D., & Sch ´ afer, M., 2012. Micropolar hyper-elastoplasticity: ¨constitutive model, consistent linearization, and simulation of 3D scale effects. International Journal for Numerical Methods in Engineering, vol. 91, n. 1, pp. 39”“66.
Belytschko, T., Lu, Y. Y., & Gu, L., 1994. Element-free Galerkin methods. International Journal for Numerical Methods in Engineering, vol. 37, n. 2, pp. 229”“256.
Chen, J. S., Hu, W., Puso, M., & Zhang, X., 2007. Strain smoothing for stabilization and regularization of Galerkin meshfree. vol. 57, pp. 57 ”“ 75.
Chen, J. S., Wu, T. C., & Belytschko, T., 2000. Regularization of material instabilities by meshfree approximations with intrinsic length scales. International Journal for Numerical Methods in Engineering, vol. 47, pp. 1303”“1322.
Chen, J. S., Zhang, X., & Belytschko, T., 2004. An implicit gradient model by a reproducing kernel strain regularization in strain localization problems. Computer Methods in Applied Mechanics and Engineering, vol. 193, pp. 2827”“2844.
Cosserat, E. & Cosserat, F., 1909. Theorie des corps d ´ eformables ´ . Hermann et fils, Paris. (in french).
Davis, T. A., 2004. A column pre-ordering strategy for the unsymmetric-pattern multifrontal method. ACM Transactions on Mathematical Software, vol. 30, n. 2, pp. 165”“195.
Davis, T. A., 2006. Direct Methods for Sparse Linear Systems. SIAM. de Borst, R., 1993. A generalization of J2-flow theory for polar continua. Computer Methods in Applied Mechanics and Engineering, vol. 103, pp. 347”“362.
de Borst, R. & Gutierrez, M. A., 1999. A unified framework for concrete damage and fracture models including size effects. International Journal of Fracture, vol. 95, n. 1-4, pp. 261”“277.
de Borst, R. & Sluys, L. J., 1991. Localization in a Cosserat continuum under static and dynamic loading. Computer Methods in Applied Mechanics and Engineering, vol. 90, n. 1-3, pp. 805”“827.
Gori, L., Penna, S. S., & Pitangueira, R. L. S., 2016. An enhanced tensorial formulation for elastic degradation in micropolar continua. Applied Mathematical Modelling, vol. , pp. ”“. (in press).
Gori, L., Pitangueira, R. L. S., Penna, S. S., & Fuina, J. S., 2015a. A generalized elasto-plastic micro-polar constitutive model. Applied Mechanics and Materials, vol. 798, pp. 505”“509.
Gori, L., Pitangueira, R. L. S., Penna, S. S., & Fuina, J. S., 2015b. Isotropic damage models based on a generalized micro-polar continuum theory. In Anais do 57 Congresso Brasileiro do Concreto, Bonito, Brazil. IBRACON - Instituto Brasileiro do Concreto.
Gori, L., Pitangueira, R. L. S., Penna, S. S., & Fuina, J. S., 2015c. A theoretical and computational framework for isotropic damage models based on a generalized micro-polar continuum theory. In Proceedings of the XXXVI Ibero-Latin American Congress on Computational Methods in Engineering, Rio de Janeiro, Brazil. ABMEC - Brazilian Association of Computational Methods in Engineering.
INSANE Project, 2016. https://www.insane.dees.ufmg.br/.
Iordache, M. M. & Willam, K., 1998. Localized failure analysis in elastoplastic Cosserat continua. Computer Methods in Applied Mechanics and Engineering, vol. 121, n. 3-4, pp. 559”“586.
Li, S., Hao, W., & Liu, W. K., 2000. Mesh-free simulations of shear banding in large deformation. International Journal of Solids and Structures, vol. 37, pp. 7185”“7206.
Li, S. & Liu, W. K., 2000. Numerical simulations of strain localization in inelastic solids using mesh-free methods. International Journal for Numerical Mehods in Engineering, vol. 48, pp. 1285”“1309.
Liang, K.-Z. & Huang, F.-Y., 1996. Boundary element method for micropolar elasticity. International Journal of Engineering Science, vol. 34, n. 5, pp. 509 ”“ 521.
Liu, W. K., Hao, S., Belytschko, T., Li, S. F., & Chang, C. T., 1999. Multiple scale meshfree methods for damage fracture and localization. Computational Material Science, vol. 16, pp. 197”“205.
Mariano, P. M. & Stazi, F. L., 2005. Computational aspects of the mechanics of complex materials. Archives of Computational Methods in Engineering, vol. 12, n. 4, pp. 391”“478.
Mazars, J., 1984. Application de le Mecanique de l’endommagement au comportement non ´lineaire et a la rupture du b ` eton de Structure ´ . PhD thesis, Universite Pierre et Marie Curie - ´Laboratoire de Mecanique et Technologie, Paris, France. (in french).
de Borst, R., 1993. A generalization of J2-flow theory for polar continua. Computer Methods in Applied Mechanics and Engineering, vol. 103, pp. 347”“362.
de Borst, R. & Gutierrez, M. A., 1999. A unified framework for concrete damage and fracture models including size effects. International Journal of Fracture, vol. 95, n. 1-4, pp. 261”“277.
de Borst, R. & Sluys, L. J., 1991. Localization in a Cosserat continuum under static and dynamic loading. Computer Methods in Applied Mechanics and Engineering, vol. 90, n. 1-3, pp. 805”“827.
Gori, L., Penna, S. S., & Pitangueira, R. L. S., 2016. An enhanced tensorial formulation for elastic degradation in micropolar continua. Applied Mathematical Modelling, vol. , pp. ”“. (in press).
Gori, L., Pitangueira, R. L. S., Penna, S. S., & Fuina, J. S., 2015a. A generalized elasto-plastic micro-polar constitutive model. Applied Mechanics and Materials, vol. 798, pp. 505”“509.
Gori, L., Pitangueira, R. L. S., Penna, S. S., & Fuina, J. S., 2015b. Isotropic damage models based on a generalized micro-polar continuum theory. In Anais do 57 Congresso Brasileiro do Concreto, Bonito, Brazil. IBRACON - Instituto Brasileiro do Concreto.
Gori, L., Pitangueira, R. L. S., Penna, S. S., & Fuina, J. S., 2015c. A theoretical and computational framework for isotropic damage models based on a generalized micro-polar continuum theory. In Proceedings of the XXXVI Ibero-Latin American Congress on Computational Methods in Engineering, Rio de Janeiro, Brazil. ABMEC - Brazilian Association of Computational Methods in Engineering.
INSANE Project, 2016. https://www.insane.dees.ufmg.br/.
Iordache, M. M. & Willam, K., 1998. Localized failure analysis in elastoplastic Cosserat continua. Computer Methods in Applied Mechanics and Engineering, vol. 121, n. 3-4, pp. 559”“586.
Li, S., Hao, W., & Liu, W. K., 2000. Mesh-free simulations of shear banding in large deformation. International Journal of Solids and Structures, vol. 37, pp. 7185”“7206.
Li, S. & Liu, W. K., 2000. Numerical simulations of strain localization in inelastic solids using mesh-free methods. International Journal for Numerical Mehods in Engineering, vol. 48, pp.1285”“1309.
Liang, K.-Z. & Huang, F.-Y., 1996. Boundary element method for micropolar elasticity. International Journal of Engineering Science, vol. 34, n. 5, pp. 509 ”“ 521.
Liu, W. K., Hao, S., Belytschko, T., Li, S. F., & Chang, C. T., 1999. Multiple scale meshfree methods for damage fracture and localization. Computational Material Science, vol. 16, pp. 197”“205.
Mariano, P. M. & Stazi, F. L., 2005. Computational aspects of the mechanics of complex materials. Archives of Computational Methods in Engineering, vol. 12, n. 4, pp. 391”“478.
Mazars, J., 1984. Application de le Mecanique de l’endommagement au comportement non ´ lineaire et a la rupture du b ` eton de Structure ´ . PhD thesis, Universite Pierre et Marie Curie - ´Laboratoire de Mecanique et Technologie, Paris, France. (in french).
Downloads
Published
How to Cite
Issue
Section
License
Given the public access policy of the journal, the use of the published texts is free, with the obligation of recognizing the original authorship and the first publication in this journal. The authors of the published contributions are entirely and exclusively responsible for their contents.
1. The authors authorize the publication of the article in this journal.
2. The authors guarantee that the contribution is original, and take full responsibility for its content in case of impugnation by third parties.
3. The authors guarantee that the contribution is not under evaluation in another journal.
4. The authors keep the copyright and convey to the journal the right of first publication, the work being licensed under a Creative Commons Attribution License-BY.
5. The authors are allowed and stimulated to publicize and distribute their work on-line after the publication in the journal.
6. The authors of the approved works authorize the journal to distribute their content, after publication, for reproduction in content indexes, virtual libraries and similars.
7. The editors reserve the right to make adjustments to the text and to adequate the article to the editorial rules of the journal.
