SCALAR DAMAGE BASED ON MICROPOLAR CONTINUA ”“ MESH-FREE APPROXIMATION
DOI:
https://doi.org/10.26512/ripe.v2i7.21714Palavras-chave:
Micropolar continua. Scalar damage. Strain localization. Mesh-free methods. Element Free Galerkin.Resumo
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.
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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).
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