The failure modelling of structures composed of quasi-brittle materials via IGABEM and Extended the Lumped Damage approach

• Autor(a) principal: Nardi, Deborah Cristina
• Data de Publicação: 2024
• Tipo de documento: Dissertação
• Idioma: eng
• Título da fonte: Biblioteca Digital de Teses e Dissertações da USP
• Texto Completo: https://www.teses.usp.br/teses/disponiveis/18/18134/tde-11042024-144829/
• topic: análise isogeométrica; análise não-linear; boundary element method; extended lumped damage mechanics; isogeometric analysis; mecânica do dano concentrado expandida; método dos elementos de contorno; nonlinear analysis

Accurately predicting the mechanical behavior of structures poses a challenge for civil engineers, requiring the translation of numerous fundamental aspects into the adopted numerical model. For instance, the type of the structure\'s material is a factor that needs to be considered. A significant range of quasi-brittle materials is present in the engineering world, due to their versatility and applicability. Ceramics and cementitious are classic examples of this class of materials. In parallel, it is known that the mechanical response is highly affected when physical phenomena such as cracking appear and start to propagate in elements composed of quasi-brittle materials. The strong material nonlinear behaviour caused by this problem can be represented in the numerical models by the damage mechanics, a theory which incorporates the internal variable of damage into the problem. In this context, the present work presents the development of a damage formulation via the Boundary Element Method (BEM). The adopted constitutive model is the Lumped Damage Mechanics for bidimensional media, the so-called Extended Lumped Damage Mechanics (XLMD). The model effectively captures the material nonlinear behavior due to crack propagation. Nonlinear analysis in the BEM context proves to be a challenging task. The main reason is the requirement for domain discretization, making the use of a boundary-based method unfeasible. In light of this, the present work proposes the coupling of XLDM in the context of an isogeometric analysis in Boundary Element Method (IGABEM). Quadrilateral cells are employed to account for the nonlinear effects via the initial stress field approach. The domain is only discretized where the damage is expected to propagate, enabling the application of BEM in the context of damage mechanics. A total of five examples are presented: the initial two ones for validating the IGABEM formulation and the later ones for validating the proposed damage approach. The results achieved by the proposed formulation are compared with numerical and experimental outcomes available in the literature. A good agreement with both experimental and numerical findings are achieved. The proposed approach is promising and improvements are proposed for future works.