Application of a microplane damage model for concrete to an isogeometric scaled boundary formulation for 3D solids

Abstract

AbstractMicroplane models have the advantage of describing damage‐induced anisotropy, which is common in quasi‐brittle materials such as concrete, in a simple and straightforward way. Over the past decades, various microplane models have been formulated to describe different loading cases and phenomena in concrete structures. They include pure damage and pure plasticity based microplane models or a combination of these two approaches. In this work, as a first step, a microplane damage model, which is derived from the principle of energy equivalence, is applied in the framework of an isogeometric 3D solid in boundary representation. Isogeometric analysis has the advantage that it can represent exactly complex geometries, which can influence the correct description of damage evolution. In addition, the use of a boundary representation in combination with NURBS and B‐splines is in accordance with the modeling technique common in CAD and allows for a straightforward application of the design model to the analysis process. The boundary is described using bi‐variate NURBS while the interior of the solid is approximated using uni‐variate B‐splines. The combination of isogeometric analysis with a model that can capture the finely distributed cracking of the concrete matrix represents a modeling strategy that can effectively support the development of thin‐walled shell structures made of textile‐reinforced concrete. Several examples are studied in order to investigate the ability of the microplane damage model to correctly describe quasi‐brittle fracture in this kind of non‐standard discretization formulation. Furthermore, a comparison to the standard finite element method is conducted.