Size effect in localized failure: testing, uncertainty, modeling
This project concerns the failure mechanisms and crack development in brittle heterogeneous materials such as concrete and fiber-reinforced concrete (FRC). The focus is on two main areas: localized failure with size effect and the probabilistic methods necessary for capturing the size effect placed within the Bayesian framework. The goal is to achieve a significant improvement in the fundamental understanding and predictive modeling of cracking and failure phenomena under long-term variable conditions including extreme events.
When loaded up to failure, structures built of heterogeneous materials exhibit a size effect along with a distinct softening behavior due to localization zone with dominant inelastic deformation. The localized failure phenomena, leading to softening response, represent material behavior accompanied by large strain gradients which makes the standard homogenization approach not applicable, and as well represents a challenge for ensuring convergence of finite element computations. Therefore, the extended finite element method (X-FEM) is used instead of the standard finite element method. This method allows to represent the crack-induced displacement discontinuity in the finite element mesh by using the Heavisede function and, combined with a multi-scale homogenization-localization framework, to model crack propagation.
The aim is to develop an intrinsic localized failure model, starting with fine scale random materials with inclusions. The inclusions are often on a very small meso-scale, whereas the overall response has to be considered at a macro-scale. The predictive model development calls for a multi-scale approach, where the computational models at the different scales will be coupled.
Since the composition of the materials is considered random, our lack of knowledge or uncertainty of the actual value can be described in a Bayesian way through a probabilistic model. The unknown parameter is then modeled as a random variable, also called the prior model, and additional information on the system through measurement or observation changes the probabilistic description to the so-called posterior model.
The probabilistic setting is required for nonlinear inelastic behavior of composites where homogenization no longer applies, since premature localized failure is in general very sensitive to fine-scale initial defects, and displays a size effect. By describing the defects in terms of their probability distribution, we can recast the durability challenge as a coupled nonlinear mechanics-probability formulation.
Publikationen im Rahmen des GRK:
Konferenzbeiträge mit Veröffentlichung:
S. Dobrilla, N. Friedman, T. Rukavina, H.G. Matthies and A. Ibrahimbegovic. Probabilistic Analysis of Fiber Reinforced Concrete. Proceedings of the CILAMCE 2018 conference; Paris/ Compiègne, France (2018).