Conference Agenda

This study investigates the mathematical algorithm for mapping the continuous random fields of material properties onto the FE meshes, and its implications for the mesh sensitivity in stochastic FE analysis of quasibrittle fracture. We adopt a continuum damage constitutive model, and develop a mechanistic mapping method. The projection of the random fields of material properties onto the FE mesh is governed by the prevailing damage pattern of the finite element. The model is applied to stochastic FE analysis of notched and unnotched flexural specimens under different loading configurations. The numerical analysis also considers different correlation lengths of the random fields of material properties. The simulation shows that, even with the proper energy regularization scheme, the commonly used local mapping and local average methods could yield considerable mesh dependence of the peak load statistics. By relating the mapping algorithm to the underlying damage pattern, the present model is able to mitigate the mesh sensitivity for different specimen geometries, loading configurations, and correlation lengths.

The macroscopic behaviour of concrete is quasi-brittle, and its fracture behaviour is greatly influenced by the fracture process zone (FPZ). The experimental studies on plain concrete show that the load-displacement response of the concrete is characterized by an initial elastic phase followed by a nonlinear behaviour up to peak load and subsequent non-linear softening response. Continuum Damage Mechanics (CDM) is a widely used approach for modeling the fracture behavior of quasi-brittle materials. In CDM, softening is represented by stiffness degradation, modeled using a monotonically decreasing damage parameter. This damage variable is characterized through area reduction in the cross-section, degradation of elastic stiffness, microcrack density, etc. However, the evolution equations in most of the models are not consistent with their physical meaning. In this work, we relate damage to a probability measure that modifies the load-carrying area or volume (in a diffused sense). The damage variable evolves in a manner analogous to transition probability density in non-conserved processes, like those observed in killed diffusion processes. The evolution equation
consists of a killing rate term that controls the rate of damage/degradation. The structure of the killing rate is such that it consists of a term that controls initial elastic behaviour, and a parameter that controls the rate of fracture. To ensure the monotonic reduction in this variable, the killing rate is ensured to always be a positive quantity. Softening in the load-displacement response is captured similarly to that of CDM through a gradual reduction in stress in the linear momentum balance equation. We validate our model by reproducing the crack pattern and load-displacement responses observed in corresponding experimental studies of plain concrete.

Cracking in quasi-brittle materials, like concrete, is known to be a nonlocal process associated with an intrinsic material length scale. To take into account these nonlocal effects in continuum damage models for concrete, many approaches have been proposed in the past decades. The latter comprise integral nonlocal formulations, implicit or explicit gradient-enhanced models, as well as the phase field approach to cohesive fracture. Among them, implicit gradient-enhanced models have proved to represent a powerful approach, when applied in Finite Element simulations. However, it is well-known that conventional gradient-enhanced models yield a nonphysical broadening of the damaged zone. To overcome this issue, the so-called localizing gradient damage model with decreasing interaction has been proposed by Poh and Sun. However, to the authors’ best knowledge, this formulation has only rarely been applied to damage-plasticity models, and a comprehensive discussion of its impact on the structural behavior is missing in the literature. In this study, we investigate the localizing gradient formulation proposed by Poh and Sun for the widely recognized concrete damage-plasticity (CDP) model by Grassl and Jir´asek. Specifically, we discuss the advantages and disadvantages compared to the conventional gradient enhancement through a simple 1D tensile test and a numerical benchmark example.

This study deals with mitigation of concentration effects due to small opening corners in RC deep beams with different reinforcement detailing. Six different reinforcement details in six RC deep beams with small utility openings were tested under three-point loading. The deformations at peak load, strains in rebars at critical locations, load-carrying capacity, load vs. deflection response, crack pattern, strut deformations and energy dissipation have been described. The test results show that the design and detailing of reinforcement influence on deformations, strain concentrations, and strain distributions in rebars. Higher quantity of horizontal reinforcement near the openings performed better with reduced deformations and enhanced load-carrying capacity, while vertical-web reinforcement near openings enhances stiffness and reduces deflections, with significant structural stability under loading. The reinforced concrete deep beams with small openings underlines the role of reinforcement detailing for better performance with ductility up to the brink of ultimate failure.

The concrete cracking is simulated by the finite element method combined with the constitutive model based on the nonlinear fracture mechanics using finite element simulation software. It is known that numerical simulations of reinforced concrete using the finite element method can be strongly influenced by the assumptions of crack spacing or crack band size, especially when large finite element sizes are used. The proposed approach attempts to address this issue by using machine learning and artificial neural network surrogate models to estimate crack spacing in reinforced concrete structures. The model uncertainties for mean and maximum crack widths are evaluated using the database of laboratory results. The reinforcement arrangement, dimensional simplification, and numerical discretization effects on the model uncertainty are investigated. The numerical model offers an adequate prediction of crack widths for the beams with a single-layer reinforcement and exhibits less accuracy for the multilayer bar arrangement. The presented numerical model represents an advanced tool for the crack width assessment in the design of reinforced concrete structures in serviceability limit states.