Analysis of reinforced concrete structures with occurrence of discrete cracks at arbitrary positions

A nonlinear analysis of in-plane loaded plates is presented, which eliminates the disadvantages of the smeared crack approach. The elements used and the computational method are discussed. An example is shown in which one or more discrete cracks are dominant

Smeared crack approach: back to the original track

This paper briefly reviews the formulations used over the last 40 years for the solution of problems involving tensile cracking, with both the discrete and the smeared crack approaches. The paper focuses on the smeared approach, identifying as its main drawbacks the observed mesh‐size and mesh‐bias spurious dependence when the method is applied ‘straightly’. A simple isotropic local damage constitutive model is considered, and the (exponential) softening modulus is regularized according to the material fracture energy and the element size. The continuum and discrete mechanical problems corresponding to both the weak discontinuity (smeared cracks) and the strong discontinuity (discrete cracks) approaches are analysed and the question of propagation of the strain localization band (crack) is identified as the main difficulty to be overcome in the numerical procedure. A tracking technique is used to ensure stability of the solution, attaining the necessary convergence properties of the corresponding discrete finite element formulation. Numerical examples show that the formulation derived is stable and remarkably robust. As a consequence, the results obtained do not suffer from spurious mesh‐size or mesh‐bias dependence, comparing very favourably with those obtained with other fracture and continuum mechanics approaches

Smeared crack approach: Back to the original track

This paper reviews briefly the formulations used over the last 40 years for the solution of problems involving tensile cracking, both with the discrete and smeared crack approaches. The paper focuses in the smeared approach, identifying as its main drawbacks the observed mesh-size and mesh-bias spurious dependence when the method is applied “straightly”. A simple isotropic local damage constitutive model is considered, and the (exponential) softening modulus is regularized according to the material fracture energy and the element size. The continuum and discrete mechanical problems corresponding to both the weak discontinuity (smeared cracks) and strong discontinuity (discrete cracks) approaches are analyzed and the question of propagation of the strain localization band (crack) is identified as the main difficulty to be overcome in the numerical procedure. A tracking technique is used to ensure uniqueness of the solution, attaining the necessary stability and convergence properties of the corresponding discrete finite element formulation. Numerical examples show that the formulation derived is well posed, stable and remarkably robust. As a consequence, the results obtained do not suffer from spurious meshsize or mesh-bias dependence, comparing very favorably with those obtained with other fracture and continuum mechanics approaches

Nonlinear elastic analysis of concrete beams based on the Smeared Crack Approach

In the present study, an analysis of plain and reinforced concrete beams under monotonic loading was made based on the Fixed Smeared Crack approach. The objectives of this research were to analyze the nonlinear behavior of the selected cases of analysis and to propose an alternative and simple model for the analysis of beams under service loadings, by means of Committee 435 of the American Concrete Institute. A brittle model for concrete and a linear-elastic behavior for steel reinforcement bars were considered. Results are presented through force-displacement curves and the sequence of cracking propagation. Also, a comparison of calculated instantaneous deflections of simply supported beams was made between the proposed model and other researches. It was verified that the proposed algorithm can predict adequately the cracking process and the deflections of beams subjected to service loadings, taking into account experimental results from other authors

Finite-discrete element modelling of masonry infill walls subjected to out-of-plane loads

In this paper, the out-of-plane response of infill walls is investigated by means of non-linear monotonic (push-over) analyses through a combined finite and discrete modelling approach. The model accounts for material deformability, crack formation, sliding, separa-tion and formation of new contacts. Masonry units are modelled as finite elements, and differ-ent material models are assumed for the masonry. Contact between masonry units, and between masonry and frame elements is modelled by means of interfaces, which permit tan-gential motion with frictional sliding. Frame elements are modelled by means of a linear-elastic material. The results of the numerical analyses are compared with those of experimen-tal tests available in the literature. The advantages and disadvantages of the adopted model-ling strategy are investigated

A Critical Evaluation of Computational Fracture Using a Smeared Crack Approach in MPM

An evaluation of the smeared crack representation of material failure using the material-point method (MPM) as a feasible computational failure approach is performed. The spatial descretization in MPM is defined by a grid of cells that represent space and a set of points that represent the deformable solid. A grid orientation bias in the numerical results is demonstrated. Solution accuracy is lost when failure surface and grid line orientations are not aligned. Causes of the grid orientation dependence are identified, but the problem remains unresolved. Limited use of the smeared crack approach in MPM for solving problems of material failure is advised

Modelling of SFRC using inverse finite element analysis

A method of inverse finite element analysis is used to determine the constitutive relationship of SFRC in tension, using primary experimental data. Based on beam bending test results and results from pull-out tests, an attempt is made to explain the physical processes taking place during the cracking stage. Basic models predicting the behaviour of SFRC in tension are proposed. © RILEM 2006

Investigation of progressive damage and fracture in laminated composites using the smeared crack approach

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/97056/1/AIAA2012-1537.pd

Modelling Localisation and Spatial Scaling of Constitutive Behaviour: a Kinematically Enriched Continuum Approach

It is well known that classical constitutive models fail to capture the post-peak material behaviour, due to localisation of deformation. In such cases the concept of Representative Volume Element (RVE) on which classical continuum models rest ceases to exist and hence the smearing out of local inhomogeneities over the whole RVE is no longer correct. This paper presents a new approach to capturing localised failure in quasi-brittle materials, focusing on the kinematic enrichment of the constitutive model to describe correctly the behaviour of a volume element with an embedded localisation band. The resulting models possess an intrinsic length scale which in this case is the width of the embedded localisation band. The behaviour therefore scales with both the width of the localisation band and the size of the volume on which the model is defined. As a consequence, size effects are automatically captured in addition to the model capability in capturing behaviour at the scale of the localisation zone.Comment: Proceedings of Asian-Pacific Conference on Fracture and Strength 2014 and the International Conference on Structural Integrity and Failure, 9-12 December, Sydney, Australi

Embedded crack model: I. Basic formulation

The recently emerged idea of enriching standard nite element interpolations by strain or displacement discontinuities has triggered the development of powerful techniques that allow ecient modelling of regions with highly localized strains, e.g. of fracture zones in concrete, or shear bands in metals or soils. The present paper describes a triangular element with an embedded displacement discontinuity that represents a crack. The constitutive model is formulated within the framework of damage theory, with crack closure eects and friction on the crack faces taken into account. Numerical aspects of the implementation are discussed. In a companion paper, the embedded crack approach is combined with the more traditional smeared crack approach.\u