Non-linear analysis of reinforced concrete plates by the boundary element method and continuum damage mechanics

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Visualisation of numerical models for paper damage mechanics

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Wavelet-Galerkin method for one-dimensional elastoplasticity and damage problems: Constitutive modeling and computational aspects

This work presents an analysis of the wavelet-Galerkin method for one-dimensional elastoplastic-damage problems. Time-stepping algorithm for non-linear dynamics is presented. Numerical treatment of the constitutive models is developed by the use of return-mapping algorithm. For spacial discretization we can use wavelet-Galerkin method instead of standard finite element method. This approach allows to locate singularities. The discrete formulation developed can be applied to the simulation of one-dimensional problems for elastic-plastic-damage models. (C) 2007 Elsevier Inc. All rights reserved.

Effect of Mechanical and Geometric Mismatching on Fatigue and Damage of Welded Joints

The future of high technology welded constructions will be characterised by higher strength materials and improved weld quality with respect to fatigue resistance. The expected implementation of high quality high strength steel welds will require that more attention be given to the issues of crack initiation and mechanical mismatching. Experiments and finite element analyses were performed within the framework of continuum damage mechanics to investigate the effect of mismatching of welded joints on void nucleation and coalescence during monotonic loading. It was found that the damage of undermatched joints mainly occurred in the sandwich layer and the damageresistance of the joints decreases with the decrease of the sandwich layer width. The damage of over-matched joints mainly occurred in the base metal adjacent to the sandwich layer and the damage resistance of the joints increases with thedecrease of the sandwich layer width. The mechanisms of the initiation of the micro voids/cracks were found to be cracking of the inclusions or the embrittled second phase, and the debonding of the inclusions from the matrix. Experimental fatigue crack growth rate testing showed that the fatigue life of under-matched central crack panel specimens is longer than that of over-matched and even-matched specimens. Further investigation by the elastic-plastic finite element analysis indicated that fatigue crack closure, which originated from the inhomogeneousyielding adjacent to the crack tip, played an important role in the fatigue crack propagation. The applicability of the J integral concept to the mismatched specimens with crack extension under cyclic loading was assessed. The concept of fatigue class used by the International Institute of Welding was introduced in the parametric numerical analysis of several welded joints. The effect of weld geometry and load condition on fatigue strength of ferrite-pearlite steel joints was systematically evaluated based on linear elastic fracture mechanics. Joint types included lap joints, angle joints and butt joints. Various combinations of the tensile and bending loads were considered during the evaluation with the emphasis focused on the existence of both root and toe cracks. For a lap joint with asmall lack-of-penetration, a reasonably large weld leg and smaller flank angle were recommended for engineering practice in order to achieve higher fatigue strength. It was found that the fatigue strength of the angle joint depended strongly on the location and orientation of the preexisting crack-like welding defects, even if the joint was welded with full penetration. It is commonly believed that the double sided butt welds can have significantly higher fatigue strength than that of a single sided welds, but fatigue crack initiation and propagation can originate from the weld root if the welding procedure results in a partial penetration. It is clearly shown that the fatigue strength of the butt joint could be improved remarkably by ensuring full penetration. Nevertheless, increasing the fatigue strength of a butt joint by increasing the size of the weld is an uneconomical alternative.

An Interface Damage Model for the Simulation of Delamination Under Variable-Mode Ratio in Composite Materials

A thermodynamically consistent damage model for the simulation of progressive delamination under variable mode ratio is presented. The model is formulated in the context of the Damage Mechanics. The constitutive equation that results from the definition of the free energy as a function of a damage variable is used to model the initiation and propagation of delamination. A new delamination initiation criterion is developed to assure that the formulation can account for changes in the loading mode in a thermodynamically consistent way. The formulation proposed accounts for crack closure effets avoiding interfacial penetration of two adjacent layers aftercomplete decohesion. The model is implemented in a finite element formulation. The numerical predictions given by the model are compared with experimental results

An Anisotropic Model of Damage and Unilateral Effect for Brittle Materials

This work deals with the initial applications and formulation of an aniscitropic plastic-damage constitutive model proposed for non-linear analysis of reinforced concrete structures submitted to a loading with change of the sign. The original constitutive model is based on the fundamental hypothesis of energy equivalence between real and continuous medium following the concepts of the Continuum Damage Mechanics. The concrete is assumed as an initial elastic isotropic medium presenting anisotropy, permanent strains and bimodularity (distinct elastic responses whether traction or compression stress states prevail) induced by damage evolution. In order to take into account the bimodularity, two damage tensors governing the rigidity in tension or compression regimes are introduced. Then, some conditions are introduced in the original version of the model in order to simulate the damage unilateral effect. The three-dimensional version of the proposed model is analyzed in order to validate its formulation when compared to micromechanical theory. The one-dimensional version of the model is applied in the analyses of a reinforced concrete beam submitted to a loading with change of the sign. Despite the parametric identification problems, the initial applications show the good performance of the model.

Wavelet-Galerkin method for one-dimensional elastoplasticity and damage problems: Constitutive modeling and computational aspects

This work presents an analysis of the wavelet-Galerkin method for one-dimensional elastoplastic-damage problems. Time-stepping algorithm for non-linear dynamics is presented. Numerical treatment of the constitutive models is developed by the use of return-mapping algorithm. For spacial discretization we can use wavelet-Galerkin method instead of standard finite element method. This approach allows to locate singularities. The discrete formulation developed can be applied to the simulation of one-dimensional problems for elastic-plastic-damage models. (C) 2007 Elsevier B.V. All rights reserved.

On a regular convex solver potential for an elastic-damage constitutive model: a theoretical analysis

This work is related with the proposition of a so-called regular or convex solver potential to be used in numerical simulations involving a certain class of constitutive elastic-damage models. All the mathematical aspects involved are based on convex analysis, which is employed aiming a consistent variational formulation of the potential and its conjugate one. It is shown that the constitutive relations for the class of damage models here considered can be derived from the solver potentials by means of sub-differentials sets. The optimality conditions of the resulting minimisation problem represent in particular a linear complementarity problem. Finally, a simple example is present in order to illustrate the possible integration errors that can be generated when finite step analysis is performed. (C) 2003 Elsevier Ltd. All rights reserved.

A fatigue damage model for seismic response of RC structures

Numerous damage models have been developed in order to analyze seismic behavior. Among the different possibilities existing in the literature, it is very clear that models developed along the lines of continuum damage mechanics are more consistent with the definition of damage as a phenomenon with mechanical consequences because they include explicitly the coupling between damage and mechanical behavior. On the other hand, for seismic processes, phenomena such as low cycle fatigue may have a pronounced effect on the overall behavior of the frames and, therefore, its consideration turns out to be very important. However, most of existing models evaluate the damage only as a function of the maximum amplitude of cyclic deformation without considering the number of cycles. In this paper, a generalization of the simplified model proposed by Cipollina et al. [Cipollina A, López-Hinojosa A, Flórez-López J. Comput Struct 1995;54:1113–26] is made in order to include the low cycle fatigue. Such a model employs in its formulation irreversible thermodynamics and internal state variable theory.

A repairability index for reinforced concrete members based on fracture mechanics

This paper proposes a repairability index for damage assessment in reinforced concrete structural members. The procedure discussed in this paper differs from the standard methods in two aspects: the structural and damage analyses are coupled and it is based on the concepts of fracture and continuum damage mechanics. The relationship between the repairability index and the well-known Park and Ang index is shown in some particular cases.

Modelization of low cycle fatigue damage in frames

Damage models based on the Continuum Damage Mechanics (CDM) include explicitly the coupling between damage and mechanical behavior and, therefore, are consistent with the definition of damage as a phenomenon with mechanical consequences. However, this kind of models is characterized by their complexity. Using the concept of lumped models, possible simplifications of the coupled models have been proposed in the literature to adapt them to the study of beams and frames. On the other hand, in most of these coupled models damage is associated only with the damage energy release rate which is shown to be the elastic strain energy. According to this, damage is a function of the maximum amplitude of cyclic deformation but does not depend on the number of cycles. Therefore, low cycle effects are not taking into account. From the simplified model proposed by Flórez-López, it is the purpose of this paper to present a formulation that allows to take into account the degradation produced not only by the peak values but also by the cumulative effects such as the low cycle fatigue. For it, the classical damage dissipative potential based on the concept of damage energy release rate is modified using a fatigue function in order to include cumulative effects. The fatigue function is determined through parameters such as the cumulative rotation and the total rotation and the number of cycles to failure. Those parameters can be measured or identified physically through the haracteristics of the RC. So the main advantage of the proposed model is the possibility of simulating the low cycle fatigue behavior without introducing parameters with no suitable physical meaning. The good performance of the proposed model is shown through a comparison between numerical and test results under cycling loading.

A Damage Model for Masonry Infilled Frames

The effect of infill walls on the behaviour of frames is widely recognized, and, for several decades now, has been the subject of numerous experimental investigations. However, the analytical modeling of infilled panels and frames under in-plane loading is difficult and generally unreliable. From the point of view of the simulation technique the models may be divided into micromodels and simplified (or macro-) models. Based on the equivalent strut approach (simplified model), in this paper a damage model is proposed for the characterization of masonry walls submitted to lateral cyclic loads. The model, developed along the lines of the Continuum Damage Mechanics, have the advantages of including explicitly the coupling between damage and mechanical behaviour and so is consistent with the definition of damage as a phenomenon with mechanical consequences.

A damage model for seismic retrofitting of structures

Numerous damage models have been developed in order to analyse the seismic behavior. Among the different possibilities existing in the literature, it is very clear that models developed along the lines of Continuum Damage Mechanics are more consistent with the definition of damage like a phenomenon with mechanical consequences as they include explicitly the coupling between damage and mechanical behavior. On the other hand, for seismic processes, phenomena such as low cycle fatigue may have a pronounced effect on the overall behavior of the frames and, therefore, its consideration turns out to be very important. However, many of existing models evaluate the damage only as a function of the maximum amplitude of cyclic deformation without considering the number of cycles. In this paper, a generalization of the simplified model proposed by Flórez is made in order to include the low cycle fatigue. Such model employs in its formulation irreversible thermodynamics and internal state variable theory.

Computational model for local damage assesment of structures

In the last years many studies have been developed to analyze the seismic behavior throug the damage concept. In fact, the evaluation of the structural damage is important in order to quantify the safety of new and existing structures and, also, to establish a framework for seismic retrofitting decision making of structures. Most proposed models are based on a post-earthquake evaluation in such a way they uncouple the computation of the structural response from that of damage. However, there are other models which include explicity the existing coupling between the degradation and the structural mechanical beaviour. Those models are closer to the physical reality and its formulation is based on the principles of Continuum Damage Mechanics. In the present work, a coupled model is formulated using a simplified application of the Continuum Damage Mechanics to the analysis of frames and allows its representation in standard finite element programs. This work is part of the activities developed by the Structural Mechanics Department (UPM) within ICONS (European Research Project on Innovative Seismic Design Concepts for New and Existing Structures).