Theoretical Formulation of a Coupled Elastic—Plastic Anisotropic Damage Model for Concrete using the Strain Energy Equivalence Concept

2008 ◽  
Vol 18 (7) ◽  
pp. 603-638 ◽  
Author(s):  
George Z. Voyiadjis ◽  
Ziad N. Taqieddin ◽  
Peter I. Kattan
2005 ◽  
Vol 72 (6) ◽  
pp. 852-861 ◽  
Author(s):  
D. Wu ◽  
S. S. Law

Many approaches on modeling of cracks in structural members have been reported in the literatures. However, most of them are explicitly developed for the purpose of studying the changes in static and dynamic responses of the structure due to the crack damage, which is a forward problem mathematically. Thereby the use of these models is inconvenient or even impossible for detecting damage in structures from vibration measurements, which is usually an inverse problem. An anisotropic damage model is proposed for a two-dimensional plate element with an edge-parallel crack. The cracked plate element is represented by a plate element with orthotropic anisotropic material expressed in terms of the virgin material stiffness and a tensor of damage variables. Instead of using the effective stress concept, strain equivalence, or strain energy equivalence principles, the vector of damage variables is identified based on the principle of equivalent static and dynamic behaviors. A nonmodel-based damage identification approach is developed incorporating the proposed anisotropic model and the estimated uniform load surface curvature (ULSC) from vibration measurements. The actual length of the crack is then predicted from the identified variables based on conservation law of potential energy for crack growth. The validity of the methodology is demonstrated by numerical examples and experiment results with comparison to results from existing strain energy equivalence theory.


2007 ◽  
Vol 353-358 ◽  
pp. 1199-1202
Author(s):  
Usik Lee ◽  
Deokki Youn ◽  
Sang Kwon Lee

A new continuum damage theory (CDT) has been proposed by Lee et al. (1997) based on the SEEP. The CDT has the apparent advantage over the other related theories because the complete constitutive law can be readily derived by simply replacing the virgin elastic stiffness with the effective orthotropic elastic stiffness obtained by using the proposed continuum damage theory. In this paper, the CDT is evaluated by comparing the mode shapes and natural frequencies of a square plate containing a small line-through crack with those of the same plate with a damaged site replaced with the effective orthotropic elastic stiffness computed by using the CDT.


2011 ◽  
Vol 133 (2) ◽  
Author(s):  
P. Grammenoudis ◽  
D. Reckwerth ◽  
Ch. Tsakmakis

Anisotropic viscoplasticity coupled with anisotropic damage has been modeled in previous works by using the energy equivalence principle appropriately adjusted. Isotropic and kinematic hardenings are present in the viscoplastic part of the model and the evolution equations for the hardening variables incorporate both static and dynamic recovery terms. The main difference to other approaches consists in the formulation of the energy equivalence principle for the plastic stress power and the rate of hardening energy stored in the material. As a practical consequence, a yield function has been established, which depends, besides effective stress variables, on specific functions of damage. The present paper addresses the capabilities of the model in predicting responses of deformation processes with complex specimen geometry. In particular, multiple notched circular specimens and plates with multiple holes under cyclic loading conditions are considered. Comparison of predicted responses with experimental results confirms the convenience of the proposed theory for describing anisotropic damage effects.


2015 ◽  
Vol 26 (6) ◽  
pp. 801-825 ◽  
Author(s):  
Muhammad A Wardeh ◽  
Houssam A Toutanji

This article presents an anisotropic damage model for concrete that couples between elasticity and continuum damage mechanics. The formulation of constitutive model is based on the elastic strain energy in the framework of irreversible thermodynamics. The thermodynamic free energy is represented as a scalar function of elastic strain and damage tensors and used to derive the constitutive law and thermodynamic conjugate force of damage that is used to derive the dissipation potential. The damage evolution law is governed by the normality rule. The formulation of elastic strain energy of damaged material is capable of modeling the concrete anisotropic behavior under different loadings without decoupling the stress or damage release rate. A series of unknown parameters in the model formulation was used to control the constitutive behavior and damage surface. A Genetic algorithm FORTRAN subroutine is used to estimate these parameters based on the coupling between the constitutive and damage evolution equations. The performance of the damage model is verified with the experimental data from the literature. The model has shown a good agreement with the experimental results. It describes the anisotropy induced by the crack development within the concrete.


Energies ◽  
2020 ◽  
Vol 13 (8) ◽  
pp. 1928 ◽  
Author(s):  
Faham Tahmasebinia ◽  
Chengguo Zhang ◽  
Ismet Canbulat ◽  
Samad Sepasgozar ◽  
Serkan Saydam

Coal burst occurrences are affected by a range of mining and geological factors. Excessive slipping between the strata layers may release a considerable amount of strain energy, which can be destructive. A competent strata is also more vulnerable to riveting a large amount of strain energy. If the stored energy in the rigid roof reaches a certain level, it will be released suddenly which can create a serious dynamic reaction leading to coal burst incidents. In this paper, a new damage model based on the modified thermomechanical continuum constitutive model in coal mass and the contact layers between the rock and coal mass is proposed. The original continuum constitutive model was initially developed for the cemented granular materials. The application of the modified continuum constitutive model is the key aspect to understand the momentum energy between the coal–rock interactions. The transformed energy between the coal mass and different strata layers will be analytically demonstrated as a function of the rock/joint quality interaction conditions. The failure and post failure in the coal mass and coal–rock joint interaction will be classified by the coal mass crushing, coal–rock interaction damage and fragment reorganisation. The outcomes of this paper will help to forecast the possibility of the coal burst occurrence based on the interaction between the coal mass and the strata layers in a coal mine.


2021 ◽  
pp. 105678952110392
Author(s):  
De-Cheng Feng ◽  
Xiaodan Ren

This paper presents a comprehensive analysis of the mesh-dependency issue for both plain concrete and reinforced concrete (RC) members under uniaxial loading. The detailed mechanisms for each case are firstly derived, and the analytical and numerical strain energies for concrete in different cases are compared to explain the phenomena of mesh-dependency. It is found that the mesh-dependency will be relieved or even eliminated with the increasing of the reinforcing ratio. Meanwhile, a concept of the critical reinforcing ratio is proposed to identify the corresponding boundary of mesh-dependency of RC members. In order to verify the above findings, several illustrative examples are performed and discussed. Finally, to overcome the mesh-dependency issue for RC members with lower reinforcing ratios, we propose a unified regularization method that modifies both stress-strain relations of steel and concrete based on the strain energy equivalence. The method is also applied to the illustrative examples for validation, and the numerical results indicate that the developed method can obtain objective results for cases with different meshes and reinforcing ratios.


2015 ◽  
Vol 784 ◽  
pp. 292-299 ◽  
Author(s):  
Stephan Wulfinghoff ◽  
Marek Fassin ◽  
Stefanie Reese

In this work, two time integration algorithms for the anisotropic damage model proposed by Lemaitre et al. (2000) are compared. Specifically, the standard implicit Euler scheme is compared to an algorithm which implicitly solves the elasto-plastic evolution equations and explicitly computes the damage update. To this end, a three dimensional bending example is solved using the finite element method and the results of the two algorithms are compared for different time step sizes.


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