Anisotropic damage mechanics based on strain energy equivalence and equivalent elliptical microcracks

1997 ◽  
Vol 34 (33-34) ◽  
pp. 4377-4397 ◽  
Author(s):  
Usik Lee ◽  
George A. Lesieutre ◽  
Lei Fang
Keyword(s):  
Strain Energy ◽  
Damage Mechanics ◽  
Anisotropic Damage ◽  
Energy Equivalence

Crack Identification in Thin Plates With Anisotropic Damage Model and Vibration Measurements

2005 ◽  
Vol 72 (6) ◽  
pp. 852-861 ◽  
Author(s):  
D. Wu ◽  
S. S. Law
Keyword(s):  
Strain Energy ◽  
Damage Model ◽  
Dynamic Responses ◽  
Thin Plates ◽  
Crack Identification ◽  
Anisotropic Damage ◽  
Plate Element ◽  
Vibration Measurements ◽  
Actual Length ◽  
Energy Equivalence

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.

A Theory of Continuum Damage Mechanics for Anisotropic Solids

1999 ◽  
Vol 66 (1) ◽  
pp. 264-268 ◽  
Author(s):  
U. Lee
Keyword(s):  
Elastic Properties ◽  
Strain Energy ◽  
Damage Mechanics ◽  
Continuum Damage Mechanics ◽  
Continuum Damage ◽  
Energy Equivalence ◽  
Damage Theory ◽  
Anisotropic Elastic ◽  
Isotropic Solids ◽  
Line Crack

This paper develops a fracture mechanics based continuum damage theory for initially anisotropic solids by extending the author’s previous damage theory for isotropic solids. The concepts of strain energy equivalence principle (SEEP) and equivalent line-crack modeling are used to develop the effective continuum elastic properties of a damaged solid in terms of the undamaged anisotropic elastic properties and a scalar damage variable.

Parameter estimation of an anisotropic damage model for concrete using genetic algorithms

2015 ◽  
Vol 26 (6) ◽  
pp. 801-825 ◽  
Author(s):  
Muhammad A Wardeh ◽  
Houssam A Toutanji
Keyword(s):  
Damage Evolution ◽  
Elastic Strain ◽  
Strain Energy ◽  
Damage Mechanics ◽  
Evolution Equations ◽  
Damage Model ◽  
Elastic Strain Energy ◽  
Constitutive Law ◽  
Anisotropic Damage ◽  
Unknown Parameters

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.

Novel Strain Energy Based Coupled Elastoplastic Damage and Healing Models for Geomaterials – Part II: Computational Aspects

2011 ◽  
Vol 21 (4) ◽  
pp. 551-576 ◽  
Author(s):  
J. W. Ju ◽  
K. Y. Yuan ◽  
A. W. Kuo ◽  
J. S. Chen
Keyword(s):  
Los Angeles ◽  
Strain Energy ◽  
Damage Mechanics ◽  
Operator Splitting ◽  
Anisotropic Damage ◽  
Computational Algorithms ◽  
Partial Recovery ◽  
Meshfree Analysis ◽  
Damage Healing ◽  
Elastoplastic Damage

In Part I of this sequel (Ju, J.W., Yuan, K.Y. and Kuo, A.W. (2010). Novel Strain Energy Based Coupled Elastoplastic Damage and Healing Models for Geomaterials – Part I: Formulations, International Journal of Damage Mechanics, DOI: 10.1177/1056789511407359), we have developed innovative strain energy based coupled elastoplastic hybrid isotropic and anisotropic damage-healing formulations for geomaterials under complex 2D earth-moving processes. Emanating from a micromechanics-based brittle (tensile) damage characterization (P+) and a ductile (mixed tension–compression) damage-healing characterization ([Formula: see text]), the proposed hybrid isotropic and anisotropic damage-healing models for soils are implemented. Entirely new computational algorithms are systematically developed based on the two-step operator splitting methodology. The elastic damage-healing predictor and the plastic corrector are consistently implemented within the existing Nonlinear Meshfree Analysis Program at University of California, Los Angeles ( Chen, J.S., Wu, C.T., Yoon, S. and You, Y. (2001) . A Stabilized Conforming Nodal Integration for Galerkin Meshfree Methods, International Journal for Numerical Methods in Engineering, 50: 435–466). Several numerical simulations featuring sophisticated earth excavation, transport, compaction, and a numerical notched soil bar under cyclic tension–compression loading are presented to illustrate the salient elastoplastic damage and healing features of soils, such as shear band and partial recovery of soil stiffness due to compression (compaction) by the proposed innovative damage-healing models and step-by-step computational algorithms.

New Tensors for Anisotropic Damage in Continuum Damage Mechanics

2012 ◽  
Vol 134 (2) ◽  
Author(s):  
George Z. Voyiadjis ◽  
Mohammed A. Yousef ◽  
Peter I. Kattan
Keyword(s):  
Mechanical Behavior ◽  
Elastic Energy ◽  
Elastic Strain ◽  
Damage Mechanics ◽  
Continuum Damage Mechanics ◽  
Damage Effect ◽  
Anisotropic Damage ◽  
Continuum Damage ◽  
Energy Equivalence ◽  
Scalar Invariant

In this work, new proposed damage tensors are studied in order to investigate the damage effect variables in the mechanical behavior of materials. All cases studied in this work are defined in terms of the elasticity of the material and based on the hypotheses of both elastic strain equivalence and elastic energy equivalence. Moreover, the new proposed damage tensors are anisotropically expressed in terms of the well-known damage effect tensor M. The principal-valued damage effect tensor is used to obtain the first scalar invariant of that tensor and its inverse, which are employed in expressing and verifying the new proposed damage tensors. The study demonstrates that most of the new proposed damage tensors are verified within the framework of continuum damage mechanics. In addition, new hybrid damage tensors are proposed which are defined in terms of the damage effect tensor and the new proposed damage tensors. The new hybrid damage tensors are eventually expressed in terms of the damage effect tensor.

Analytical examination of mesh-dependency issue for uniaxial RC elements and new fracture energy-based regularization technique

2021 ◽  
pp. 105678952110392
Author(s):  
De-Cheng Feng ◽  
Xiaodan Ren
Keyword(s):  
Reinforced Concrete ◽  
Fracture Energy ◽  
Regularization Method ◽  
Strain Energy ◽  
Plain Concrete ◽  
Comprehensive Analysis ◽  
Stress Strain ◽  
Regularization Technique ◽  
Mesh Dependency ◽  
Energy Equivalence

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.

scholarly journals A bi-dissipative damage model for concrete

2015 ◽  
Vol 8 (1) ◽  
pp. 49-65
Author(s):  
J. J. C. Pituba ◽  
W. M. Pereira Júnior
Keyword(s):  
Reinforced Concrete ◽  
Structural Engineering ◽  
Damage Mechanics ◽  
Damage Model ◽  
Continuum Damage Mechanics ◽  
Concrete Material ◽  
Framed Structures ◽  
Energy Equivalence ◽  
Proposed Model ◽  
Damage Processes

This work deals with an improvement of an anisotropic damage model in order to analyze reinforced concrete structures submitted to reversal loading. The original constitutive model is based on the fundamental hypothesis of energy equivalence between real and continuous media following the concepts of the Continuum Damage Mechanics. The concrete is assumed as an initial elastic isotropic medium presenting anisotropy, permanent strains and bimodularity 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. However, the original model is not capable to simulate the influence of the previous damage processes in compression regimes. In order to avoid this problem, some conditions are introduced to simulate the damage unilateral effect. It has noted that the damage model is agreement with to micromechanical theory conditions when dealing to unilateral effect in concrete material. Finally, the proposed model is applied in the analyses of reinforced concrete framed structures submitted to reversal loading. These numerical applications show the good performance of the model and its potentialities to simulate practical problems in structural engineering.

Shakedown-Ratcheting Analysis of a Spherical Pressure Vessel by Anisotropic Continuum Damage Mechanics

2018 ◽  
Author(s):  
Ali Nayebi ◽  
Azam Surmiri ◽  
Hojjatollah Rokhgireh
Keyword(s):  
Pressure Vessel ◽  
Damage Mechanics ◽  
Kinematic Hardening ◽  
Continuum Damage Mechanics ◽  
Mapping Method ◽  
Anisotropic Damage ◽  
Continuum Damage ◽  
Interaction Diagram ◽  
Plastic Shakedown ◽  
Spherical Pressure

In cyclic loading and when plastic flow occurs, discontinuities grow. In this research, interaction diagram of Bree has been developed when the spherical pressure vessel contains discontinuities such as voids and microcracks. Bree’s diagram is used for ratcheting assessment of pressurized equipment in ASME III NH. Nature of these defects leads to an anisotropic damage. Anisotropic Continuum Damage Mechanics (CDM) is considered to account effects of these discontinuities on the behavior of the structure. Shakedown – ratcheting response of a hollow sphere under constant internal pressure and cyclic thermal loadings are studied by using anisotropic CDM theory coupled with nonlinear kinematic hardening of Armstrong-Frederick m’s model (A-F). Return mapping method is used to solve numerically the developed relations. Elastic, elastic shakedown, plastic shakedown and ratcheting regions are illustrated in the modified Bree’s diagram. Influence of anisotropic damage due to the plastic deformation is studied and it was shown that the plastic shakedown region is diminished because of the developed damage.

Sign in / Sign up

Export Citation Format

Share Document