An Elastoplastic-anisotropic Damage Model for Concrete

2011 ◽  
Vol 261-263 ◽  
pp. 371-375
Author(s):  
Jun Liu ◽  
Gao Lin
Keyword(s):  
Effective Stress ◽  
Damage Mechanics ◽  
Damage Model ◽  
Nonlinear Behavior ◽  
Continuum Damage Mechanics ◽  
Anisotropic Damage ◽  
Softening Effect ◽  
Damage Constitutive Model ◽  
Structural Levels ◽  
Damage Tensor

An elastoplastic-anisotropic damage constitutive model for the description of nonlinear behavior of concrete is presented. The yield surface is developed in effective stress spaces, which takes into account the hardening effect and better match the experimental data. The stiffness degradation and softening effect are considered in the framework of continuum damage mechanics formulation. The second-order damage tensor is used to characterize the anisotropy induced by the orientation of microcracks. In order to simulate the unilateral effect, the elastic Helmholtz free energy is decomposed into a volumetric part and a deviatoric part. The different behavior under tensile and compressive loadings is modeled by using different variables in effective stress and damage tensor. Numerical results of the model accord well with experimental results at the material and structural levels.

Anisotropic Damage Effect Tensors for the Symmetrization of the Effective Stress Tensor

1997 ◽  
Vol 64 (1) ◽  
pp. 106-110 ◽  
Author(s):  
G. Z. Voyiadjis ◽  
T. Park
Keyword(s):  
Stress Tensor ◽  
Effective Stress ◽  
Fourth Order ◽  
Damage Mechanics ◽  
Continuum Theory ◽  
Continuum Damage Mechanics ◽  
Damage Effect ◽  
Anisotropic Damage ◽  
Tensor Algebra ◽  
Physical Description

Based on the concept of the effective stress and on the description of anisotropic damage deformation within the framework of continuum damage mechanics, a fourth order damage effective tensor is properly defined. For a general state of deformation and damage, it is seen that the effective stress tensor is usually asymmetric. Its symmetrization is necessary for a continuum theory to be valid in the classical sense. In order to transform the current stress tensor to a symmetric effective stress tensor, a fourth order damage effect tensor should be defined such that it follows the rules of tensor algebra and maintains a physical description of damage. Moreover, an explicit expression of the damage effect tensor is of particular importance in order to obtain the constitutive relation in the damaged material. The damage effect tensor in this work is explicitly characterized in terms of a kinematic measure of damage through a second-order damage tensor. In this work, tensorial forms are used for the derivation of such a linear transformation tensor which is then converted to a matrix form.

A Developed Damage Constitutive Model for Circular Steel Tubes of Reticulated Shells

2020 ◽  
Vol 20 (09) ◽  
pp. 2050106
Author(s):  
Sheng He ◽  
Haosen Wang ◽  
Stéphane P. A. Bordas ◽  
Peng Yu
Keyword(s):  
Constitutive Model ◽  
Damage Mechanics ◽  
Dynamic Instability ◽  
Damage Model ◽  
Nonlinear Dynamic Analysis ◽  
Continuum Damage Mechanics ◽  
Steel Tubes ◽  
Mapping Algorithm ◽  
Comparison Results ◽  
Damage Constitutive Model

The aim of this paper is that the precise description of damage behavior is crucial to well catch the mechanical behavior of structures in the dynamic numerical simulation, and address the issue on the coupled plastic-damage constitutive model for circular steel tubes of reticulated shells under severe earthquake. Continuum Damage Mechanics (CDM) constitutive model established by Lemaitre is reviewed at the beginning. Then, an improved damage model for circular steel tubes of reticulated shells is developed based on Lemaitre’s model by replacing the original damage evolution law with a new one suitable for circular steel tubes. In addition, we introduce the stress update process. In this procedure, the well-known operator split strategy, which leads to the standard elastic predictor/return mapping algorithm, is adopted to solve the evolution problem of the improved model. Exploiting user-defined material subroutine, the implementation of the model is achieved within software ANSYS using BEAM189 element. Finally, the dynamic response of reticulated shells under severe earthquake are numerically simulated with the proposed model and with the conventional Prandtl-Reuss model, respectively. The comparison results show that the consideration of material damage accumulation, on the one hand, may change the failure mode of reticulated shells from dynamic instability to strength failure; on the other, may reduce the dynamic ultimate load obviously. This consideration should be taken into account when conducting nonlinear dynamic analysis of reticulated shells.

Cross-Ply Laminates under Static Three-Point Bending: A Numerical Development Model

2012 ◽  
Vol 498 ◽  
pp. 42-54 ◽  
Author(s):  
S. Benbelaid ◽  
B. Bezzazi ◽  
A. Bezazi
Keyword(s):  
Numerical Model ◽  
Damage Mechanics ◽  
Progressive Failure ◽  
Damage Model ◽  
Continuum Damage Mechanics ◽  
Failure Criteria ◽  
Continuum Damage ◽  
Damage Development ◽  
Element Analysis ◽  
Progressive Failure Analysis

This paper considers damage development mechanisms in cross-ply laminates using an accurate numerical model. Under static three points bending, two modes of damage progression in cross-ply laminates are predominated: transverse cracking and delamination. However, this second mode of damage is not accounted in our numerical model. After a general review of experimental approaches of observed behavior of laminates, the focus is laid on predicting laminate behavior based on continuum damage mechanics. In this study, a continuum damage model based on ply failure criteria is presented, which is initially proposed by Ladevèze. To reveal the effect of different stacking sequence of the laminate; such as thickness and the interior or exterior disposition of the 0° and 90° oriented layers in the laminate, an equivalent damage accumulation which cover all ply failure mechanisms has been predicted. However, the solution algorithm using finite element analysis which implements progressive failure analysis is summarized. The results of the numerical computation have been justified by the previous published experimental observations of the authors.

A Nonlinear Damage Model of Hardening-Softening Materials

2017 ◽  
Vol 140 (1) ◽  
Author(s):  
M. Ganjiani
Keyword(s):  
Damage Mechanics ◽  
Damage Model ◽  
Continuum Damage Mechanics ◽  
Tensile Tests ◽  
Internal Variable ◽  
Integration Algorithm ◽  
Finite Element Program ◽  
Variable Theory ◽  
Numerical Predictions ◽  
Type Variable

In this paper, an elastoplastic-damage constitutive model is presented. The formulation is cast within the framework of continuum damage mechanics (CDM) by means of the internal variable theory of thermodynamics. The damage is assumed as a tensor type variable and its evolution is developed based on the energy equivalence hypothesis. In order to discriminate the plastic and damage deformation, two surfaces named as plastic and damage are introduced. The damage surface has been developed so that it can model the nonlinear variation of damage. The details of the model besides its implicit integration algorithm are presented. The model is implemented as a user-defined subroutine user-defined material (UMAT) in the abaqus/standard finite element program for numerical simulation purposes. In the regard of investigating the capability of model, the shear and tensile tests are experimentally conducted, and corresponding results are compared with those predicted numerically. These comparisons are also accomplished for several experiments available in the literature. Satisfactory agreement between experiments and numerical predictions provided by the model implies the capability of the model to predict the plastic deformation as well as damage evolution in the materials.

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.

scholarly journals On continuum damage mechanics

2019 ◽  
Vol 52 (3) ◽  
pp. 125-147
Author(s):  
Kari Juhani Santaoja
Keyword(s):  
Stress Tensor ◽  
Effective Stress ◽  
Elastic Strain ◽  
Damage Mechanics ◽  
Volume Fraction ◽  
Strain Tensor ◽  
Continuum Damage Mechanics ◽  
Continuum Damage ◽  
The Matrix ◽  
Elastic Strain Tensor

A material containing spherical microvoids with a Hookean matrix response was shown to take the appearance usually applied in continuum damage mechanics. However, the commonly used variable damage D was replaced with the void volume fraction f , which has a clear physical meaning, and the elastic strain tensor \Bold {ε}^e with the damage-elastic strain tensor \Bold {ε}^{de}. The postulate of strain equivalence with the effective stress concept was reformulated and applied to a case where the response of the matrix obeys Hooke’s law. In contrast to many other studies, in the derived relation between the effective stress tensor \Bold {\Tilde{σ}} and the stress tensor \Bold {σ}, the tensor \Bold {\Tilde{σ}} is symmetric. A uniaxial bar model was introduce for clarifying the derived results. Other candidates for damage were demonstrated by studying the effect of carbide coarsening on creep rate.

Numerical Prediction of Failure within Small Curvature Bending of Advanced High Strength Steels

2015 ◽  
Vol 639 ◽  
pp. 419-426
Author(s):  
Ioannis Tsoupis ◽  
Marion Merklein
Keyword(s):  
Crack Initiation ◽  
Damage Mechanics ◽  
Numerical Study ◽  
Damage Model ◽  
High Strength Steels ◽  
High Strength ◽  
Continuum Damage Mechanics ◽  
Calibration Method ◽  
Damage Parameter ◽  
Small Curvature

Within this paper a numerical study of the Continuum Damage Mechanics based damage model Lemaitre in commercial software LS-DYNA is performed in order to correctly predict failure in terms of crack occurrence within small curvature bending of AHSS steels. A strain based calibration method is used for the effective adaption of the Lemaitre model to the bending operation, which is based on the comparison and adaption of the numerically calculated and the experimentally measured deformation field on the outer surface of the bent specimen. Within this method the material dependent damage parameter S is systematically varied in the simulation in order to represent maximum major strain. The new method is proved by numerical simulation of experiments provoking crack initiation using smaller bending radii. It can be shown that failure in terms of crack initiation can be correctly predicted by the model with the damage parameters, which were determined by the method of strain based calibration and an additional optimisation of the parameter Dc. Thus, within this study a user friendly and effective way for the application of Lemaitre damage model to small curvature bending processes of AHSS steels is developed.

A Damage Model for Adhesively Bonded Single-Lap Thick Composite Joints

2012 ◽  
Vol 134 (4) ◽  
Author(s):  
Sayed A. Nassar ◽  
Jianghui Mao ◽  
Xianjie Yang ◽  
Douglas Templeton
Keyword(s):  
Damage Mechanics ◽  
Resin Composite ◽  
Analytical Data ◽  
Damage Model ◽  
Continuum Damage Mechanics ◽  
Epoxy Adhesive ◽  
Failure Behavior ◽  
Adhesively Bonded ◽  
Damage Initiation ◽  
Damage Models

A proposed damage model is used for investigating the deformation and interfacial failure behavior of an adhesively bonded single-lap thick joint made of S2 glass/SC-15 epoxy resin composite material. The bonding material is 3M Scotch-Weld Epoxy Adhesive DP405 Black. Continuum damage mechanics models are used to describe the damage initiation and final failure at or near the interface. The effect of adhesive overlap length, thickness, and plasticity on the interfacial shear and normal stresses is studied. Experimental and analytical data are used to validate the proposed damage models.

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