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.

scholarly journals Evolution Mechanisms of Thermal Shock Cracks in Ceramic Sheet

2016 ◽  
Vol 83 (7) ◽  
Author(s):  
Xianghong Xu ◽  
Zhongkang Lin ◽  
Shilong Sheng ◽  
Wenjun Yuan
Keyword(s):  
Thermal Shock ◽  
Elastic Strain ◽  
Strain Energy ◽  
Damage Mechanics ◽  
Interaction Mechanism ◽  
Elastic Strain Energy ◽  
Water Quenching ◽  
Multiple Cracks ◽  
Failure Evolution ◽  
Cracks Interaction

Knowledge of crack initiation, propagation, and corresponding thermal shock failure evolution is prerequisite for effective maintenance of civil engineering so as to avoid disaster. Experimental analysis of the cracking in the ceramic sheets subsequent to water quenching has been conducted. Based on statistical mesoscopic damage mechanics, it was revealed that there are four stages in the process of thermal shock evolution of ceramics subjected to water quenching. The multiple cracks interaction mechanism has been analyzed from the viewpoint of the evolution of the elastic strain energy and stress intensity factor.

Viscoplastic Constitutive Modeling of Anisotropic Damage Under Nonproportional Loading

2000 ◽  
Vol 123 (4) ◽  
pp. 403-408 ◽  
Author(s):  
C. L. Chow ◽  
X. J. Yang ◽  
Edmund Chu
Keyword(s):  
Constitutive Modeling ◽  
Damage Evolution ◽  
Damage Mechanics ◽  
Evolution Equations ◽  
Forming Limit ◽  
Anisotropic Damage ◽  
Limit Curve ◽  
Forming Limit Curve ◽  
Localized Necking ◽  
Theory Of Damage

Based on the theory of damage mechanics, a viscoplastic constitutive modeling of anisotropic damage for the prediction of forming limit curve (FLC) is developed. The model takes into account the effect of rotation of principal damage coordinates on the deformation and damage behaviors. With the aid of the damage viscoplastic potential, the damage evolution equations are established. Based on a proposed damage criterion for localized necking, the model is employed to predict the FLC of aluminum 6111-T4 sheet alloy. The predicted results agree well with those determined experimentally.

Fatigue Damage Model for Numerical Assessment of Fatigue Characteristics

2008 ◽  
Vol 580-582 ◽  
pp. 663-666 ◽  
Author(s):  
Chi Seung Lee ◽  
Myung Hyun Kim ◽  
Min Sung Chun ◽  
Tak Kee Lee ◽  
Jae Myung Lee
Keyword(s):  
Damage Evolution ◽  
Damage Mechanics ◽  
Evolution Equations ◽  
Numerical Technique ◽  
Damage Model ◽  
Internal Damage ◽  
Numerical Assessment ◽  
Fatigue Characteristics ◽  
Evolution Behavior ◽  
Relationship Assessment

The aim of this study is the development of a numerical technique applicable for the fatigue assessment based on the damage mechanics approach. The generalized elasto-visco-plastic constitutive equation, which can consider the internal damage evolution behavior, is developed in order to numerically evaluate the material fatigue responses. Explicit information of the relationships between the mechanical properties and material constants, which are required for the mechanical constitutive and damage evolution equations, are derived. The performance of the developed technique has been verified using the S-N relationship assessment for STS304 stainless steel.

Viscoplastic Constitutive Modeling of Anisotropic Damage Under Nonproportional Loading

2000 ◽  
Author(s):  
C. L. Chow ◽  
X. J. Yang ◽  
Edmund Chu
Keyword(s):  
Constitutive Modeling ◽  
Damage Evolution ◽  
Damage Mechanics ◽  
Evolution Equations ◽  
Forming Limit ◽  
Anisotropic Damage ◽  
Limit Curve ◽  
Forming Limit Curve ◽  
Localized Necking ◽  
Theory Of Damage

Abstract Based on the theory of damage mechanics, a viscoplastic constitutive modeling of anisotropic damage for the prediction of forming limit curve (FLC) is developed. The model takes into account the effect of rotation of principal damage coordinates on the deformation and damage behaviors. With the aid of the damage viscoplastic potential, the damage evolution equations are established. Based on a proposed damage criterion for localized necking, the model is employed to predict the FLC of aluminum 6111-T4 sheet alloy. The predicted results agree well with those determined experimentally.

Research on Fracture Damage Coupled with Crack Arrest by Anchorage Model of Discontinuous Jointed Rock Mass under the State of Complex Stress

2007 ◽  
Vol 348-349 ◽  
pp. 189-192
Author(s):  
Le Wen Zhang ◽  
Shu Cai Li ◽  
Ying Wang
Keyword(s):  
Rock Mass ◽  
Constitutive Relation ◽  
Damage Evolution ◽  
Strain Energy ◽  
Damage Mechanics ◽  
Evolution Equations ◽  
Equivalent Strain ◽  
The State ◽  
Shear Stresses ◽  
Fracture Damage

Based on the hypothesis of equivalent strain energy and the theories of fracture mechanics and damage mechanics，the constitutive model and fracture damage mechanism of bolted discontinuous jointed rockmass are systematically studied under the state of complex stresses. Initially ， considering the equivalent strain energy ， the constitutive relation of anchored discontinuous jointed rockmass is derived under the state of compression-shear stresses. The constitutive relation under the state of tension-shear stresses is also developed according to the theory of self-consistence. Next，the damage evolution equations of discontinuous multi-crack rockmass under compression-shear and tension-shear are put forward according to the wing crack-initiating criterion. Finally，based on the above constitutive models and the damage evolution equations three-dimensional finite element procedures have been developed to evaluate the stability and deformability of the surrounding rock mass during excavation and supporting. The calculated results indicate that above-mentioned constitutive relation and the damage evolution equations are available.

Do muscles function as adaptable locomotor springs?

2002 ◽  
Vol 205 (15) ◽  
pp. 2211-2216 ◽  
Author(s):  
Stan L. Lindstedt ◽  
Trude E. Reich ◽  
Paul Keim ◽  
Paul C. LaStayo
Keyword(s):  
Skeletal Muscle ◽  
Elastic Strain ◽  
Strain Energy ◽  
Elastic Strain Energy ◽  
Normal Animal ◽  
Eccentric Contractions ◽  
Normal Muscle ◽  
Energetic Costs ◽  
Locomotor Muscles ◽  
Power Outputs

SUMMARYDuring normal animal movements, the forces produced by the locomotor muscles may be greater than, equal to or less than the forces acting on those muscles, the consequences of which significantly affect both the maximum force produced and the energy consumed by the muscles. Lengthening (eccentric)contractions result in the greatest muscle forces at the lowest relative energetic costs. Eccentric contractions play a key role in storing elastic strain energy which, when recovered in subsequent contractions, has been shown to result in enhanced force, work or power outputs. We present data that support the concept that this ability of muscle to store and recover elastic strain energy is an adaptable property of skeletal muscle. Further, we speculate that a crucial element in that muscle spring may be the protein titin. It too seems to adapt to muscle use, and its stiffness seems to be`tuned' to the frequency of normal muscle use.

Comparison of Two Time-Integration Algorithms for an Anisotropic Damage Model Coupled with Plasticity

2015 ◽  
Vol 784 ◽  
pp. 292-299 ◽  
Author(s):  
Stephan Wulfinghoff ◽  
Marek Fassin ◽  
Stefanie Reese
Keyword(s):  
Evolution Equations ◽  
Damage Model ◽  
Time Integration ◽  
Three Dimensional ◽  
Anisotropic Damage ◽  
Euler Scheme ◽  
The Finite Element Method ◽  
Time Step ◽  
Implicit Euler Scheme ◽  
Integration Algorithms

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.

Failure Predictions for DP Steel Cross-die Test using Anisotropic Damage

2011 ◽  
Vol 21 (5) ◽  
pp. 713-754 ◽  
Author(s):  
M. S. Niazi ◽  
H. H. Wisselink ◽  
T. Meinders ◽  
J. Huétink
Keyword(s):  
Strain Rate ◽  
Damage Evolution ◽  
Damage Model ◽  
Anisotropic Damage ◽  
Continuum Damage ◽  
Anisotropic Plasticity ◽  
Continuum Damage Model ◽  
Damage Models ◽  
Isotropic Damage ◽  
Failure Predictions

The Lemaitre's continuum damage model is well known in the field of damage mechanics. The anisotropic damage model given by Lemaitre is relatively simple, applicable to nonproportional loads and uses only four damage parameters. The hypothesis of strain equivalence is used to map the effective stress to the nominal stress. Both the isotropic and anisotropic damage models from Lemaitre are implemented in an in-house implicit finite element code. The damage model is coupled with an elasto-plastic material model using anisotropic plasticity (Hill-48 yield criterion) and strain-rate dependent isotropic hardening. The Lemaitre continuum damage model is based on the small strain assumption; therefore, the model is implemented in an incremental co-rotational framework to make it applicable for large strains. The damage dissipation potential was slightly adapted to incorporate a different damage evolution behavior under compression and tension. A tensile test and a low-cycle fatigue test were used to determine the damage parameters. The damage evolution was modified to incorporate strain rate sensitivity by making two of the damage parameters a function of strain rate. The model is applied to predict failure in a cross-die deep drawing process, which is well known for having a wide variety of strains and strain path changes. The failure predictions obtained from the anisotropic damage models are in good agreement with the experimental results, whereas the predictions obtained from the isotropic damage model are slightly conservative. The anisotropic damage model predicts the crack direction more accurately compared to the predictions based on principal stress directions using the isotropic damage model. The set of damage parameters, determined in a uniaxial condition, gives a good failure prediction under other triaxiality conditions.

Sign in / Sign up

Export Citation Format

Share Document