A Damage Model for Nonlinear Tensile Behavior of Cortical Bone

1999 ◽  
Vol 121 (5) ◽  
pp. 533-541 ◽  
Author(s):  
M. T. Fondrk ◽  
E. H. Bahniuk ◽  
D. T. Davy
Keyword(s):  
Experimental Data ◽  
Cortical Bone ◽  
Internal State ◽  
Damage Model ◽  
Experimental Studies ◽  
Inelastic Strain ◽  
Damage Parameter ◽  
Tensile Behavior ◽  
State Variables ◽  
Bending Loading

To describe the time-dependent nonlinear tensile behavior observed in experimental studies of cortical bone, a damage model was developed using two internal state variables (ISV’s). One ISV is a damage parameter that represents the loss of stiffness. A rule for the evolution of this ISV was defined based on previously observed creep behavior. The second ISV represents the inelastic strain due to viscosity and internal friction. The model was tested by simulating experiments in tensile and bending loading. Using average values from previous creep studies for parameters in the damage evolution rule, the model tended to underestimate the maximum nonlinear strains and to overestimate the nonlinear strain accumulated after load reversal in the tensile test simulations. Varying the parameters for the individual tests produced excellent fits to the experimental data. Similarly, the model simulations of the bending tests could produce excellent fits to the experimental data. The results demonstrate that the 2-ISV model combining damage (stiffness loss) with slip and viscous behavior could capture the nonlinear tensile behavior of cortical bone in axial and bending loading.

Elastoviscoplastic Models with Relaxed Configurations and Internal State Variables

1990 ◽  
Vol 43 (7) ◽  
pp. 131-151 ◽  
Author(s):  
Sanda Cleja T¸igoiu ◽  
Eugen Soo´s
Keyword(s):  
Experimental Data ◽  
Structural Analysis ◽  
Internal State ◽  
State Variables ◽  
Internal State Variables ◽  
Local Current

We present the microstructural basis, the initial macroscopical formulations, and a possible axiomatic reconstruction of the elastoviscoplastic model for metals based on the use of the local, current, relaxed configurations. Structural analysis and experimental data show that using these configurations offers advantages for the formulation of the material laws when the deformations are small or moderately large. Our review aims to be a concise, historical, and critical exposition of the main stages, contributions and results, which led, during the late sixties and the beginning of seventies, to the formulation of the fundamental ideas lying at the basis of the model. We delineate the role played by Lee, Liu, Teodosiu, Sidoroff, Mandel, and Kratochvil in the first formulation of the theory between 1966 and 1972, as well as the contributions of Dafalias and Loret to the development of the model between 1983 and 1985. Finally, we discuss some results obtained between 1985 and 1988 with models based on local current relaxed configurations.

A constitutive model for anisotropic, kinematic hardening materials

1997 ◽  
Vol 32 (3) ◽  
pp. 175-181
Author(s):  
W Deng ◽  
A Asundi ◽  
C W Woo
Keyword(s):  
Inelastic Deformation ◽  
Internal State ◽  
Kinematic Hardening ◽  
Small Deformation ◽  
Inelastic Strain ◽  
State Variables ◽  
Internal State Variables ◽  
Deformation Plasticity ◽  
Independent Variable ◽  
Evolution Laws

Based on previous work by the authors, a model for anisotropic, kinematic hardening materials is constructed to describe constitutive equations and evolution laws in rate-independent, small deformation plasticity on the basis of thermodynamics. Unlike other theories developed earlier wherein only internal state variables are chosen to describe inelastic deformation, the present paper also considers inelastic strain as an independent variable. This can be shown to reduce to the well-known plastic strain in the case of rate-independent plasticity.

Creep Failure Simulations for 316H at 550°C

2012 ◽  
Author(s):  
Nak Hyun Kim ◽  
Yun Jae Kim ◽  
Catrin M. Davies ◽  
Kamran M. Nikbin ◽  
David W. Dean
Keyword(s):  
Experimental Data ◽  
Damage Model ◽  
Creep Damage ◽  
Inelastic Strain ◽  
Compact Tension ◽  
Creep Failure ◽  
Creep Ductility ◽  
Summation Rule ◽  
Creep Damage Model ◽  
Damage Summation

In this work a method to simulate failure due to creep is proposed using finite element damage analysis. The creep damage model is based on the creep ductility exhaustion concept. Incremental damage is defined by the ratio of incremental inelastic (plastic & creep) strain and multi-axial ductility. A simple linear damage summation rule is applied. When accumulated damage becomes unity, element stresses are reduced to almost zero to simulate progressive crack growth. The model is validated through comparison with experimental data on various sized compact tension, C(T), specimens of 316H stainless steel at 550 °C. The influence of the inelastic strain rate on the uniaxial ductility is considered. Good agreement is found between the simulated results and the experimental data.

A Domain Evolution Model for the Ferroelastic Hysteresis of Piezoceramic Materials

Aerospace ◽  
2003 ◽  
Author(s):  
V. Narayanan ◽  
X. Lu ◽  
S. Hanagud
Keyword(s):  
Distribution Function ◽  
Mechanical Loading ◽  
Domain Switching ◽  
Internal State ◽  
Mechanical Strain ◽  
Inelastic Strain ◽  
State Variables ◽  
Domain Evolution ◽  
Internal State Variables ◽  
Piezoelectric Strain

In this paper, we model the thermo-ferroelastic hysteresis phenomena under large mechanical loading by using internal state variables that are associated with a statistical description of microstructural domain characterization. This work is to extend our previous work [1, 2] to include the ferroelastic effects. Under large mechanical loading, the total bulk strain includes the mechanical strain and the bulk piezoelectric strain. The piezoelectric strain is the accompanying strain with the evolution of the domain network, which is described by a domain orientation distribution function. In ferroelastic hysteresis, the domain evolution, which is mainly contributed by 90° domain switching, is delineated by the evolution of the associated domain distribution function and further simplified by the evolution of the associated internal state variables that are the parameters of the domain distribution function. For the mechanical field, the mechanical strain is divided into two parts- the elastic strain and the inelastic strain. The inelastic strain is the corresponding internal variable to describe the inelastic behavior under large mechanical loading. Therefore, the remnant strain contains two parts: the remnant piezoelectric strain and remnant inelastic strain. The dissipation and the associated temperature increase per unit cycle in the ferroelastic hysteresis are studied.

Thermodynamic Formulation of Endochronic Cyclic Viscoplasticity With Damage- Application to Eutectic Sn/Pb Solder Alloy

2007 ◽  
Vol 23 (4) ◽  
pp. 433-444 ◽  
Author(s):  
C. F. Lee ◽  
Y. C. Chen
Keyword(s):  
Internal State ◽  
Low Cycle Fatigue ◽  
Cyclic Stress ◽  
Irreversible Thermodynamics ◽  
Damage Parameter ◽  
Fatigue Tests ◽  
Future Research ◽  
Mathematical Form ◽  
State Variables ◽  
Endochronic Theory

AbstractIn this paper, an endochronic theory of cyclic viscoplasticy with damage is established based on the irreversible thermodynamics of continuous media with internal state variables containing an isotropic damage parameter. The constitutive equations derived have the same mathematical form as those of convectional endochronic theory without damage, except the effective stress with damage is used. This result coincides with the Lemaitre's statements of stain equivalence principle.Using the experimental cyclic stress-strain curves of 63Sn/37Pb solder bars, corrected from the uniaxially constant displacement amplitude cyclic tests under MTS Tytron microtester, the computational results of cyclic stess-strain curves with several degrees of damage can reproduce the experimental data quite well. Based on compressive buckling appeared in the vicinity of the compressive end parts of the hysteresis loop, the critical values of damage are determined between 0.3 and 0.4.The evolution equation of damage proposed in terms of the intrinsic damage time scale and its results in the modified Coffin-Manson LCF law can be extended in the future research for a statistical theory of life distribution under low cycle fatigue tests.

Three-Dimensional Continuum Damage Model for Polymer Matrix Composites

Materials ◽  
2004 ◽  
Author(s):  
Ever J. Barbero ◽  
Joan A. Mayugo ◽  
Paolo Lonetti
Keyword(s):  
Experimental Data ◽  
Parameter Identification ◽  
Polymer Matrix ◽  
Composite Laminates ◽  
Damage Mechanics ◽  
Failure Modes ◽  
Polymer Matrix Composites ◽  
Internal State ◽  
Material Behavior ◽  
State Variables

A constitutive model for fiber reinforced composite materials with damage and unrecoverable deformation, which for the first time accounts for thru-the-thickness damage, is presented. The formulation is based on Continuous Damage Mechanics coupled with Classical Plasticity Theory in a consistent thermodynamic framework using internal state variables. A novel formulation of the parameter identification is included in order to describe the main failure modes of polymer matrix composite laminae. The new parameter identification is simpler than those available in the literature. It is also more sensitive and allows for better control of material behavior to match experimental data. Furthermore, it uses material properties that are simpler to test than previous models. The model uses a small number of adjustable parameters, which are identified from available experimental data. Comparisons with experimental data for composite laminates under in plane and torsion loading are shown to validate the model. The new model, although simpler than previous ones, is able to model all experimentally observed behavior of laminates that were previously modeled with more complex models.

Studying the effect of a hydrostatic stress/strain reduction factor on damage mechanics of concrete materials

2013 ◽  
Vol 22 (5-6) ◽  
pp. 149-159
Author(s):  
Ziad N. Taqieddin ◽  
George Z. Voyiadjis
Keyword(s):  
Damage Mechanics ◽  
Internal State ◽  
Hydrostatic Stress ◽  
Damage Model ◽  
Reduction Factor ◽  
State Variables ◽  
Elastic Plastic ◽  
Damage Models ◽  
Plastic Damage ◽  
Concrete Materials

AbstractIn the non-linear finite element analysis (NFEA) of concrete materials, continuum damage mechanics (CDM) provides a powerful framework for the derivation of constitutive models capable of describing the mechanical behavior of such materials. The internal state variables of CDM can be introduced to the elastic analysis of concrete to form elastic-damage models (no inelastic strains), or to the elastic-plastic analysis in order to form coupled/uncoupled elastic-plastic-damage models. Experimental evidence that is well documented in literature shows that the susceptibility of concrete to damage and failure is distinguished under deviatoric loading from that corresponding to hydrostatic loading. A reduction factor is usually introduced into a CDM model to reduce the susceptibility of concrete to hydrostatic stresses/strains. In this work, the effect of a hydrostatic stress/strain reduction factor on the performances of two NFEA concrete models will be studied. These two (independently published) models did not provide any results showing such effect. One of these two models is an elastic-damage model, whereas the other is an uncoupled elastic-plastic-damage model. Simulations and comparisons are carried out between the performances of the two models under uniaxial tensile and compressive loading conditions. Simulations are also provided for the uncoupled elastic-plastic-damage model under the following additional loading conditions: biaxial tension and biaxial compression, uniaxial cyclic loading, and varying ratios of triaxial compressive loadings. These simulations clearly show the effect of the reduction factor on the numerically depicted behaviors of concrete materials. To have rational comparisons, the hydrostatic stress reduction factor applied to each model is chosen to be a function of the internal state variables common to both models. Therefore, once the two models are calibrated to simulate the experimental behaviors, their corresponding reduction factors are readily available at every increment of the iterative NFEA procedures.

Damage Coupled With Heat Conduction in Uniaxially Reinforced Composites

1988 ◽  
Vol 55 (3) ◽  
pp. 641-647 ◽  
Author(s):  
Y. Weitsman
Keyword(s):  
Heat Conduction ◽  
Mechanical Response ◽  
Internal State ◽  
Constitutive Relations ◽  
Damage Model ◽  
Irreversible Thermodynamics ◽  
Continuum Damage ◽  
State Variables ◽  
Damage Growth ◽  
Continuum Damage Model

This paper presents a continuum damage model for a unidirectionally reinforced composite based upon fundamental concepts of continuum mechanics and irreversible thermodynamics. Damage is incorporated by two symmetric, second-rank, tensor-valued, internal state variables which represent the total areas of “active” and “passive” cracks contained within a representative material volume element. Constitutive relations are derived for both the mechanical response and heat flux in the presence of damage. It is shown that damage growth contributes to dissipation in the coupled heat conduction process. A specific fracture mechanics solution is employed to relate “microlevel” crack growth processes to “macrolevel” damage growth expressions. This approach lends itself to a probabilistic formulation of the continuum damage model.

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