A Continuum Damage Model for Viscoelastic Materials

1988 ◽  
Vol 55 (4) ◽  
pp. 773-780 ◽  
Author(s):  
Y. Weitsman
Keyword(s):  
Degrees Of Freedom ◽  
Internal State ◽  
Constitutive Relations ◽  
Damage Model ◽  
Uniaxial Stress ◽  
Continuum Damage ◽  
State Variables ◽  
Viscoelastic Materials ◽  
Continuum Damage Model ◽  
Special Cases

This paper presents a continuum damage model for viscoelastic materials. “Damage” is expressed by two symmetric, second rank tensors which are related to the total areas of “active” and “passive” microcracks within a representative volume element of the multifractured material. Viscoelasticity is introduced through scalar valued internal state variables that represent the internal degrees-of-freedom associated with the motions of long chain polymeric molecules. The constitutive relations are established from basic considerations of continuum mechanics and irreversible thermodynamics, with detailed expressions derived for the case of initially isotropic materials. It is shown that damage causes softening of the material moduli as well as changes in material symmetry. The special cases of uniaxial damage under uniaxial stress and the interaction of damage with moisture diffusion are also considered.

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.

Nonlinear Dynamic Response of Piezoelectric Plates Considering Damage Effects

2006 ◽  
Vol 324-325 ◽  
pp. 299-302 ◽  
Author(s):  
Yi Ming Fu ◽  
Xian Qiao Wang
Keyword(s):  
Dynamic Response ◽  
Nonlinear Dynamic ◽  
Internal State ◽  
Constitutive Relations ◽  
Damage Model ◽  
State Variables ◽  
Nonlinear Dynamic Response ◽  
Internal State Variables ◽  
Nonlinear Dynamic Equations ◽  
Piezoelectric Plates

Based on the Talreja’s tensor valued internal state variables damage model and the Helmhotlz free energy of piezoelectric material, the constitutive relations of the piezoelectric plates with damage are derived. Then, the nonlinear dynamic equations of the piezoelectric plates considering damage are established. By using the finite difference method and the Newmark scheme, these equations are solved and the effects of damage and electric loads on the nonlinear dynamic response of piezoelectric plates are discussed.

Modified Dyson Continuum Damage Model for Austenitic Steel Alloy

2018 ◽  
Vol 140 (4) ◽  
Author(s):  
Seok Jun Kang ◽  
Hoomin Lee ◽  
Jae Boong Choi ◽  
Moon Ki Kim
Keyword(s):  
Damage Model ◽  
Life Time ◽  
Continuum Damage ◽  
Creep Life ◽  
Creep Tests ◽  
Continuum Damage Model ◽  
Thermal Plant ◽  
Uniaxial Creep ◽  
Term Creep

Ultrasuper critical (USC) thermal plants are now in operation around the globe. Their applications include superheaters and reheaters, which generally require high temperature/pressure conditions. To withstand these harsh conditions, an austenitic heat-resistant HR3C (ASME TP310NbN) steel was developed for metal creep resistance. As the designed life time of a typical thermal plant is 150,000 h, it is very important to predict long-term creep behavior. In this study, a three-state variable continuum damage model (CDM) was modified for better estimation of long-term creep life. Accelerated uniaxial creep tests were performed to determine the material parameters. Also, the rupture type and microstructural precipitation were observed by scanning electron microscopy. The creep life of HR3C steel was predicted using only relatively short-term creep test data and was then successfully verified by comparison with the long-term creep data.

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.

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