scholarly journals Mathematical Modeling of Phenomenological Material Properties – Differential Operator Forms of Constitutive Equations

2014 ◽  
Vol 22 (4) ◽  
pp. 19-24 ◽  
Author(s):  
Mária Minárová
Keyword(s):  
Mathematical Modeling ◽  
Differential Operator ◽  
Material Properties ◽  
Constitutive Equations ◽  
Stress Strain ◽  
Rheological Models

Abstract The paper deals with rheological models and creep and relaxation tests on matters which are represented by models. Three models based on two fundamental components (Hooke’s elastic and Newton’s viscous compounds) are performed. The models originated from several fundamental matters by their parallel or serial connections. The corresponding constitutive equations are derived. The behavior of the models under the creep and relaxation tests is observed and is expressed by corresponding stress - strain formulas and illustrated in the figures.

scholarly journals Application Of More Complex Rheological Models In Continuum Mechanics

2015 ◽  
Vol 15 (2) ◽  
Author(s):  
Mária Minárová ◽  
Jozef Sumec
Keyword(s):  
Mathematical Modeling ◽  
Relaxation Process ◽  
Rheological Properties ◽  
Continuum Mechanics ◽  
Rheological Behavior ◽  
Constitutive Equations ◽  
Structural Materials ◽  
Rheological Models ◽  
Complex Models ◽  
Maxwell Models

Abstract The paper deals with mathematical modeling of the structural materials representing their rheological properties. The materials are modeled by more complex models (enhancement of Voigt and Maxwell models). The constitutive equations are derived; the relationships within the creep and relaxation process are developed. The rheological behavior of the materials is introduced.

scholarly journals Infarcted Left Ventricles Have Stiffer Material Properties and Lower Stiffness Variation: Three-Dimensional Echo-Based Modeling to Quantify In Vivo Ventricle Material Properties

2015 ◽  
Vol 137 (8) ◽  
Author(s):  
Longling Fan ◽  
Jing Yao ◽  
Chun Yang ◽  
Dalin Tang ◽  
Di Xu
Keyword(s):  
Wall Thickness ◽  
Material Properties ◽  
Strain Curve ◽  
Stress And Strain ◽  
Stress Strain ◽  
Material Stiffness ◽  
The Mean ◽  
Lv Volume ◽  
Parameter Values

Methods to quantify ventricle material properties noninvasively using in vivo data are of great important in clinical applications. An ultrasound echo-based computational modeling approach was proposed to quantify left ventricle (LV) material properties, curvature, and stress/strain conditions and find differences between normal LV and LV with infarct. Echo image data were acquired from five patients with myocardial infarction (I-Group) and five healthy volunteers as control (H-Group). Finite element models were constructed to obtain ventricle stress and strain conditions. Material stiffening and softening were used to model ventricle active contraction and relaxation. Systolic and diastolic material parameter values were obtained by adjusting the models to match echo volume data. Young's modulus (YM) value was obtained for each material stress–strain curve for easy comparison. LV wall thickness, circumferential and longitudinal curvatures (C- and L-curvature), material parameter values, and stress/strain values were recorded for analysis. Using the mean value of H-Group as the base value, at end-diastole, I-Group mean YM value for the fiber direction stress–strain curve was 54% stiffer than that of H-Group (136.24 kPa versus 88.68 kPa). At end-systole, the mean YM values from the two groups were similar (175.84 kPa versus 200.2 kPa). More interestingly, H-Group end-systole mean YM was 126% higher that its end-diastole value, while I-Group end-systole mean YM was only 29% higher that its end-diastole value. This indicated that H-Group had much greater systole–diastole material stiffness variations. At beginning-of-ejection (BE), LV ejection fraction (LVEF) showed positive correlation with C-curvature, stress, and strain, and negative correlation with LV volume, respectively. At beginning-of-filling (BF), LVEF showed positive correlation with C-curvature and strain, but negative correlation with stress and LV volume, respectively. Using averaged values of two groups at BE, I-Group stress, strain, and wall thickness were 32%, 29%, and 18% lower (thinner), respectively, compared to those of H-Group. L-curvature from I-Group was 61% higher than that from H-Group. Difference in C-curvature between the two groups was not statistically significant. Our results indicated that our modeling approach has the potential to determine in vivo ventricle material properties, which in turn could lead to methods to infer presence of infarct from LV contractibility and material stiffness variations. Quantitative differences in LV volume, curvatures, stress, strain, and wall thickness between the two groups were provided.

Material properties and stress-strain curves for titanium-clad bimetallic steels

2019 ◽  
Vol 162 ◽  
pp. 105756 ◽  
Author(s):  
Xinpei Liu ◽  
Risheng Bai ◽  
Brian Uy ◽  
Huiyong Ban
Keyword(s):  
Material Properties ◽  
Stress Strain

Data Assimilation of Coupled Fluid Flow and Geomechanics Using the Ensemble Kalman Filter

SPE Journal ◽  
2010 ◽  
Vol 15 (02) ◽  
pp. 382-394 ◽  
Author(s):  
Haibin Chang ◽  
Yan Chen ◽  
Dongxiao Zhang
Keyword(s):  
Fluid Flow ◽  
Kalman Filter ◽  
Data Assimilation ◽  
Material Properties ◽  
Ensemble Kalman Filter ◽  
Oil Field ◽  
Reservoir Rock ◽  
Model Parameters ◽  
Stress Strain ◽  
Reservoir Flow

Summary In reservoir history matching or data assimilation, dynamic data, such as production rates and pressures, are used to constrain reservoir models and to update model parameters. As such, even if under certain conceptualization the model parameters do not vary with time, the estimate of such parameters may change with the available observations and, thus, with time. In reality, the production process may lead to changes in both the flow and geomechanics fields, which are dynamically coupled. For example, the variations in the stress/strain field lead to changes in porosity and permeability of the reservoir and, hence, in the flow field. In weak formations, such as the Lost Hills oil field, fluid extraction may cause a large compaction to the reservoir rock and a significant subsidence at the land surface, resulting in huge economic losses and detrimental environmental consequences. The strong nonlinear coupling between reservoir flow and geomechanics poses a challenge to constructing a reliable model for predicting oil recovery in such reservoirs. On the other hand, the subsidence and other geomechanics observations can provide additional insight into the nature of the reservoir rock and help constrain the reservoir model if used wisely. In this study, the ensemble-Kalman-filter (EnKF) approach is used to estimate reservoir flow and material properties by jointly assimilating dynamic flow and geomechanics observations. The resulting model can be used for managing and optimizing production operations and for mitigating the land subsidence. The use of surface displacement observations improves the match to both production and displacement data. Localization is used to facilitate the assimilation of a large amount of data and to mitigate the effect of spurious correlations resulting from small ensembles. Because the stress, strain, and displacement fields are updated together with the material properties in the EnKF, the issue of consistency at the analysis step of the EnKF is investigated. A 3D problem with reservoir fluid-flow and mechanical parameters close to those of the Lost Hills oil field is used to test the applicability.

Sign in / Sign up

Export Citation Format

Share Document