Folding deformation modeling and simulation of 4D printed bilayer structures considering the thickness ratio

2019 ◽  
Vol 25 (2) ◽  
pp. 348-361 ◽  
Author(s):  
Zhenyu Liu ◽  
Han Liu ◽  
Guifang Duan ◽  
Jianrong Tan
Keyword(s):  
Energy Density ◽  
Modeling And Simulation ◽  
Density Function ◽  
Thickness Ratio ◽  
Equivalent Transformation ◽  
Deformation Model ◽  
Bilayer Structure ◽  
Bending Deformation ◽  
Stretching Deformation ◽  
Deformation Models

This paper addresses the problem of deformation modeling and simulation of 4D printed polymeric bilayer structures considering the thickness ratio. Through an equivalent transformation, the folding deformation model is transformed into two simpler deformation models, stretching and bending, which greatly reduces the complexity of the modeling problem. The stretching deformation model is developed by Hooke’s law, and based on the final strain of the stretching deformation, which is determined by the thickness ratio, a new hyperelastic energy density function considering the thickness ratio is defined to calculate the energy of the bilayer structure during the bending deformation. According to the new energy density function, the bending deformation model considering the thickness ratio is developed by minimizing the energy of the bilayer structure during the bending deformation. Numerical simulations show encouraging results obtained by the proposed model.

scholarly journals Constructing Adaptive Deformation Models for Estimating DEM Error in SBAS-InSAR Based on Hypothesis Testing

2021 ◽  
Vol 13 (10) ◽  
pp. 2006
Author(s):  
Jun Hu ◽  
Qiaoqiao Ge ◽  
Jihong Liu ◽  
Wenyan Yang ◽  
Zhigui Du ◽  
...  
Keyword(s):  
Time Series ◽  
Hypothesis Testing ◽  
Surface Deformation ◽  
A Priori ◽  
Least Square ◽  
Deformation Model ◽  
Phase Time ◽  
Testing Theory ◽  
Sbas Insar ◽  
Deformation Models

The Interferometric Synthetic Aperture Radar (InSAR) technique has been widely used to obtain the ground surface deformation of geohazards (e.g., mining subsidence and landslides). As one of the inherent errors in the interferometric phase, the digital elevation model (DEM) error is usually estimated with the help of an a priori deformation model. However, it is difficult to determine an a priori deformation model that can fit the deformation time series well, leading to possible bias in the estimation of DEM error and the deformation time series. In this paper, we propose a method that can construct an adaptive deformation model, based on a set of predefined functions and the hypothesis testing theory in the framework of the small baseline subset InSAR (SBAS-InSAR) method. Since it is difficult to fit the deformation time series over a long time span by using only one function, the phase time series is first divided into several groups with overlapping regions. In each group, the hypothesis testing theory is employed to adaptively select the optimal deformation model from the predefined functions. The parameters of adaptive deformation models and the DEM error can be modeled with the phase time series and solved by a least square method. Simulations and real data experiments in the Pingchuan mining area, Gaunsu Province, China, demonstrate that, compared to the state-of-the-art deformation modeling strategy (e.g., the linear deformation model and the function group deformation model), the proposed method can significantly improve the accuracy of DEM error estimation and can benefit the estimation of deformation time series.

An energy density function for papillary muscle encompassing both elastic and contractile properties

1981 ◽  
Vol 52 (5) ◽  
pp. 3674-3687 ◽  
Author(s):  
Willem Klip ◽  
Lloyd L. Hefner ◽  
Thomas C. Donald ◽  
David N. S. Reeves ◽  
Jane B. Hazelrig ◽  
...  
Keyword(s):  
Energy Density ◽  
Density Function ◽  
Papillary Muscle ◽  
Contractile Properties

The strain energy density function

1986 ◽  
pp. 237-253
Author(s):  
G. C. Sih ◽  
J. G. Michopoulos ◽  
S. C. Chou
Keyword(s):  
Energy Density ◽  
Density Function ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Strain Energy Density Function

scholarly journals An Improved Time-Series Model Considering Rheological Parameters for Surface Deformation Monitoring of Soft Clay Subgrade

Sensors ◽  
2019 ◽  
Vol 19 (14) ◽  
pp. 3073 ◽  
Author(s):  
Xing ◽  
Chen ◽  
Yuan ◽  
Shi
Keyword(s):  
Time Series ◽  
Surface Deformation ◽  
Soft Clay ◽  
Deformation Monitoring ◽  
Rheological Parameters ◽  
Deformation Model ◽  
Rheological Parameter ◽  
Functional Relationships ◽  
Soft Clay Subgrade ◽  
Deformation Models

Building deformation models consistent with reality is a crucial step for time-series deformation monitoring. Most deformation models are empirical mathematical models, lacking consideration of the physical mechanisms of observed objects. In this study, we propose an improved time-series deformation model considering rheological parameters (viscosity and elasticity) based on the Kelvin model. The functional relationships between the rheological parameters and deformation along the Synthetic Aperture Radar ( SAR) line of sight are constructed, and a method for rheological parameter estimation is provided. To assess the feasibility and accuracy of the presented model, both simulated and real deformation data over a stretch of the Lungui highway (built on soft clay subgrade in Guangdong province, China) are investigated with TerraSAR-X satellite imagery. With the proposed deformation model, the unknown rheological parameters over all the high coherence points are obtained and the deformation time-series are generated. The high-pass (HP) deformation component and external leveling ground measurements are utilized to assess the modeling accuracy. The results show that the root mean square of the residual deformation is ±1.6 mm, whereas that of the ground leveling measurements is ±5.0 mm, indicating an improvement in the proposed model by 53%, and 34% compared to the pure linear velocity model. The results indicate the reliability of the presented model for the application of deformation monitoring of soft clay highways. The estimated rheological parameters can be provided as a reference index for the interpretation of long-term highway deformation and the stability control of subgrade construction engineering.

An adaptive meshing automatic scheme based on the strain energy density function

1997 ◽  
Vol 14 (6) ◽  
pp. 604-629 ◽  
Author(s):  
A. Hernández ◽  
J. Albizuri ◽  
M.B.G. Ajuria ◽  
M.V. Hormaza
Keyword(s):  
Energy Density ◽  
Density Function ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Adaptive Meshing ◽  
Strain Energy Density Function

Large Deformation Analysis of the Arterial Cross Section

1971 ◽  
Vol 93 (2) ◽  
pp. 138-145 ◽  
Author(s):  
B. R. Simon ◽  
A. S. Kobayashi ◽  
D. E. Strandness ◽  
C. A. Wiederhielm
Keyword(s):  
Finite Element ◽  
Energy Density ◽  
Numerical Integration ◽  
Density Function ◽  
Cross Section ◽  
Finite Deformation ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Exponential Form ◽  
Strain Energy Density Function

Possible relations between arterial wall stresses and deformations and mechanisms contributing to atherosclerosis are discussed. Necessary material properties are determined experimentally and from available data in the literature by assuming the arterial response to be a static finite deformation of a thick-walled cylinder constrained in a state of plane strain and composed of an incompressible, nonlinear elastic, transversely isotropic material. Experimental justification from the literature and supporting theoretical considerations are presented for each assumption. The partial derivative of the strain energy density function δW1/δI , necessary for in-plane stress calculation, is determined to be of exponential form using in situ biaxial test results from the canine abdominal aorta. An axisymmetric numerical integration solution is developed and used as a check for finite element results. The large deformation finite element theory of Oden is modified to include aortic material nonlinearity and directional properties and is used for a structural analysis of the aortic cross section. Results of this investigation are: (a) Fung’s exponential form for the strain energy density function of soft tissues is found to be valid for the aorta in the biaxial states considered; (b) finite deformation analyses by the finite element method and numerical integration solution reveal that significant tangential stress gradients are present in arteries commonly assumed to be “thin-walled” tubes using linear theory.

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