Mechanics of Fractal-Inspired Horseshoe Microstructures for Applications in Stretchable Electronics

2016 ◽  
Vol 83 (11) ◽  
Author(s):  
Qiang Ma ◽  
Yihui Zhang
Keyword(s):  
Theoretical Model ◽  
Analytic Solutions ◽  
Design Guidelines ◽  
Stretchable Electronics ◽  
Stress Strain ◽  
Practical Applications ◽  
Mechanical Responses ◽  
Nonlinear Stress ◽  
Fractal Patterns ◽  
Nonlinear Deformations

Fractal-inspired designs represent an emerging class of strategy for stretchable electronics, which have been demonstrated to be particularly useful for various applications, such as stretchable batteries and biointegrated electrophysiological electrodes. The fractal-inspired constructs usually undergo complicated, nonlinear deformations under mechanical loading, because of the highly complex and diverse microstructures inherent in high-order fractal patterns. The underlying relations between the nonlinear mechanical responses and microstructure geometry are essential in practical applications, which require a relevant mechanics theory to serve as the basis of a design approach. Here, a theoretical model inspired by the mechanism of ordered unraveling is developed to study the nonlinear stress–strain curves and elastic stretchability for a class of fractal-inspired horseshoe microstructures. Analytic solutions were obtained for some key mechanical quantities, such as the elastic modulus and the tangent modulus at the beginning of each deformation stage. Both the finite-element analyses (FEA) and experiments were carried out to validate the model. Systematic analyses of the microstructure–property relationship dictate how to leverage the various geometric parameters to tune the multistage, J-shaped stress–strain curves. Moreover, a demonstrative example shows the utility of the theoretical model in design optimization of fractal-inspired microstructures used as electrophysiological electrodes, aiming to achieve maximum elastic stretchability for prescribed filling ratios. The results indicate a substantial enhancement (e.g., >4 times) of elastic stretchability by using fractal designs, as compared to traditional horseshoe designs. This study can serve as design guidelines of fractal-inspired microstructures in different stretchable electronic systems.

scholarly journals Experimental Investigation on the Behavior of Iron Powder-Reinforced Sand under Electromagnetic Field

2018 ◽  
Vol 2018 ◽  
pp. 1-15
Author(s):  
Ying Lai ◽  
Bin Zhu ◽  
Xiangtian Xu
Keyword(s):  
Electromagnetic Field ◽  
Iron Powder ◽  
Soil Improvement ◽  
Triaxial Tests ◽  
Future Research ◽  
Initial Stiffness ◽  
Stress Strain ◽  
Practical Applications ◽  
Nonlinear Stress ◽  
Chang Model

Applications of soil improvement have proliferated in recent years. To date, we have limited studies on the quantitative analyses of the autoadaptive material and specifically to model its stress-strain relationship. This paper explored an autoadaptive material, iron-powdered Ottawa sand, which was temporarily solidified by applying an electromagnetic field. A series of compression triaxial tests were carried out with various relative densities of specimens (60% and 80%), in four electromagnetic fields (0 A, 0.5 A, 1 A, and 2 A) and under three confining pressures (103 kPa, 206 kPa, and 310 kPa). The test results indicate that the strength of specimens increased while initial stiffness and brittleness reduced by adding iron powder. Moreover, the strength of the specimens increased by increasing the magnitude of the applied electromagnetic field. The behavior of the iron-powdered sand was described by using a revised Duncan–Chang model. The revised model was evaluated by comparing the simulated results with the corresponding test data. The comparison showed that the revised model can better capture the nonlinear stress-strain behavior of the specimens. With the application of the revised Duncan–Chang model, the standard error of the estimate between the experimental and predicted results is lowered down to 0.39 from 4.7. Future research is geared towards practical applications for temporary solidification of soil.

A Computational Model of Bio-Inspired Soft Network Materials for Analyzing Their Anisotropic Mechanical Properties

2018 ◽  
Vol 85 (7) ◽  
Author(s):  
Enrui Zhang ◽  
Yuan Liu ◽  
Yihui Zhang
Keyword(s):  
Computational Model ◽  
Rotational Symmetry ◽  
Strain Curve ◽  
Mechanical Anisotropy ◽  
Stress Strain ◽  
Good Correspondence ◽  
Mechanical Responses ◽  
Synthetic Materials ◽  
Nonlinear Stress ◽  
Anisotropic Mechanical Properties

Soft network materials constructed with horseshoe microstructures represent a class of bio-inspired synthetic materials that can be tailored precisely to match the nonlinear, J-shaped, stress–strain curves of human skins. Under a large level of stretching, the nonlinear deformations associated with the drastic changes of microstructure geometries can lead to an evident mechanical anisotropy, even for honeycomb and triangular lattices with a sixfold rotational symmetry. Such anisotropic mechanical responses are essential for certain targeted applications of these synthetic materials. By introducing appropriate periodic boundary conditions that apply to large deformations, this work presents an efficient computational model of soft network materials based on the analyses of representative unit cells. This model is validated through comparison of predicted deformed configurations with full-scale finite element analyses (FEA) for different loading angles and loading strains. Based on this model, the anisotropic mechanical responses, including the nonlinear stress–strain curves and Poisson's ratios, are systematically analyzed for three representative lattice topologies (square, triangular and honeycomb). An analytic solution of the geometry-based critical strain was found to show a good correspondence to the critical transition point of the calculated J-shaped stress–strain curve for different network geometries and loading angles. Furthermore, the nonlinear Poisson's ratio, which can be either negative or positive, was shown to depend highly on both the loading angle and the loading strain.

Anisotropic Mechanics of Cellular Substrate Under Finite Deformation

2018 ◽  
Vol 85 (7) ◽  
Author(s):  
Feng Zhu ◽  
Hanbin Xiao ◽  
Yeguang Xue ◽  
Xue Feng ◽  
Yonggang Huang ◽  
...  
Keyword(s):  
Cell Walls ◽  
Constitutive Models ◽  
Applied Strain ◽  
Stretchable Electronics ◽  
Stress Strain ◽  
Element Analysis ◽  
Natural Motion ◽  
Nonlinear Stress ◽  
Comparison Of The Results ◽  
Nonlinear Elastic

The use of cellular substrates for stretchable electronics minimizes not only disruptions to the natural diffusive or convective flow of bio-fluids, but also the constraints on the natural motion of the skin. The existing analytic constitutive models for the equivalent medium of the cellular substrate under finite stretching are only applicable for stretching along the cell walls. This paper aims at establishing an analytic constitutive model for the anisotropic equivalent medium of the cellular substrate under finite stretching along any direction. The model gives the nonlinear stress–strain curves of the cellular substrate that agree very well with the finite element analysis (FEA) without any parameter fitting. For the applied strain <10%, the stress–strain curves are the same for different directions of stretching, but their differences become significant as the applied strain increases, displaying the deformation-induced anisotropy. Comparison of the results for linear and nonlinear elastic cell walls clearly suggests that the nonlinear stress–strain curves of the cellular substrate mainly result from the finite rotation of cell walls.

scholarly journals An Inelastic Theoretical Model regarding the Load-Carrying Capacity of PSL Bending Component

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Baolu Sheng ◽  
Yuling Bian ◽  
Dong He ◽  
Aiping Zhou
Keyword(s):  
Theoretical Model ◽  
Compressive Stress ◽  
Carrying Capacity ◽  
Building Design ◽  
Load Carrying Capacity ◽  
Stress Strain ◽  
Nonlinear Bending ◽  
Nonlinear Stress ◽  
Load Carrying ◽  
Strain Relationship

Parallel strand lumber (PSL) is an attractive structural wood composite which may have prospective use in building constructions. Conducting nonlinear analysis for the bending of PSL beams is a critical step in the determination of ultimate strength and deflection of them, which is an essential requirement of the building design philosophy based on probability of ultimate state. For the purposes of this article, an inelastic theoretical model regarding the load-carrying capacity of the PSL bending component has been developed. Based on the uniaxial loading tests, the stress-strain behaviors of PSL composite in the grain direction were measured. 4-point bending experiments were also performed in this study to investigate the failure mechanism of the PSL components. The results show that the tensile stress-strain relationship of PSL materials in the grain direction remains linear until breaking, while the compressive stress-strain relationship exhibits nonlinear characteristics once the compressive stress exceeds the proportional limit, which can be expressed by a quadratic polynomial. The failure mode of the PSL beam can be summarized that the fibres in the top of the broken section were buckling and those in the bottom of the section were broken when failure occurred. Significant nonlinear behavior was exhibited based on the load-deflection curves of the PSL beams. To predict the nonlinear bending performance of the PSL beams, a theoretical model that could consider the nonlinear stress-strain relations of PSL and predict the damage modes of the PSL beams was developed. Well agreements can be observed between the results of calculations and experiments.

scholarly journals Black rubber and the non-linear elastic response of scale invariant solids

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Matteo Baggioli ◽  
Víctor Cáncer Castillo ◽  
Oriol Pujolàs
Keyword(s):  
Strain Curve ◽  
Effective Field ◽  
Elastic Response ◽  
Elastic Behaviour ◽  
Scale Invariant ◽  
Stress Strain ◽  
Nonlinear Stress ◽  
Hyper Elastic ◽  
Simple Class ◽  
Nonlinear Elastic

Abstract We discuss the nonlinear elastic response in scale invariant solids. Following previous work, we split the analysis into two basic options: according to whether scale invariance (SI) is a manifest or a spontaneously broken symmetry. In the latter case, one can employ effective field theory methods, whereas in the former we use holographic methods. We focus on a simple class of holographic models that exhibit elastic behaviour, and obtain their nonlinear stress-strain curves as well as an estimate of the elasticity bounds — the maximum possible deformation in the elastic (reversible) regime. The bounds differ substantially in the manifest or spontaneously broken SI cases, even when the same stress- strain curve is assumed in both cases. Additionally, the hyper-elastic subset of models (that allow for large deformations) is found to have stress-strain curves akin to natural rubber. The holographic instances in this category, which we dub black rubber, display richer stress- strain curves — with two different power-law regimes at different magnitudes of the strain.

Cord/Rubber Material Properties

1985 ◽  
Vol 58 (4) ◽  
pp. 830-856 ◽  
Author(s):  
R. J. Cembrola ◽  
T. J. Dudek
Keyword(s):  
Finite Element ◽  
Material Model ◽  
Rubber Composites ◽  
Stress Strain ◽  
Element Analysis ◽  
Rubber Layer ◽  
Strain Behavior ◽  
Nonlinear Stress ◽  
Interlaminar Shear ◽  
Mechanics Of Composite Materials

Abstract Recent developments in nonlinear finite element methods (FEM) and mechanics of composite materials have made it possible to handle complex tire mechanics problems involving large deformations and moderate strains. The development of an accurate material model for cord/rubber composites is a necessary requirement for the application of these powerful finite element programs to practical problems but involves numerous complexities. Difficulties associated with the application of classical lamination theory to cord/rubber composites were reviewed. The complexity of the material characterization of cord/rubber composites by experimental means was also discussed. This complexity arises from the highly anisotropic properties of twisted cords and the nonlinear stress—strain behavior of the laminates. Micromechanics theories, which have been successfully applied to hard composites (i.e., graphite—epoxy) have been shown to be inadequate in predicting some of the properties of the calendered fabric ply material from the properties of the cord and rubber. Finite element models which include an interply rubber layer to account for the interlaminar shear have been shown to give a better representation of cord/rubber laminate behavior in tension and bending. The application of finite element analysis to more refined models of complex structures like tires, however, requires the development of a more realistic material model which would account for the nonlinear stress—strain properties of cord/rubber composites.

A New Nonlinear Stress-Strain Model for Soils at Various Strain Levels

2013 ◽  
Vol 631-632 ◽  
pp. 782-788
Author(s):  
Cheng Chen ◽  
Zheng Ming Zhou
Keyword(s):  
Compression Test ◽  
Triaxial Compression ◽  
Small Strain ◽  
Empirical Formulas ◽  
Stress Strain ◽  
Strain Behaviour ◽  
Proposed Model ◽  
Nonlinear Stress ◽  
London Clay ◽  
Strain Model

Soils have nonlinear stiffness and develops irrecoverable strains even at very small strain levels. Accurate modeling of stress-strain behaviour at various strain levels is very important for predicting the deformation of soils. Some existing stress-strain models are reviewed and evaluated firstly. And then a new simple non-linear stress-strain model is proposed. Four undetermined parameters involved in the proposed model can be obtained through maximum Young’s module, deformation module, and limit deviator stress and linearity index of soils that can be measured from experiment directly or calculated by empirical formulas indirectly. The effectiveness of the proposed stress-strain model is examined by predicting stress-strain curves measured in plane-strain compression test on Toyota sand and undrained triaxial compression test on London clay. The fitting results of the proposed model are in good agreement with experimental data, which verify the effectiveness of the model.

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