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 A Nonlinear Mechanics Model of Zigzag Cellular Substrates for Stretchable Electronics

2020 ◽  
Vol 87 (6) ◽  
Author(s):  
Shiwei Zhao ◽  
Feng Zhu ◽  
Zhengang Yan ◽  
Daochun Li ◽  
Jinwu Xiang ◽  
...  
Keyword(s):  
Finite Element Analysis ◽  
Analytical Model ◽  
Strain Curve ◽  
Stretchable Electronics ◽  
Electronic Systems ◽  
Stress Strain Curve ◽  
Element Analysis ◽  
Natural Motion ◽  
Mechanics Model ◽  
Nonlinear Stress

Abstract The use of cellular elastomer substrates not only reduces its restriction on natural diffusion or convection of biofluids in the realm of stretchable electronics but also enhances the stretchability of the electronic systems. An analytical model of “zigzag” cellular substrates under finite deformation is established and validated in this paper. The deformed shape, nonlinear stress–strain curve, and Poisson’s ratio–strain curve of the cellular elastomer substrate calculated using the reported analytical model agree well with those from finite element analysis (FEA). Results show that lower restriction on the natural motion of human skin could be achieved by the proposed zigzag cellular substrates compared with the previously reported hexagonal cellular substrates, manifesting another leap toward mechanically “invisible” wearable, stretchable electronic systems.

Improved nonlinear stress-strain relation for carbon-epoxy composites and identification of material parameters

2011 ◽  
Vol 45 (9) ◽  
pp. 1045-1057 ◽  
Author(s):  
Tomáš Kroupa ◽  
Vladislav Laš ◽  
Robert Zemčík
Keyword(s):  
Mathematical Optimization ◽  
Optimization Method ◽  
Tensile Tests ◽  
Epoxy Composites ◽  
Stress Strain ◽  
Element Analysis ◽  
Material Parameters ◽  
Stress Strain Relation ◽  
Nonlinear Stress ◽  
Comparison Of The Results

This study focuses on the comparison of selected nonlinear stress—strain relations for unidirectional continuous fiber carbon—epoxy composites and the identification of their parameters under tensile loading. Simple tensile tests of thin strips with various fiber orientations are performed. One linear relation, two types of nonlinear stress—strain relations taken from literature, and one improved relation are analyzed and used within the identification process. All the relationships are deduced from polynomial expansion of complementary energy density. The process, using a combination of the mathematical optimization method and finite element analysis, is described with the necessary details. Failure analysis for the determination of the first failure using Puck’s action plane concept is also performed. The tensile and shear strengths are investigated. The comparison of the results obtained from the identified material parameters with the results obtained using the material parameters given by manufacturer is included.

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.

Parametric Variational Principle for Bi-Modulus Materials and Its Application to Nacreous Bio-Composites

2016 ◽  
Vol 08 (06) ◽  
pp. 1650082 ◽  
Author(s):  
Liang Zhang ◽  
Huiting Zhang ◽  
Jian Wu ◽  
Bo Yan ◽  
Mengkai Lu
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Variational Principle ◽  
Principal Stress ◽  
Stress Strain ◽  
Element Analysis ◽  
Parametric Variational Principle ◽  
Strain Relation ◽  
Stress Strain Relation ◽  
Nonlinear Stress

Bi-modulus materials have different moduli in tension and compression and the stress–strain relation depends on principal stress that is unknown before displacement is determined. Establishment of variational principle is important for mechanical analysis of materials. First, parametric variational principle (PVP) is proposed for static analysis of bi-modulus materials and structures. A parametric variable indicating state of principal stress is included in the potential energy formulation and the nonlinear stress–strain relation is evolved into a linear complementarity constraint. Convergence of finite element analysis is thus improved. Then the proposed variational principle is extended to a dynamic problem and the dynamic equation can be derived based on Hamilton’s principle. Finite element analysis of nacreous bio-composites is performed, in which a unilateral contact behavior between two hard mineral bricks is modeled using the bi-modulus stress–strain relation. Effective modulus of composites can be determined numerically and stress mechanism of “tension–shear chain” in nacre is revealed. A delayed effect on stress propagation is found around the “gaps” between mineral bricks, when a tension force is loaded to nacreous bio-composites dynamically.

Constitutive modelling of the mechanical response of a polycaprolactone based polyurethane elastomer: Finite element analysis and experimental validation through a bulge test

2020 ◽  
pp. 030932472095833
Author(s):  
Nahuel Rull ◽  
Asanka Basnayake ◽  
Michael Heitzmann ◽  
Patricia M. Frontini
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Mechanical Response ◽  
Strain Curve ◽  
Image Correlation ◽  
Bulge Test ◽  
Polyurethane Elastomer ◽  
Stress Strain ◽  
Element Analysis ◽  
Nonlinear Stress

The mechanical behaviour of a high performance polycaprolactone based polyurethane elastomer (PCL) up to large strain levels, cyclic loading and equibiaxial stress has been assessed. The PCL can be categorised as a rubber-like material, thus, showing nonlinear stress-strain behaviour. The materials elastic network is based on a high molecular weight PCL polyol which gives the material its elastomeric behaviour similar to polyurethanes. In this work, mechanical testing capturing the major features of the stress-strain curve under different loading conditions is performed. Both, uni-axial loading-unloading curves and bulge test are thoroughly studied through the addition of digital image correlation (DIC) to measure the strain field. Results show the presence of hysteresis and loading configuration dependence. Then, two well-known hyperelastic constitutive models, the Arruda-Boyce eight-chain and Bergström-Boyce, were fitted to the uni-axial monotonic and cyclic test data and compared to the bulge test experimental results through finite element analysis (FEA) in Abaqus.

scholarly journals Biomechanical characterization of the periodontal ligament: Orthodontic tooth movement

2016 ◽  
Vol 87 (2) ◽  
pp. 183-192 ◽  
Author(s):  
Richard Uhlir ◽  
Virginia Mayo ◽  
Pei Hua Lin ◽  
Si Chen ◽  
Yan-Ting Lee ◽  
...  
Keyword(s):  
Experimental Data ◽  
Stainless Steel ◽  
Periodontal Ligament ◽  
Tooth Movement ◽  
Anatomical Location ◽  
Stress Strain ◽  
Element Analysis ◽  
Strain Behavior ◽  
Nonlinear Stress ◽  
Force Vectors

ABSTRACT Objective: To quantify the biomechanical properties of the bovine periodontal ligament (PDL) in postmortem sections and to apply these properties to study orthodontic tooth intrusion using finite element analysis (FEA). We hypothesized that PDL's property inherited heterogeneous (anatomical dependency) and nonlinear stress-strain behavior that could aid FEA to delineate force vectors with various rectangular archwires. Materials and Methods: A dynamic mechanical analyzer was used to quantify the stress-strain behavior of bovine PDL. Uniaxial tension tests using three force levels (0.5, 1, and 3 N) and samples from two anatomical locations (circumferential and longitudinal) were performed to calculate modulus. The Mooney-Rivlin hyperelastic (MRH) model was applied to the experimental data and used in an FEA of orthodontic intrusion rebounded via a 0.45-mm step bend with three archwire configurations of two materials (stainless steel and TMA). Results: Force levels and anatomical location were statistically significant in their effects on modulus (P &lt; .05). The apical part had a greater stiffness than did the middle part. The MRH model was found to approximate the experimental data well (r = 0.99), and it demonstrated a reasonable stress-strain outcome within the PDL and bone for FEA intrusion simulation. The force acting on the tooth increased five times from the 0.016 × 0.022-inch TMA to the 0.019 × 0.025-inch stainless steel. Conclusions: The PDL is a nonhomogeneous tissue in which the modulus changed in relation to location. PDL nonlinear constitutive model estimated quantitative force vectors for the first time to compare intrusive tooth movement in 3-D space in response to various rectangular archwires.

scholarly journals Nonlinear Elastic Foundation Plate Model Study on Overlying Strata Movement in Working Face with Solid Backfilling Mining

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Baifu An ◽  
Nailu Li ◽  
Qiaomei Yi ◽  
Dong Zhang ◽  
Hailong Wang
Keyword(s):  
Elastic Foundation ◽  
Mechanical Analysis ◽  
Stress Strain ◽  
Nonlinear Elastic Foundation ◽  
Model Study ◽  
Working Face ◽  
Geological Conditions ◽  
Nonlinear Stress ◽  
Foundation Plate ◽  
Nonlinear Elastic

Although solid backfilling materials are featured with obvious nonlinear stress-strain properties, for a long time, they have been usually simplified as linear elastic materials for approximate calculation in mechanical analysis, so it is difficult to accurately reflect their deformation process. Based on test results of solid backfilling materials’ compaction characteristics, this paper provides a solution method to generate their elastic foundation coefficient. One multiparameter elastic foundation has been used to reflect stress-strain characteristics of solid backfilling material. In addition, the paper establishes a thin plate on a nonlinear elastic foundation model by adopting semianalytical and seminumerical method and obtains the relational expression between roof deflection, roof stress, and backfilling material’s compressive deformation. In combination with geological conditions in a specific mine, the paper probes into what influence both backfilling material’s particle size and the initial compaction force that the backfilling material bears could exert on roof subsidence and stress. Finally, the proposed model has been verified with measured data from industrial tests.

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.

Irregular Hexagonal Cellular Substrate for Stretchable Electronics

2019 ◽  
Vol 86 (3) ◽  
Author(s):  
Feng Zhu ◽  
Hanbin Xiao ◽  
Haibo Li ◽  
Yonggang Huang ◽  
Yinji Ma
Keyword(s):  
Convective Flow ◽  
Stretchable Electronics ◽  
Analytic Model ◽  
Stress Strain ◽  
Natural Motion ◽  
Strain Relation ◽  
Stress Strain Relation ◽  
Large Anisotropy

The existing regular hexagonal cellular substrate for stretchable electronics minimizes the disruptions to the natural diffusive or convective flow of bio-fluids. Its anisotropy is insignificant, which is not ideal for mounting on skins that involve directional stretching. This paper proposes an irregular hexagonal cellular substrate with large anisotropy to minimize the constraints on the natural motion of the skin, and establishes an analytic model to study its stress–strain relation under finite stretching.

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