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.

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.

Modeling Stress Strain Curves for Nonlinear Analysis

2008 ◽  
Vol 575-578 ◽  
pp. 539-544 ◽  
Author(s):  
Hu Sheng Gao
Keyword(s):  
Strain Curve ◽  
Test Sample ◽  
Sudden Onset ◽  
Stress Strain ◽  
Engineering Structures ◽  
Nonlinear Stress ◽  
Modeling Stress ◽  
Discontinuous Yielding ◽  
Lüders Band ◽  
Yielding Point

Methods of modeling stress strain curves for nonlinear stress analysis are discussed in order to obtain comparable results between different finite element analysts and between different versions of designs. The most common method for modeling stress strain curves is to use Ramberg- Osgood equation. For materials with significant discontinuous yielding, Ramburg-Osgood approximation leads to some problems near discontinuous yielding point. Discontinuous yielding occurs when sudden onset of plastic deformation associated Luders band takes place in a uniform test sample. For engineering structures and machine components, the propagation of Luders band may not occur in deformation process because of non-uniform stress distribution caused by stress concentration, complicated loading condition etc. A modified Ramberg-Osgood method for modeling stress strain curve is proposed.

Buckling of Rectangular Cross-Ply Laminated Plates With Nonlinear Stress-Strain Behavior

1979 ◽  
Vol 46 (3) ◽  
pp. 637-643 ◽  
Author(s):  
Harold S. Morgan ◽  
Robert M. Jones
Keyword(s):  
Strain Curve ◽  
Material Model ◽  
Laminated Plates ◽  
Nonlinear Material ◽  
Stress Strain ◽  
Buckling Loads ◽  
Strain Behavior ◽  
Reinforced Composite ◽  
Nonlinear Stress ◽  
Behavior Characteristic

The Jones-Nelson-Morgan nonlinear material model is used in the derivation of a buckling criterion for laminated plates with nonlinear stress-strain behavior characteristic of many fiber-reinforced composite materials. A search procedure is developed to solve this buckling criterion which is transcendental because of interdependence of the buckling load and the coefficients relating the variations in laminate forces and moments to the variations in strains and curvatures. The effect of stress-strain curve nonlinearities on laminate buckling loads is illustrated by comparing solutions of the buckling criterion to buckling loads for laminates with linear stress-strain behavior.

scholarly journals Nonlinear vibrations of soil strata according to instrumental and numerical data

2021 ◽  
Author(s):  
В.Б. Заалишвили ◽  
Д.А. Мельков ◽  
А.Ф. Габараев ◽  
Т.И. Мерзликин
Keyword(s):  
Spectral Composition ◽  
Strain Curve ◽  
High Rate ◽  
Main Peak ◽  
Nonlinear Phenomena ◽  
Stress Strain ◽  
Soil Medium ◽  
Nonlinear Properties ◽  
Modern Development ◽  
Nonlinear Stress

Исследования нелинейных явлений в грунтах, начатые в России почти 60 лет назад, явились стимулом современного развития исследований сейсмоаномальных явлений в комплексе геофизических показателей, наблюдающихся при сильных и разрушительных землетрясениях. Кроме чисто научных интересов большой интерес вызывает вопрос прогнозирования поведения грунтов и сооружений с точки зрения адекватности ожидаемому проявлению сейсмического воздействия. Адекватное изучение нелинейности, являющейся неотъемлемой характеристикой природных явлений, позволит приблизить соответствующее антисейсмические мероприятия к реальным особенностям проявлений сейсмического эффекта при сильных землетрясениях. Цельюработы являлось построение расчетной модели, описывающей явления, наблюдаемые в грунтовой среде при сильных сейсмических воздействиях и сопоставление расчетных данных с результатами инструментальных наблюдений. Методы. В работе анализируется иснтрументальная запись, полученная на слабых грунтах, на сонове вейвлет нанализа. Моделируются импульсы различной проолжитлеьности в среде с различной стпенью проявления нелинейных свойст (кртутизны нелиненйой заивисисмоти напряжение -деформация) методом конечных элементов. Результаты. В результате установлены различия в спектральном составе моделируемых импульсов. Сильное проявление нелинейных свойств характеризуется резкими изменениями фаз колебаний, в фазах высокой скорости нарастания амплитуд. В нелинейных спектрах происходит перераспределение энергии в более высокочастотную область, кратную основному пику, тем сильнее, чем сильнее нелинейность кривой наряжение-деформация. Studies of nonlinear phenomena in soils, which began in Russia almost 60 years ago, have stimulated the modern development of studies of seismically anomalous phenomena in the complex of geophysical indicators observed during strong and destructive earthquakes. In addition to scientific interests, the issue of forecasting the behavior of soils and structures from the point of view of adequacy to the expected manifestation of seismic impact is of great interest. An adequate study of nonlinearity, which is an integral characteristic of natural phenomena, will make it possible to bring the corresponding antiseismic measures closer to the real features of the manifestations of the seismic effect during strong earthquakes. Aim. The aim of the work was to build a computational model describing the phenomena observed in a soil medium under strong seismic effects and to compare the computed data with the results of instrumental observations. Methods.The paper analyzes an instrumental record obtained on soft soils using wavelet analysis. With the help of the finite element method pulses of different duration are modeled in a medium with different degrees of nonlinear properties manifestation (steepness of nonlinear stress-strain dependence). Results. As a result, differences in the spectral composition of the modeled pulses were determined. A strong manifestation of nonlinear properties is characterized by sharp changes in the phases of vibrations, in the phases of a high rate of amplitude rise. In nonlinear spectra, the energy is redistributed to a higher frequency region, which is a multiple of the main peak and the stronger the nonlinearity of the stress-strain curve is stronger.

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 The role of actin protrusion dynamics in cell migration through a degradable viscoelastic extracellular matrix: Insights from a computational model

2019 ◽  
Author(s):  
Tommy Heck ◽  
Diego A. Vargas ◽  
Bart Smeets ◽  
Herman Ramon ◽  
Paul Van Liedekerke ◽  
...  
Keyword(s):  
Extracellular Matrix ◽  
Cell Migration ◽  
Computational Model ◽  
Mechanical Anisotropy ◽  
Valuable Contribution ◽  
Anisotropic Mechanical Properties ◽  
Subcellular Processes ◽  
3D Cell Migration ◽  
Cell Strength

AbstractActin protrusion dynamics plays an important role in the regulation of three-dimensional (3D) cell migration. Cells form protrusions that adhere to the surrounding extracellular matrix (ECM), mechanically probe the ECM and contract in order to displace the cell body. This results in cell migration that can be directed by the mechanical anisotropy of the ECM. However, the subcellular processes that regulate protrusion dynamics in 3D cell migration are difficult to investigate experimentally and therefore not well understood. Here, we present a computational model of cell migration through a degradable viscoelastic ECM. The cell is modeled as an active deformable object that captures the viscoelastic behavior of the actin cortex and the subcellular processes underlying 3D cell migration. The ECM is regarded as a viscoelastic material, with or without anisotropy due to fibrillar strain stiffening, and modeled by means of the meshless Lagrangian smoothed particle hydrodynamics (SPH) method. ECM degradation is captured by local fluidization of the material and permits cell migration through the ECM. We demonstrate that changes in ECM stiffness and cell strength affect cell migration and are accompanied by changes in number, lifetime and length of protrusions. Interestingly, directly changing the total protrusion number or the average lifetime or length of protrusions does not affect cell migration. A stochastic variability in protrusion lifetime proves to be enough to explain differences in cell migration velocity. Force-dependent adhesion disassembly does not result in faster migration, but can make migration more efficient. We also demonstrate that when a number of simultaneous protrusions is enforced, the optimal number of simultaneous protrusions is one or two, depending on ECM anisotropy. Together, the model provides non-trivial new insights in the role of protrusions in 3D cell migration and can be a valuable contribution to increase the understanding of 3D cell migration mechanics.Author summaryThe ability of cells to migrate through a tissue in the human body is vital for many processes such as tissue development, growth and regeneration. At the same time, abnormal cell migration is also playing an important role in many diseases such as cancer. If we want to be able to explain the origin of these abnormalities and develop new treatment strategies, we have to understand how cells are able to regulate their migration. Since it is challenging to investigate cell migration through a biological tissue in experiments, computational modeling can provide a valuable contribution. We have developed a computational model of cell migration through a deformable and degradable material that describes both mechanics of the cell and the surrounding material and subcellular processes underlying cell migration. This model captures the formation of long and thin protrusions that adhere to the surrounding material and that pull the cell forward. It provides new non-trivial insights in the role of these protrusions in cell migration and the regulation of protrusion dynamics by cell strength and anisotropic mechanical properties of the surrounding material. Therefore, we believe that this model can be a valuable tool to further improve the understanding of cell migration.

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.

Effect of Pre-Stress on the Dynamic Tensile Behavior of the TMJ Disc

2013 ◽  
Vol 136 (1) ◽  
Author(s):  
J. Lomakin ◽  
P. A. Sprouse ◽  
M. S. Detamore ◽  
S. H. Gehrke
Keyword(s):  
Mechanical Properties ◽  
Strain Rate ◽  
Strain Curve ◽  
Dynamic Mechanical Properties ◽  
Polymer Materials ◽  
Stress Strain ◽  
Dynamic Mechanical ◽  
Highly Nonlinear ◽  
Nonlinear Stress ◽  
Tmj Disc

Previous dynamic analyses of the temporomandibular joint (TMJ) disc have not included a true preload, i.e., a step stress or strain beyond the initial tare load. However, due to the highly nonlinear stress-strain response of the TMJ disc, we hypothesized that the dynamic mechanical properties would greatly depend on the preload, which could then, in part, account for the large variation in the tensile stiffnesses reported for the TMJ disc in the literature. This study is the first to report the dynamic mechanical properties as a function of prestress. As hypothesized, the storage modulus (E′) of the disc varied by a factor of 25 in the mediolateral direction and a factor of 200 in the anteroposterior direction, depending on the prestress. Multiple constant strain rate sweeps were extracted and superimposed via strain-rate frequency superposition (SRFS), which demonstrated that the strain rate amplitude and strain rate were both important factors in determining the TMJ disc material properties, which is an effect not typically seen with synthetic materials. The presented analysis demonstrated, for the first time, the applicability of viscoelastic models, previously applied to synthetic polymer materials, to a complex hierarchical biomaterial such as the TMJ disc, providing a uniquely comprehensive way to capture the viscoelastic response of biological materials. Finally, we emphasize that the use of a preload, preferably which falls within the linear region of the stress-strain curve, is critical to provide reproducible results for tensile analysis of musculoskeletal tissues. Therefore, we recommend that future dynamic mechanical analyses of the TMJ disc be performed at a controlled prestress corresponding to a strain range of 5–10%.

Evaluation of yield strength by ultrasonic reconstruction of quadratic nonlinear Stress–Strain curve

2020 ◽  
Vol 112 ◽  
pp. 102242
Author(s):  
Jongbeom Kim ◽  
Chang-Soo Kim ◽  
Kyung-Cho Kim ◽  
Kyung-Young Jhang
Keyword(s):  
Yield Strength ◽  
Strain Curve ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Nonlinear Stress
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