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.

scholarly journals On the behavior of slackline webbings under dynamic loads and the simulation of leash falls

2018 ◽  
Vol 233 (1) ◽  
pp. 75-85
Author(s):  
Panos J Athanasiadis
Keyword(s):  
Standardized Test ◽  
Strain Curve ◽  
Effective Modulus ◽  
Dynamic Loads ◽  
Elastic Response ◽  
Elastic Behavior ◽  
Stress Strain ◽  
Different Types ◽  
The Impact ◽  
Minimal Research

Slackline is a new and rapidly expanding sport, which has had minimal research published on it in terms of sport physics and engineering. Slackline dynamics strongly depend upon the elastic response of used webbing, typically made of polyester or nylon. Depending on the stress and strain rates applied, polymers are known to exhibit a visco-elastic behavior characterized by hysteresis effects. Through a series of carefully executed experiments, this study examined the behavior of slackline webbing under dynamic loads to determine the departures from the respective static response (stress–strain curves). Such knowledge is fundamental for the accurate simulation of slackline dynamics, so as to predict peak forces and aid safe rigging. The results demonstrate that the effective modulus during leash falls was significantly higher than the slope of the respective stress–strain curve, indicating a stiffer response. Also, the effective modulus increased with the applied pretension. Using the moduli determined experimentally for the rigged slacklines with different types of webbing, the respective leash falls were simulated numerically with high accuracy. A standardized test is proposed, to be adopted by the International Slackline Association and slackline webbing manufacturers, is proposed in order to provide key information on the response of each webbing available in the market under typical dynamic loads, similar to the “impact force” test designed for dynamic ropes by the International Climbing and Mountaineering Federation.

Duncan-Chang Nonlinear Elastic Model Considered Loess Structure

2011 ◽  
Vol 90-93 ◽  
pp. 176-181
Author(s):  
Chang Lu Chen ◽  
Sheng Jun Shao ◽  
Lin Ma
Keyword(s):  
Nonlinear Model ◽  
Stress Ratio ◽  
Structural Parameters ◽  
Strain Curve ◽  
Triaxial Tests ◽  
Model Parameters ◽  
Elastic Model ◽  
Stress Strain ◽  
Nonlinear Elastic ◽  
Intact Loess

Duncan-Chang nonlinear model has been modified and applied to the structural loess calculation. Based on structural studies and conventional triaxial tests, this paper has analyzed the mechanical properties of intact loess and the relationship between the stress ratio structural parameters and the strain, then the expression of generalized shear strain and stress ratio structural parameters are given to facilitate the engineering applications. On this basis, the stress-strain curve of intact loess was corrected by the use of the stress ratio structural parameters. The form of the intact loess stress-strain curves which have been revised has changed hardening from the softening or weak softening. The results show that the modified stress-strain curves of intact loess can apply Duncan- Chang nonlinear model to calculate and the model parameters are reasonable and effective. This method provides Duncan-Chang nonlinear model which is widely used in engineering with a new ways and means in intact structural loess application.

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.

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.

A hyper-elastic thermal aging constitutive model for rubber-like materials

2019 ◽  
Vol 52 (8) ◽  
pp. 677-700
Author(s):  
Ahmed G Korba ◽  
Abhishek Kumar ◽  
Mark Barkey
Keyword(s):  
Natural Rubber ◽  
Thermal Aging ◽  
Biaxial Loading ◽  
Strain Curve ◽  
Aging Effect ◽  
Elastic Materials ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Hyper Elastic ◽  
Uniaxial And Biaxial Loading

Different phenomenological, empirical, and micromechanical constitutive models have been proposed to describe the behavior of incompressible isotropic hyper-elastic materials. Among these models, very few have accounted for the thermal aging effect on the model constants and parameters. This article introduces a new empirical constitutive hyper-elastic model for thermally aged hyper-elastic materials. The model named “the weight function based (WFB) model” considers the effect of aging temperature and time on its parameters. The WFB model formulation can facilitate fatigue analysis and lifetime prediction of rubber-like materials under aging conditions. The WFB model in this article defines all rubber-like material properties, such as fracture stretch, strength, and stiffness, by predicting the full stress–strain curve at any aging time and temperature. The WFB model was tested on natural rubber for uniaxial and biaxial loading conditions. More than 100 specimens were aged and tested uniaxially under various temperatures and aging times to extract the stress–strain behavior. The temperatures used in the test ranged from 76.7°C to 115.5°C, and the aging time ranged from 0 to 600 hours (hrs). A classical bulge test experiment was generated to extract the biaxial natural rubber material behavior. An ABAQUS finite element analysis model was created to simulate and verify the generated biaxial stress–strain curve. The proposed model represents the aging effect on the tested natural rubber under uniaxial and biaxial loading conditions with an acceptable error margin of less than 10% compared to experimental data.

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.

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