Nonlinear Elastic Analysis of the Hardness Test on Rubber-Like Materials

1991 ◽  
Vol 64 (2) ◽  
pp. 202-210 ◽  
Author(s):  
W. V. Chang ◽  
S. C. Sun
Keyword(s):  
Finite Element ◽  
Linear Elasticity ◽  
Elastic Moduli ◽  
Indentation Depth ◽  
Nonlinear Effects ◽  
Hardness Test ◽  
Constitutive Law ◽  
Total Load ◽  
Depth Difference ◽  
Nonlinear Elastic

Abstract Both the Ogden-Tschoegl nonlinear elastic constitutive law and a contact algorithm in the general-purpose finite-element program AFEM have been used to examine the use of IRHD values to relate the elastic properties of elastomers. We are aware that large deformations of rubber specimens and complicated interface conditions are involved in this so-called simple test. However, from the finite-element results, we find that the linearly elastic Hertz contact solution is a reasonably accurate model. This can be attributed to several points. First, the hardness test involves mainly compression and shear deformation and the linearly elastic behavior is more closely followed in rubbers for the above two types of deformation. Second, although nonlinear effects become significant in soft rubbers and higher indentation cases, the ASTM D 1415 standard defines larger indentation depth differences for smaller IRHD values. The definition itself compensates for the nonlinear effects. Third, although the interfacial stress field changed due to different frictional conditions, we calculated the IRHD values only from indentation depth difference and total load applied to the steel ball. Both the indentation depth difference and the total load are obtained from far-field conditions and do not change significantly. We should note that using linear elasticity to correlate the elastic moduli and IRHD values is simply a special case in rubber elasticity. We conveniently get rubber's elastic moduli from IRHD values based on linear elasticity, but the complete rubber-like material behavior has to be obtained from more general experiments and described by a nonlinear constitutive law such as the Ogden-Tschoegl model.

Modeling Method of Constitutive Law of Rubber Hyperelasticity Based on Finite Element Simulations

2003 ◽  
Vol 76 (1) ◽  
pp. 271-285 ◽  
Author(s):  
Li-Rong Wang ◽  
Zhen-Hua Lu
Keyword(s):  
Finite Element ◽  
Finite Element Simulations ◽  
Constitutive Law ◽  
Modeling Technique ◽  
Characteristic Analysis ◽  
Rubber Material ◽  
Element Simulation ◽  
Tension And Compression ◽  
Nonlinear Elastic ◽  
Elastic Characteristics

Abstract This paper is to present a method and procedure for modeling the constitutive law of anti-vibration rubber hyperelasticity based on finite element simulations. The hyperelasticity of rubber-like material is briefly summarized first. Then a method and procedure for determining an accurate constitutive law of rubber hyperelasticity from uniaxial tension and compression experiment data is presented and implemented. Due to nonlinear elastic properties of rubber and application limitations of various forms of constitutive law, results of finite element simulation to rubber material experiments show that different forms of constitutive law have to be adopted in different ranges of strain. The proposed procedure to obtain an appropriate constitutive law of rubber hyperelasticity of vibration isolator provides engineers with an effective modeling technique for design and analysis of anti-vibration rubber components. Finally, models of three kinds of rubber materials of a hydraulically damped rubber mount (HDM) are determined by tests and finite element simulations and applied to static and dynamic characteristic analysis of the HDM. The predicted elastic characteristics of the HDM and its major rubber components agree well with experimental data, which demonstrates the practicability and effectiveness of the presented modeling technique to modeling engineering rubber materials in dynamic systems.

Analysis of Indentation: Implications for Measuring Mechanical Properties With Atomic Force Microscopy

1999 ◽  
Vol 121 (5) ◽  
pp. 462-471 ◽  
Author(s):  
K. D. Costa ◽  
F. C. P. Yin
Keyword(s):  
Indentation Depth ◽  
Constitutive Law ◽  
Elastic Materials ◽  
Force Microscopy ◽  
Linear Elastic ◽  
Afm Indentation ◽  
Atomic Force ◽  
Afm Probe ◽  
Nonlinear Elastic ◽  
Indenter Geometry

Indentation using the atomic force microscope (AFM) has potential to measure detailed micromechanical properties of soft biological samples. However, interpretation of the results is complicated by the tapered shape of the AFM probe tip, and its small size relative to the depth of indentation. Finite element models (FEMs) were used to examine effects of indentation depth, tip geometry, and material nonlinearity and heterogeneity on the finite indentation response. Widely applied infinitesimal strain models agreed with FEM results for linear elastic materials, but yielded substantial errors in the estimated properties for nonlinear elastic materials. By accounting for the indenter geometry to compute an apparent elastic modulus as a function of indentation depth, nonlinearity and heterogeneity of material properties may be identified. Furthermore, combined finite indentation and biaxial stretch may reveal the specific functional form of the constitutive law—a requirement for quantitative estimates of material constants to be extracted from AFM indentation data.

Characterization of Material Behavior of the Fused Deposition Modeling Processed Parts

2017 ◽  
Author(s):  
Madhukar Somireddy ◽  
Aleksander Czekanski
Keyword(s):  
Finite Element ◽  
Elastic Moduli ◽  
Fused Deposition Modeling ◽  
Material Behavior ◽  
Constitutive Law ◽  
Finite Element Models ◽  
Strength Parameters ◽  
Fused Deposition ◽  
Deposition Modeling

In the present research, one of the additive manufacturing techniques, fused deposition modeling (FDM) fabricated parts are considered for investigation of their material behavior. The FDM process is a layer upon layer deposition of a material to build three dimensional parts and such parts behave as laminated composite structures. Each layer of the part acts as a unidirectional fiber reinforced lamina, which is treated as an orthotropic material. The mesostructure of a part fabricated via fused deposition modeling process is accounted for in the investigation of its mechanical behavior. The finite element (FE) procedure for characterization of a material constitutive law for the FDM processed parts is presented. In the analysis, the mesostructure of the part obtained via FDM process is replicated in the finite element models. Finite element models of tensile specimens are developed with mesostructure that would be obtained from FDM process, then uniaxial tensile test simulations are conducted. The elastic moduli of a lamina are calculated from the linear analysis and the strength parameters are obtained from the nonlinear finite element analysis. The present work provides a FE methodology to find elastic moduli and strength parameters of a FDM processed part by accounting its mesostructure in the analysis.

EFFECT OF MECHANICAL PROPERTIES OF THE SUBSTRATE TISSUES ON THE DETERMINATION OF ELASTIC MODULUS OF THE SCLERA USING INDENTATION TEST

2016 ◽  
Vol 16 (07) ◽  
pp. 1650085
Author(s):  
XIUQING QIAN ◽  
KUNYA ZHANG ◽  
ZHICHENG LIU
Keyword(s):  
Mechanical Properties ◽  
Finite Element Method ◽  
Finite Element ◽  
Elastic Modulus ◽  
Elastic Moduli ◽  
Indentation Depth ◽  
Vitreous Body ◽  
Indentation Test ◽  
Posterior Pole

The sclera is an important connective tissue that protects the sensitive layers within the eyeball. Identifying the mechanical properties of the sclera near the posterior pole is necessary to analyze the deformation of the sclera and stresses changing in the optic nerve head tissues. We propose a method to determine the mechanical properties of the sclera using dimensional analysis, finite element method and the indentation test. The elastic moduli of the sclera for different indentation depths and positions were identified. We found that the elastic moduli of the sclera varied with indentation depth. This was due to the effect of the mechanical properties of the substrate tissues inside the sclera. The elastic modulus of the choroid had the biggest effect on the determination of elastic modulus of the sclera, whereas that of the vitreous body could be ignored when the ratio of the indentation depth to the thickness of the sclera was less than 0.5. The effects of mechanical properties of the substrate tissues become more pronounced at greater indentation depths.

Nonlinear and dispersive acoustic wave propagation

Geophysics ◽  
2004 ◽  
Vol 69 (3) ◽  
pp. 840-848 ◽  
Author(s):  
Ketil Hokstad
Keyword(s):  
Wave Equation ◽  
Acoustic Wave ◽  
Elastic Moduli ◽  
Nonlinear Effects ◽  
Acoustic Wave Equation ◽  
Acoustic Wave Propagation ◽  
Stress Strain Relation ◽  
Nonlinear Stress ◽  
Ricker Wavelet ◽  
Nonlinear Elastic

Because of cracks and poor consolidation, rocks may have large third‐and fourth‐order nonlinear elastic moduli. Even though strains are small, nonlinear effects may be important in acoustic wave transmission experiments. A nonlinear and dispersive extension of Hooke's law is proposed. Combined with Newton's law, this gives a nonlinear and dispersive acoustic wave equation. For some combinations of nonlinear and dispersive parameters, the wave equation can be reduced to the Korteweg‐deVries equation, such that analytical solutions can be obtained. Finite‐difference simulations with an initial Ricker wavelet show that the nonlinear terms in the wave equation steepen the wavefront and higher harmonics in the frequency spectrum. When dispersion is included, a nonlinear stress–strain relation with hysteresis is observed.

scholarly journals 3D Finite Element Analysis of Rotary Instruments in Root Canal Dentine with Different Elastic Moduli

2021 ◽  
Vol 11 (6) ◽  
pp. 2547 ◽  
Author(s):  
Carlo Prati ◽  
João Paulo Mendes Tribst ◽  
Amanda Maria de Oliveira Dal Piva ◽  
Alexandre Luiz Souto Borges ◽  
Maurizio Ventre ◽  
...  
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Root Canal ◽  
Elastic Moduli ◽  
Reaction Force ◽  
Von Mises Stress ◽  
Elastic Behavior ◽  
Element Analysis ◽  
Heat Treated ◽  
Von Mises

The aim of the present investigation was to calculate the stress distribution generated in the root dentine canal during mechanical rotation of five different NiTi endodontic instruments by means of a finite element analysis (FEA). Two conventional alloy NiTi instruments F360 25/04 and F6 Skytaper 25/06, in comparison to three heat treated alloys NiTI Hyflex CM 25/04, Protaper Next 25/06 and One Curve 25/06 were considered and analyzed. The instruments’ flexibility (reaction force) and geometrical features (cross section, conicity) were previously investigated. For each instrument, dentine root canals with two different elastic moduli(18 and 42 GPa) were simulated with defined apical ratios. Ten different CAD instrument models were created and their mechanical behaviors were analyzed by a 3D-FEA. Static structural analyses were performed with a non-failure condition, since a linear elastic behavior was assumed for all components. All the instruments generated a stress area concentration in correspondence to the root canal curvature at approx. 7 mm from the apex. The maximum values were found when instruments were analyzed in the highest elastic modulus dentine canal. Strain and von Mises stress patterns showed a higher concentration in the first part of curved radius of all the instruments. Conventional Ni-Ti endodontic instruments demonstrated higher stress magnitudes, regardless of the conicity of 4% and 6%, and they showed the highest von Mises stress values in sound, as well as in mineralized dentine canals. Heat-treated endodontic instruments with higher flexibility values showed a reduced stress concentration map. Hyflex CM 25/04 displayed the lowest von Mises stress values of, respectively, 35.73 and 44.30 GPa for sound and mineralized dentine. The mechanical behavior of all rotary endodontic instruments was influenced by the different elastic moduli and by the dentine canal rigidity.

Finite Element Analysis of Creep Damage Behavior Near the Cavity on Bimaterial Interface

2006 ◽  
Vol 324-325 ◽  
pp. 951-954 ◽  
Author(s):  
Qing Min Yu ◽  
Zhu Feng Yue ◽  
Yong Shou Liu
Keyword(s):  
Finite Element ◽  
Elastic Moduli ◽  
Elastic Stress ◽  
Creep Damage ◽  
Ductile Material ◽  
Bimaterial Interface ◽  
Modulus Ratio ◽  
Element Analysis ◽  
Damage Law ◽  
The Difference

Fracture along an interface between materials plays a major role in failure of material. In this investigation, finite element calculations with Kachanov–Rabotnov damage law were carried out to study the creep damage distribution near the interface cavity in bimaterial specimens. The specimens with central hole were divided into three types. The material parameters of K-R law used in this paper were chosen for a brittle material and ductile material. All calculations were performed under four load cases. Due to the difference between elastic moduli of the bounded materials, the elastic stress field as a function of the Young’s modulus ratio (R=E1/E2) was determined. At the same time, the influence of model type on elastic stress distribution near the cavity was considered. Under the same conditions, the material with larger modulus is subjected to larger stress. The creep damage calculations show that the location of the maximum damage is different for each model. The distributions of creep damage for all three models are dependent on the material properties and load cases.

Atomistic Simulations of Nanoindentation on Cu (111) with a Void

2008 ◽  
Vol 33-37 ◽  
pp. 919-924
Author(s):  
Chung Ming Tan ◽  
Yeau Ren Jeng ◽  
Yung Chuan Chiou
Keyword(s):  
Finite Element ◽  
Stress Concentration ◽  
Indentation Depth ◽  
Equilibrium Configuration ◽  
Complete System ◽  
Internal Surface ◽  
Atomistic Simulations ◽  
Element Formulation ◽  
Variable Parameters ◽  
Deformed State

This paper employs static atomistic simulations to investigate the effect of a void on the nanoindentation of Cu(111). The simulations minimize the potential energy of the complete system via finite element formulation to identify the equilibrium configuration of any deformed state. The size and depth of the void are treated as two variable parameters. The numerical results reveal that the void disappears when the indentation depth is sufficiently large. A stress concentration is observed at the internal surface of the void in all simulations cases. The results indicate that the presence of a void has a significant influence on the nanohardness extracted from the nanoindentation tests.

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