Post-buckling of linearly tapered column made of nonlinear elastic materials obeying the generalized Ludwick constitutive law

2012 ◽  
Vol 65 (1) ◽  
pp. 83-96 ◽  
Author(s):  
Wasuroot Saetiew ◽  
Somchai Chucheepsakul
Keyword(s):  
Constitutive Law ◽  
Elastic Materials ◽  
Post Buckling ◽  
Generalized Ludwick Constitutive Law ◽  
Nonlinear Elastic ◽  
Tapered Column

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.

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.

scholarly journals Catastrophic Instabilities in the Fracture of Nanotube Bundles

2010 ◽  
Vol 76 ◽  
pp. 159-164
Author(s):  
Nicola Maria Pugno ◽  
Tamer Abdalrahman
Keyword(s):  
Strain Curve ◽  
Smooth Curve ◽  
Constitutive Law ◽  
Catastrophic Failure ◽  
Weibull Statistics ◽  
Simple Modification ◽  
Recent Letter ◽  
Nanotube Bundles ◽  
Nonlinear Elastic ◽  
Versus Strain

In a recent letter, Xiao et al. [3] interpreted experimental results on the failure of nanotube bundles using Weibull Statistics. The prediction of the force versus strain curve was a smooth curve, only partially able to capture the observed discrete behavior of the bundle. In particular, abrupt jumps in the force, at nearly constant strains, were clearly observed experimentally, each of them corresponding to the failure of a sub-bundle. Accordingly, we have developed a simple modification of the Weibull Statistics able to treat the observed catastrophic failure of the bundle, considering a linear or nonlinear elastic constitutive law.

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.

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