An Approximate Method for Analysis of Solitary Waves in Nonlinear Elastic Materials

2016 ◽  
Vol 52 (3) ◽  
pp. 282-289 ◽  
Author(s):  
J. J. Rushchitsky ◽  
V. N. Yurchuk
Keyword(s):  
Approximate Method ◽  
Solitary Waves ◽  
Elastic Materials ◽  
Nonlinear Elastic

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.

scholarly journals Solitary waves on nonlinear elastic rods. II.

1987 ◽  
Vol 81 (6) ◽  
pp. 1718-1722 ◽  
Author(s):  
M. P. Soerensen ◽  
P. L. Christiansen ◽  
P. S. Lomdahl ◽  
O. Skovgaard
Keyword(s):  
Solitary Waves ◽  
Elastic Rods ◽  
Nonlinear Elastic

Effective Constitutive Equations for Porous Elastic Materials at Finite Strains and Superimposed Finite Strains

2003 ◽  
Vol 70 (6) ◽  
pp. 809-816 ◽  
Author(s):  
V. A. Levin ◽  
K. M. Zingermann
Keyword(s):  
Plane Strain ◽  
Constitutive Equations ◽  
Rigid Motion ◽  
Finite Deformations ◽  
Finite Strains ◽  
Effective Characteristics ◽  
Elastic Materials ◽  
Preliminary Loading ◽  
Nonlinear Elastic

A method is developed for derivation of effective constitutive equations for porous nonlinear-elastic materials undergoing finite strains. It is shown that the effective constitutive equations that are derived using the proposed approach do not change if a rigid motion is superimposed on the deformation. An approach is proposed for the computation of effective characteristics for nonlinear-elastic materials in which pores are originated after a preliminary loading. This approach is based on the theory of superimposed finite deformations. The results of computations are presented for plane strain, when pores are distributed uniformly.

scholarly journals APPROXIMATE TECHNIQUES FOR DISPERSIVE SHOCK WAVES IN NONLINEAR MEDIA

2012 ◽  
Vol 21 (03) ◽  
pp. 1250035 ◽  
Author(s):  
T. R. MARCHANT ◽  
NOEL F. SMYTH
Keyword(s):  
Shock Wave ◽  
Approximate Method ◽  
Nonlinear Wave ◽  
Solitary Waves ◽  
Wave Equations ◽  
Leading Edge ◽  
Nonlinear Wave Equations ◽  
Trailing Edge ◽  
Nonlinear Media ◽  
Linear Waves

Many optical and other nonlinear media are governed by dispersive, or diffractive, wave equations, for which initial jump discontinuities are resolved into a dispersive shock wave. The dispersive shock wave smooths the initial discontinuity and is a modulated wavetrain consisting of solitary waves at its leading edge and linear waves at its trailing edge. For integrable equations the dispersive shock wave solution can be found using Whitham modulation theory. For nonlinear wave equations which are hyperbolic outside the dispersive shock region, the amplitudes of the solitary waves at the leading edge and the linear waves at the trailing edge of the dispersive shock can be determined. In this paper an approximate method is presented for calculating the amplitude of the lead solitary waves of a dispersive shock for general nonlinear wave equations, even if these equations are not hyperbolic in the dispersionless limit. The approximate method is validated using known dispersive shock solutions and then applied to calculate approximate dispersive shock solutions for equations governing nonlinear optical media, such as nematic liquid crystals, thermal glasses and colloids. These approximate solutions are compared with numerical results and excellent comparisons are obtained.

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