scholarly journals Lamé problem for a multilayer cylinder made of nonlinear elastic materials under finite strains

2019 ◽  
Vol 1353 ◽  
pp. 012068
Author(s):  
K M Zingerman ◽  
O A Ryabova ◽  
D D Muhin ◽  
I A Kaplunov
Keyword(s):  
Finite Strains ◽  
Elastic Materials ◽  
Multilayer Cylinder ◽  
Lamé Problem ◽  
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.

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.

Sign in / Sign up

Export Citation Format

Share Document