An exact solution to the Lame problem for a hollow sphere for new types of nonlinear elastic materials in the case of large deformations

2021 ◽  
pp. 104345
Author(s):  
V.A. Levin ◽  
Y.Y. Podladchikov ◽  
K.M. Zingerman
Keyword(s):  
Exact Solution ◽  
Hollow Sphere ◽  
Large Deformations ◽  
Elastic Materials ◽  
Lamé Problem ◽  
Nonlinear Elastic

scholarly journals Large deformations of a cylindrical tube with prestressed coatings

2019 ◽  
Vol 484 (5) ◽  
pp. 542-546
Author(s):  
L. M. Zubov
Keyword(s):  
Exact Solution ◽  
Hollow Cylinder ◽  
Large Deformations ◽  
Cylindrical Tube ◽  
Longitudinal Force ◽  
Circular Cylinders ◽  
Elastic Materials ◽  
External Pressures ◽  
Nonlinear Elastic

The problem of large deformations in a combined nonlinear elastic hollow cylinder under internal and external pressures, loaded with a longitudinal force and torque at the end faces, is under consideration. The combined cylinder is a tube with the internal and external coatings in the form of prestressed hollow circular cylinders. An exact solution to the problem is found, which is valid for any model of isotropic incompressible elastic materials.

scholarly journals Spherically Symmetric Tensor Fields and Their Application in Nonlinear Theory of Dislocations

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 830
Author(s):  
Evgeniya V. Goloveshkina ◽  
Leonid M. Zubov
Keyword(s):  
Nonlinear Theory ◽  
Hollow Sphere ◽  
Tensor Field ◽  
Exact Analytical Solution ◽  
Symmetric Tensor ◽  
Symmetric Distribution ◽  
Spherically Symmetric ◽  
Tensor Fields ◽  
Spherically Symmetric Distribution ◽  
Nonlinear Elastic

The concept of a spherically symmetric second-rank tensor field is formulated. A general representation of such a tensor field is derived. Results related to tensor analysis of spherically symmetric fields and their geometric properties are presented. Using these results, a formulation of the spherically symmetric problem of the nonlinear theory of dislocations is given. For an isotropic nonlinear elastic material with an arbitrary spherically symmetric distribution of dislocations, this problem is reduced to a nonlinear boundary value problem for a system of ordinary differential equations. In the case of an incompressible isotropic material and a spherically symmetric distribution of screw dislocations in the radial direction, an exact analytical solution is found for the equilibrium of a hollow sphere loaded from the outside and from the inside by hydrostatic pressures. This solution is suitable for any models of an isotropic incompressible body, i. e., universal in the specified class of materials. Based on the obtained solution, numerical calculations on the effect of dislocations on the stress state of an elastic hollow sphere at large deformations are carried out.

Simulation of the Impact Behaviour of Diffusion-Bonded and Adhered Perforated Hollow Sphere Structures (PHSS)

2009 ◽  
Vol 294 ◽  
pp. 27-38 ◽  
Author(s):  
Fabian Ferrano ◽  
Marco Speich ◽  
Wolfgang Rimkus ◽  
Markus Merkel ◽  
Andreas Öchsner
Keyword(s):  
Mechanical Properties ◽  
Finite Element Method ◽  
Finite Element ◽  
Mechanical Behaviour ◽  
Hollow Sphere ◽  
Large Deformations ◽  
The Finite Element Method ◽  
Impact Behaviour ◽  
New Type ◽  
The Impact

This paper investigates the mechanical properties of a new type of hollow sphere structure. For this new type, the sphere shell is perforated by several holes in order to open up the inner sphere volume and surface. The mechanical behaviour of perforated sphere structures under large deformations and strains in a primitive cubic arrangement is numerically evaluated by using the finite element method for different hole diameters and different joining techniques.

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.

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