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Continuum mechanics; nonlinear elasticity

Sundaraelangovan selvam's picture

What is the physical meaning of Green-Lagrangian strain and Eulerian-Almansi strain measures?

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Hello, researchers. I have difficulty in understanding the physical meaning of Green-Lagrangian strain (E) and Eulerian-Almansi strain (A) measures. Mathematically speaking, I can derive the equations of these strains in different ways. But physically speaking, it's a bit harder to understand how these strains (E and A) can be pictured and how to give a proper physical definition for them. In a simple case, considering a uni-axial bar (Please refer the attached file), Engineering strain can be understood easily, but in E and A equations, from where do the squares of the lengths originate?

peppezurlo's picture

Catastrophic thinning of dielectric elastomers

Consider a thin dielectric plate with conducting faces: when will it break if a voltage is applied? If it is rigid it will break once its dielectric strength is overcome by the voltage. But what if it is highly stretchable, like the elastomers used for soft actuators, stretchable electronics, or energy harvesters? The precise answer to that question is not known. 

Nonlinear structural analysis on ABAQUS

Dear iMechanica users,

I am working on a metallic foam model, and due to its nature of geometry and physical properties, I considered geometrical and physical nonlinearities. What is the significance of NLGEOM = ON and NLGEOM = OFF besides, it includes or excludes the geomterical nonlinearity in ABAQUS? I want to know the basic change that has been incorporated when I switch the NLGEOM between ON and OFF. Also, a theoretical explanation on how this change is caried out. 

Anisotropic stiffness of isotropic material

Dear colleagues,

 

Consider a simple non-linear elastic material with stress given as

σ = D(εdev) εdev + B εiso

where εdev is the norm of εdev, D is a function of εdev and B is constant. The material is isotropic since the principal directions of  σ and ε will coincide.

If we differentiate σ wrt ε to obtain the material stiffness the form of the stiffness tensor will be

Payam Soltani's picture

Nonlinear vibration of a nanoplate embedded on a Pasternak-type foundation using nonlocal continuum theory

Nonlinear vibration of a nanoplate embedded on a Pasternak-type foundation using nonlocal continuum theory

BY: Payam Soltani, V. Kamali , O. Pashaei Narenjbon,  A. Farshidianfar 

Abstract:

Nonlocal plate continuum model is utilized to investigate the nonlinear vibration behaviour of a singlelayer

nanoplate. The isotropic nanoplate is assumed to be embedded on a Pasternak-type elastic foundation with the

Konstantin Volokh's picture

Nice and low-cost introductory texts

There are two very nice companion texts on continuum mechanics and nonlinear elasticity printed by Dover recently: "Continuum mechanics" by Spencer and "An introduction to the theory of elasticity" by Atkin and Fox. Great and fairly affordable reading!

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