Continuum mechanics; nonlinear elasticity

cohesive zone element

Are there any papers/documents on one dimensional bar problem with a cohesive zone element formulation? It should be a zero length non-linear spring in this case right? I am more interested in setting up the problem from the virtual work principles rather than a discussion of the results.

Thanks

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?

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

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 