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Overview of solid mechanics


This video (LINK)  attempts to give the big picture of solid mechanics along with the brief explanation of the constituent topics.


This is an educational outreach initiative targeted at all engineers interested in mechanics and seek simpler explanations. Kindly share if you learn something out of this !




Strain calculation in ABAQUS

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I have some troubles in calculating the strain in ABAQUS. I have the following Model with one element (see picture) and a linear elastic isotropic Material (Steel), which is sheared in the x-direction. The analytical result of the strain tensor gives me in xz-direction 0.25 (see picture). The result in ABAQUS is 0.5. I ran the same simulation in CalculiX CrunchiX and got the expected strain of 0.25 in the xz-direction

Can anyone tell me how ABAQUS calculates the strain for a linear static analysis? Why is the ABAQUS result exactly 50% higher?

How obtain tension strain concrete(σt0) in damaged plasticity model in ABAQUS?

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How obtain tension strain concrete(σt0) in damaged plasticity model in ABAQUS?

hello engineers

i need help about concrete damaged plasticity

fo example :

if Compressive stress (Fu)= 51.2 MPa

and tension stress (σ t)=0.3 x 51.2^(2/3)=4.136

1)why (σ t) is 2.36 in picture(uploaded)?

2)what is tension strain ? and how? i cant understand.

i cant obtain εt = total tensile strain.

how obtain εcr ?

please help


Carl T. Herakovich's picture

New Ebook on Elastic Solids at Amazon

This treatise provides a broad overview of the definitions of
fundamental quantities and methods of analysis for the use of solid materials
in structural components. The presentation is limited to the linear elastic
range of material behavior where there is a one to one relationship between
load and displacement.  Fundamental
methods of analysis and typical results for structures made of elastic solid materials
subjected to axial, bending, torsion, thermal, and internal pressure loading;

Stress/strain of a body performing a translation

Hello all,

I am having task to determine the strength analysis (stress/strain) of a translating machine part (body). The part is driven by a set of gears, placed on the top of the body. The input is a constant acceleration value to the propultion engine. Firstly I should do a 2D analysis with a retangle representing the machine part. 

How to supply a visualization for the displacement gradient tensor

Hi all, 

[Warning: The writing is long, as is usually the case with my posts :)]

It all began with a paper that I proposed for an upcoming conference in India. The extended abstract got accepted, of course, but my work is still in progress, and today I am not sure if I can meet the deadline. So, I may perhaps withdraw it, and then submit a longer version of it to a journal, later.

Mohr's Circle---When Was the Last Time You Used It in Your Professional Engineering Work?

As a consultant in computational mechanics, I currently help write some FEM-related code, and while doing this job, an episode from a recent past came to my mind. Let me go right on to the technical issue, keeping aside the (not so good) particulars of that episode. (In case you are curious: it happened outside of my current job, during a job interview.)

If you are a design engineer, FE analyst, researcher, or any professional dealing with stress analysis in your work, I seek answers to a couple of questions from you:

Question 1:

Ahmad Rafsanjani's picture

Writing User Subroutines with ABAQUS

Dear All,

 I think that many students are looking for some tutorials about writing a UMAT in ABAQUS.

You can find a comprehensive tutorial for elastic problems.

This file contains: 

• Motivation

jintting's picture

Strain Energy Derivation

Dear Sirs,

I'm trying to derive an strain energy in a small volume 2a x 2b x 2t.

I can derive "The rest terms are ommited" by myself . 

By the way, I can't derive the DT2 term in the 2nd row of the figure.

Please help with reference or tips.


Jin Kim

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Producing Stress Analysis from Strain data

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I am doing research on the stresses that are produced when a retainer (a thermoplastic sheet) is placed on the teeth. We've designed the project so that we take an initial scan of the sheet and a final "shifted" scan of the sheet. We'd like to compare, find the strain, and calculate the stress neccessary to produce this strain.

I was hoping to use FEA for it possible? I have access to Abaqus and Ansys, and where can i find the commands that allow me to do this.

Stress or strain: which one is more fundamental?

In between stress and strain, which one is the more fundamental physical quantity? Or is it the case that each is defined independent of the other and so nothing can be said about their order? Is this the case?

Liu's picture

Void-induced strain localization at interfaces

We published this paper in APL on a study of the deformation near interfaces. It provides insight in the strain localization at the interface and its influence on the deformation in bulk metals. 

Abstract An optical full-field strain mapping technique has been used to provide direct evidence for the existence of a highly localized strain at the interface of stacked Nb/Nb bilayers during the compression tests loaded normal to the interface. No such strain localization is found in the bulk Nb away from the interface. The strain localization at the interfaces is due to a high void fraction resulting from the rough surfaces of Nb in contact, which prevents the extension of deformation bands in bulk Nb crossing the interface, while no distinguished feature from the stress-strain curve is detected.

Wei Hong's picture

Dynamics of terraces on a silicon surface due to the combined action of strain and electric current

A (001) surface of silicon consists of terraces of two variants, which have an identical atomic structure, except for a 90° rotation. We formulate a model to evolve the terraces under the combined action of electric current and applied strain. The electric current motivates adatoms to diffuse by a wind force, while the applied strain motivates adatoms to diffuse by changing the concentration of adatoms in equilibrium with each step. To promote one variant of terraces over the other, the wind force acts on the anisotropy in diffusivity, and the applied strain acts on the anisotropy in surface stress. Our model reproduces experimental observations of stationary states, in which the relative width of the two variants becomes independent of time. Our model also predicts a new instability, in which a small change in experimental variables (e.g., the applied strain and the electric current) may cause a large change in the relative width of the two variants.

Wei Hong's picture

Persistent step-flow growth of strained films on vicinal substrates

We propose a model of persistent step flow, emphasizing dominant kinetic processes and strain effects. Within this model, we construct a morphological phase diagram, delineating a regime of step flow from regimes of step bunching and island formation. In particular, we predict the existence of concurrent step bunching and island formation, a new growth mode that competes with step flow for phase space, and show that the deposition flux and temperature must be chosen within a window in order to achieve persistent step flow. The model rationalizes the diverse growth modes observed in pulsed laser deposition of SrRuO3 on SrTiO3

 Physical Review Letters 95, 095501 (2005)

Augustin Louis Cauchy (August 21, 1789 – May 23, 1857)

Augustin Louis Cauchy ( 21 August 1789 - 23 May 1857) was a French mathematician and mechanician. In mechanics, he in 1822 formalized the stress concept in the context of three-dimensional thoery, showed its properties as consisting of a 3 by 3 symmetric arrays of numbers that transform as a tensor, derived the equations of motion for a continuum in terms of the components of stress, and gave the specific development of the theory of linear elasticity for isotropic solids. As part of his work, Cauchy also introduced the equations which express the six components of strain, three extensinal and three shear, in terms of derivatives of displacements for the case when all those derivatives are much smaller than unity; similar expressions had been given earlier by Euler in expressing rates of straining in terms of the derivatives of the velocity field in a fluid. (cited from Mechanics of Solids by J.R. Rice) Read more...

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