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Stress is defined as the quantity equal to ... what?

In introducing the very concept of the stress tensor to the beginning student, text-books always present only indirect relations involving the concept. Thus, you have the relations like "traction = (stress-transposed)(unit normal)" (i.e. Cauchy's formula, for uniform stress), or the relations for the coordinate transformations of the stress tensor, or the divergence theorem (for non-uniform stress). These are immediately followed or interspersed with alternative notations, and the rules for using them.

But what you never ever get to see, in text-books or references, is this: a *direct* definition of the stress tensor, i.e. an equation in which there is only the stress tensor on the left hand-side, and some expression involving some *other* quantities on right hand-side. Why? What possibly could be the conceptual and pedagogical advantages of giving a direct definition of this kind, and its physical meaning? I would like to ponder on these matters here, giving my answers to these and similar questions in the process.

Yaning Li's picture

Ph. D position: Mechanics and 3D Printing

Level: Ph.D, start from Fall 2018
When: Apply Now by sending CV to  yaning.li@unh.edu
Fellowship: Deadline 02/25/2018.  (again directly sending CV to yaning.li@unh.edu) https://ceps.unh.edu/graduate-fellowships
Project: NSF/CAREER award on Chiral Auxetic Composites

Angelo Simone's picture

Short Course on Enriched Finite Element Methods at WCCM in NY

We'd like to announce an upcoming short course in Enriched Finite Element Methods at the 13th World Congress in Computational Mechanics (http://www.wccm2018.org/). The course will be held on Sunday 22nd July at the New York Marriott Marquis hotel.

More information can be found on the flyer and at the course page.

Fundamentals of Simpleware Training, Reading, UK, Feb 6th

This one-day intensive training course intends to give new and existing users sufficient knowledge of the basic functionality of Simpleware software for converting 3D image data (MRI, CT...) into mdoels for CAD, CAE, and 3D Prrinting applications. It will allow you to develop workflows based your areas of research and future projects.

Learn more about this training day.

oliver oreilly's picture

Tossing your Smartphone

If you are teaching a course on vehicle dynamics, navigation, robotics, or rotations you might be interested in exploiting the fact that your students' smartphones are equipped with inertial navigation units (IMUs). Daniel Kawano and Prithvi Akella have harnessed the data from the IMU using the Matlab mobile app and used this data to determine the motion of a smart phone:

kolman's picture

An ECCOMAS Advanced Course on Computational Structural Dynamics, Prague, 2018

We would like to announce An ECCOMAS Advanced Course on Computational Structural Dynamics 2018, shortcourse2018.it.cas.cz . The short course on computational structural dynamics will be held form June 4 to June 8, 2018 in Prague, Czech Republic.

Yaning Li's picture

Ph. D position in Mechanics of Materials

One Ph.D position is open for Fall 2018 in Mechanical Engineering at the Univesrity of New Hampshire.

 

The student will work on the NSF/CAREER project on Mechanics of Chiral Auxetic Mechanical Metamaterials.

(theory, finite element simulations, 3D printing, and mechanical experiments)

 

The candidate will also have opportunity to apply for the CEPS fellowship. 

 

More information can be found at

http://www.unh.edu/yaning-lab/

Francois Barthelat's picture

Two new PhD positions in bioinspired architectured materials and structures, McGill University

We have new openings for two PhD students –fully funded - in the Laboratory of Advanced Materials and Bioinspiration at McGill University, starting Fall 2018 (Application deadline: 01/15/2018)

Stavros Gaitanaros's picture

PhD Position on the Mechanical Properties of DNA Nanostructures

Applications are invited for a PhD position at Johns Hopkins University (beginning Fall 2018) on a collaborative project between the labs of Extreme Mechanics of Architected Materials (Prof. Stavros Gaitanaros) and Mechanochemistry And Functional Imaging Applications (Prof. Yun Chen) at Johns Hopkins University.
The project will focus on the combination of multi-scale modeling and experiments in order to examine the mechanical behavior of DNA origami nanostructures.

Neda.km's picture

Strong background in Mathematics, Nonlinear Dynamics, Vibrations and Control

Hi 

I have B.Sc from Sharif University of Technology, Iran and M.S. from Northeastern University in  Boston, US, both in Mechanical Engineering.

Ashby PhD Scholarship in the Mechanics of Materials

A fully funded PhD scholarship exists in the area of Mechanics of Materials, endowed in honour of Prof M F Ashby. The successful applicant will have a 1st class degree (and ideally a Masters degree) in an appropriate field. The precise topic of the PhD can be fixed after the scholarship has been awarded.

Further details may be obtained from Ms Hambro-Fernandez (Div-C@eng.cam.ac.uk)

rajan_prithivi's picture

Basics of plasticity theory in 6 min

This video explains the very fundamental points with regard to plasticity theory. It covers the following -

 

1) Why study plasticity ?

2) Additive decomposition of strain

3) stress and strength

4) Yield condition , flow rule & hardening rule

 

-Prithivi

Updated solution manual for Metamaterial book

The derivations of some equations and solutions to problems from my metamaterials books are now available for download from ResearchGate at https://www.researchgate.net/publication/320611794_Mechanical_metamaterials_some_derivations_and_examples.

-- Biswajit

Shiva Rudraraju's picture

PhD positions in Computational Mechanics at the University of Wisconsin Madison

Looking for prospective PhD students with strong background in solid mechanics and numerical methods to join the Computational Mechanics and Multiphysics Group at the University of Wisconsin Madison. Background in modeling contact or contact mechanics is a big plus but not essential.  

The research scope is in the broader areas of mechanics driven multiphysics in morphogenesis/embroyogenesis phenomena (Biophysics) and microstructure evolution in metallic alloys.   

Ph.D. Student Positions in Computational Materials Science and Mechanics

Several Ph.D. student positions are available in Professor El-Azab’s group with the School of Materials Engineering, Purdue University. The group performs advanced theoretical and computational research in the areas of mesoscale plasticity and dislocation dynamics, radiation effects in materials, microstructure evolution, phase field method development, and computational methods for materials science and mechanics. Applicants with MS in mechanical, aerospace, or materials engineering, with background in microstructure science, continuum mechanics and elasticity, numerical methods or computational techniques such as finite element method are highly preferred. Knowledge of at least one advanced programming language such as Fortran or C++ is required. Exceptional applicants with BS degree will also be considered. The openings are for spring 2018, summer 2018 and fall 2018. Applicants must meet Purdue University and School of Materials Engineering admission criteria. For inquiry please send email to Professor El-Azab (aelazab@purdue.edu).

Tangent modulus of the Mooney-Rivlin based Neo-hookean - Could you check my derivation??

Choose a channel featured in the header of iMechanica: 

Hello.

 

I study solid mechanics at a graduate school.

 

I tried to derive tangent modulus of the Mooney-Rivlin based Neo-Hookean material.

 

There might be no error in my derivation, but answer is wrong with referred right answer.

 

So, could you check my derivation?

 

I attached my derivation as a figure.

Tangent modulus of the Mooney-Rivlin based Neo-hookean - Could you check my derivation??

Hello.

 

I study solid mechanics at a graduate school.

 

I tried to derive tangent modulus of the Mooney-Rivlin based Neo-Hookean material.

 

There might be no error in my derivation, but answer is wrong with referred right answer.

 

So, could you check my derivation?

 

I attached my derivation as a figure.

 

 

 

Thanks in advance.

Ph.D. Student Positions in Computational Materials and Mechanics

Several Ph.D. student positions are available in Professor El-Azab’s group with the School of Materials Engineering, Purdue University. The group performs advanced theoretical and computational research in the areas of mesoscale plasticity and dislocation dynamics, radiation effects in materials, microstructure evolution, phase field method development, and computational methods for materials science and mechanics. Applicants with MS in mechanical, aerospace, or materials engineering, with background in microstructure science, continuum mechanics and elasticity, numerical methods or computational techniques such as finite element method are highly preferred. Knowledge of an advanced programming languages such as Fortran or C++ is required. Exceptional applicants with BS degree will also be considered. The openings are for fall 2018 semester but those who wish start in the spring or summer 2018 will be accommodated. Applicants must meet Purdue University and School of Materials Engineering admission criteria. For inquiry please send email to Professor El-Azab (aelazab@purdue.edu).

Derivatives of Tensors

Hi all,

I am looking for a general definition of the derivative of a tenorial product (e.g. when the expression for Stress contains nonlinear terms in deformation gradient, F ).

I start with a very simple example:

∂F_pq/∂F_mn = δ_pm  δ_qn , i.e. Kronecker delta with first index of F_pq and first index of  F_mn, and second Kronecker delta for second pair of indices q & n.

rajan_prithivi's picture

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 !

 

Thanks,

Prithivi

marco.paggi's picture

CISM course ''Modelling and Simulation of Tribological Problems in Technology''

Advanced Course at the International Centre for Mechanical Sciences (CISM, Udine, Italy)

 

Modelling and Simulation of Tribological Problems in Technology

May 28, 2018 — June 1, 2018 

Coordinators:

Marco Paggi (IMT School for Advanced Studies Lucca, Lucca, Italy)

David A. Hills (University of Oxford, Oxford, Great Britain)

Assistant, Associate, or Full Professor

The Department of Materials Science and Engineering at Texas A&M University invites applications for a tenured or tenure-track faculty position in the area of mechanical behavior of advanced structural materials.  Although candidates at the assistant professor level are preferred, exceptionally well qualified candidates will be considered for appointment at the rank of associate or full professor.

FEA simulation of double joints in shear loading

Choose a channel featured in the header of iMechanica: 

Hi all,

 

I have a question about an FEA simulation. Particularly, about the boumndary conditions that need to be applied to run this simulation. 

 

attempt1:

 

I fixed the right end of the plates and applied loading to the left end. This resulted in stresses go through only the top joint region (W1 in figure attached). 

 

From our understanding, the deformation is got to be symmetric on both the plates. But, when we applied these BCs, it is not smmetric. 

 

 

attempt-2:

 

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