education

New article: Plotting ellipsoids with R.  http://www.parresianz.com/r/plotting-ellipsoids-in-R/

-- Biswajit

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

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 [at] purdue.edu).

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.

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 [at] purdue.edu).

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.

However the problem arises when we have a product of two or more tensors. Is the following (using chain rule) a valid derivative?

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

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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