https://www.bc.edu/content/dam/files/schools/cas_sites/physics/pdf/Ren/p85.pdf

Advances in the science and technology of carbon nanotubes and their composites: a review

We review the field of cavity optomechanics, which explores the interaction between electromagnetic radiation and nano- or micromechanical motion This review covers the basics of optical cavities and mechanical resonators, their mutual optomechanical interaction mediated by the radiation pressure force, the large variety of experimental systems which exhibit this interaction, optical measurements of mechanical motion, dynamical backaction amplification and cooling, nonlinear dynamics, multimode optomechanics, and proposals for future cavity quantum optomechanics experiments In addition, we describe the perspectives for fundamental quantum physics and for possible applications of optomechanical devices

Cavity Optomechanics

Built upon the two original books by Mike Crisfield and their own lecture notes, renowned scientist Rene de Borst and his team offer a thoroughly updated yet condensed edition that retains and builds upon the excellent reputation and appeal amongst students and engineers alike for which Crisfield's first edition is acclaimed. Together with numerous additions and updates, the new authors have retained the core content of the original publication, while bringing an improved focus on new developments and ideas. This edition offers the latest insights in non-linear finite element technology, including non-linear solution strategies, computational plasticity, damage mechanics, time-dependent effects, hyperelasticity and large-strain elasto-plasticity. The authors' integrated and consistent style and unrivalled engineering approach assures this book's unique position within the computational mechanics literature.

Non-Linear Finite Element Analysis of Solids and Structures: de Borst/Non-Linear Finite Element Analysis of Solids and Structures

Initial-value ordinary differential equation solution via variable order Adams method (SIVA/DIVA) package is collection of subroutines for solution of nonstiff ordinary differential equations. There are versions for single-precision and double-precision arithmetic. Requires fewer evaluations of derivatives than other variable-order Adams predictor/ corrector methods. Option for direct integration of second-order equations makes integration of trajectory problems significantly more efficient. Written in FORTRAN 77.

Solving Ordinary Differential Equations

Overview of constitutive laws, kinematics, homogenization and multiscale methods in crystal plasticity finite-element modeling: Theory, experiments, applications

Finite element implementation of incompressible, transversely isotropic hyperelasticity

https://www.giref.ulaval.ca/~deteix/bois/documents_references/article4.pdf

A theory of finite viscoelasticity and numerical aspects

Rate-independent plasticity and viscoplasticity in which the boundary of the elastic domain is defined by an arbitrary number of yield surfaces intersecting in a non-smooth fashion are considered in detail. It is shown that the standard Kuhn-Tucker optimality conditions lead to the only computationally useful characterization of plastic loading. On the computational side, an unconditionally convergent return mapping algorithm is developed which places no restrictions (aside from convexity) on the functional forms of the yield condition, flow rule and hardening law. The proposed general purpose procedure is amenable to exact linearization leading to a closed-form expression of the so-called consistent (algorithmic) tangent moduli. For viscoplasticity, a closed-form algorithm is developed based on the rate-independent solution. The methodology is applied to structural elements in which the elastic domain possesses a non-smooth boundary. Numerical simulations are presented that illustrate the excellent performance of the algorithm.

Non‐smooth multisurface plasticity and viscoplasticity. Loading/unloading conditions and numerical algorithms

The problem of Mullins' effect in carbon black-filled rubbers is treated from a micro-mechanical viewpoint and a complete continuum constitutive model is developed. To begin with, a first-order accurate free energy function is derived for the composite in terms of the free energy densities of the constituents. Second, an exact relation between averaged macroscopic nonlinear strain measures and averaged nonlinear matrix material strain measures is derived under the assumption of affinely rotating particles and a C0 continuous motion. Third, the notion of strain-induced matrix-particle debonding is incorporated into the free energy density for the material by exploiting ideas from statistical mechanics. The accuracy of the resulting constitutive model is then demonstrated via comparisons to published experimental data.

Sanjay Govindjee

Papers

Finite element implementation of incompressible, transversely isotropic hyperelasticity

A theory of finite viscoelasticity and numerical aspects

Non‐smooth multisurface plasticity and viscoplasticity. Loading/unloading conditions and numerical algorithms

A micro-mechanically based continuum damage model for carbon black-filled rubbers incorporating Mullins' effect

On the use of continuum mechanics to estimate the properties of nanotubes