English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

The spectral decomposition of a symmetric, second-order tensor is widelyadopted in many fields of Computational Mechanics. As an example, inelasto-plasticity under large strain and rotations, given the Cauchydeformation tensor, it is a fundamental step to compute the logarithmic straintensor.  Recently, this approach has been also adopted in small-strain isotropicplasticity to reconstruct the stress tensor as a function of its eigenvalues,allowing the formulation of predictor-corrector return algorithms in theinvariants space. These algorithms not only reduce the number of unknowns atthe constitutive level, but also allow the correct handling of stress states inwhich the plastic normals are undefined, thus ensuring a better convergencewith respect to the standard approach.  While the eigenvalues of a symmetric, second-order tensor can be simplycomputed as a function of the tensor invariants, the computation of itseigenbasis can be more difficult, especially when two or more eigenvalues arecoincident. Moreover, when a Newton-Rhapson algorithm is adopted to solvenonlinear problems in Computational Mechanics, also the tensorial derivativesof the eigenbasis, whose computation is still more complicate, are required toassemble the tangent matrix.  A simple and comprehensive method is presented, which can be adopted tocompute a closed form representation of a second-order tensor, as well as theirderivatives with respect to the tensor itself, allowing a simplerimplementation of spectral decomposition of a tensor in Computational Mechanicsapplications.

A closed form exact formulation of the spectral representation of a second-order symmetric tensor and of its derivatives