μMECH library

μMECH is a C/C++ subroutine library for analytical solutions of micromechanical problems. It is a free software released under the GNU LGPL.

The library µMECH was principally designed to provide finite element packages with microstructure informed enrichment functions. It contains subroutines evaluating mechanical fields (strains, stresses, displacements) inside a composite media consisting of ellipsoidal-like inclusions embedded in an infinite matrix. The implemented, purely analytical, solutions to internal and external fields (inside and outside inclusion domains, respectively) are based on the J. D. Eshelby work and is fully accomplished in three dimensions. Moreover, the implemented algorithms extend the classical Eshelby's solution to take into account perturbations due to the presence of adjacent inclusions so as to deal with a non-dilute media.

So far, the code offers the solution to micromechanical fields within the random heterogeneous media containing inclusions of various shapes, as e.g. general elipsoid, sphere, penny, etc.

Documentation

Download

For developers

Comments for doxygen (czech, Unicode/UTF-8 format). See problem.h in source code.

Referencing

When referencing µMECH in a publication, please cite at least one of the following papers:

  • L. Svoboda, S. Šulc, T. Janda, J. Vorel, J. Novák, muMECH micromechanics library, Advances in Engineering Software, 2016, 100, 148-160, http://dx.doi.org/10.1016/j.advengsoft.2016.07.010
  • Novák, J. and Kaczmarczyk, L. and Grassl, P. and Zeman, J. and Pearce, C. J., A micromechanics-enhanced finite element formulation for modelling heterogeneous materials. Computer Methods in Applied Mechanics and Engineering 201:53--64, 2012, 1103.5633.
  • Oberrecht, S. P. and Novák, J. and Krysl, P., B-bar FEMs for anisotropic elasticity. International Journal for Numerical Methods in Engineering 98:92--104, 2014, DOI: 10.1002/name.4621.
  • N. Mishra, J. Vondřejc, and J. Zeman, A comparative study on low-memory iterative solvers for FFT-based homogenization of periodic media, Journal of Computational Physics, 2016, 321, 151-168, http://dx.doi.org/10.1016/j.jcp.2016.05.041
  • J. Zeman, T.W.J. de Geus, J. Vondřejc, R.H.J. Peerlings, and M.G.D. Geers, A finite element perspective on non-linear FFT-based micromechanical simulations, International Journal for Numerical Methods in Engineering, 2016, 00:2-35, DOI: 10.1002/nme.5381
  • P. Hlaváček, V. Šmilauer, F. Škvára, L. Kopecký, R. Šulc, Inorganic foams made from alkali-activated fly ash:Mechanical, chemical and physical properties, Journal of the European Ceramic Society, 35, 703-709, 2014. doi:10.1016/j.jeurceramsoc.2014.08.024

Credits

The following people have made significant contributions to μMECH - Jan Novák, Tomáš Janda, Martin Horák, Jan Vorel, Lukáš Zrůbek, Stanislav Šulc and Ladislav Termit Svoboda.

μMECH library polynomial

The core functions of μMECH library was rewritten in .NET(F#) and enriched with Eshelby solution for polynomial eigenstrains. The code is a free software released under the GNU LGPL.

Download

Polytop solution 2D

The MATLAB implementation of Eshelby solutions for polytops in 2D. The code is a free software released under the GNU LGPL.

Download

Integration of rapidly oscilatory functions

The MATLAB implementation of the method for integration of rapidly oscilatory functions, development version. The code is a free software released under the GNU LGPL.

Download

Acknowledgments and partners

Funding by following associations/organizations under specified pojects is gratefully acknowledged.

  • Grant Agency of the Czech Republic
    - Project No. 13-22230S (A hybrid multiscale predictive modelling tool for heterogeneous solids),
    - Project No. P105-12-0331 (Efficient solvers for transport processes in saturated and unsaturated porous media).