The hybrid Capriccio method: A 1D study for further advancement

readme.txt:

Abstract:
(from [1])

Polymers and, in particular, polymer composites are known for the enormous adjustability of their mechanical, chemical, and thermal behavior. Multiscale methods are increasingly employed to unravel the polymer microstructure’s impact on the material properties. These methods combine the accuracy of particle-based techniques with the efficiency of continuum mechanical approaches. Amorphous polymers pose a special challenge since their microstructure does not continue periodically, and therefore special attention needs to be paid to the particle domain boundary.
In this study, we introduce a coupling via an interface between the continuum and the particle domain. Padding atoms as particle representations of the continuum, which serve as interaction partners for the atoms in the particle region, allow for the transfer of displacements and forces between the domains. We present a straightforward 1D example with simple interactions, evaluate the scheme’s performance, discuss the resulting energy contributions, and identify an optimal set of coupling parameters. Eventually, this forms the basis for future 3D implementations. [1]

Contact:

Maximilian Ries
Institute of Applied Mechanics
Friedrich-Alexander-Universiät Erlangen-Nürnberg
Egerlandstr. 5
91058 Erlangen

License:

Creative Commons Attribution 4.0 International

Context:

Supplement to conference paper:
[1] M. Ries, P. Steinmann, S.Pfaller, "The Hybrid Capriccio Method: A 1D Study for Further Advancement",
14th WCCM-ECCOMAS Congress 2020, DOI: 10.23967/wccm-eccomas.2020.335, 2021.

The results published discussed in above publication were generated with the code provided here.
The code is written and tested in Matlab versions R2018b and R2019b.

File structure:

- optimization.m
    Main file, executes the optimization run, to obtain an ideal parameter set for the model specified in parameters.m

- parameters.m
    Specifies the investigated model:
    * nFE          % # of FE elements in pure FE domain
    * nFEP         % # of FE elements in padding region
    * nBFE        % # of particle bonds in an FE element
    * nBA          % # of particle bonds in the pure particle domain
    * knn           % (next neighbour stiffness)
    * ksn           % (second next neighbour stiffness)
    * kFE         % (continuum stiffness)
    * ac             % (weighting factor continuum)
    * an               % (weighting factor of bonds within padding region)  
    * ad            % (weighting factor of bonds between pad atoms and pure atoms)
    * F         % external load

- capriccio_BB_one_d_generic.m
    Solves the 1D problem specified in parameters.m

- capriccio_BB_one_d_generic_plot.m
    Visualizes the the resulting displacement over degree of freedom,  cf. [1]

- capriccio_nelder_mead.m
    Executes capriccio_BB_one_d_generic.m and optimizes the weighting factors with the Nelder-Mead algorithm.

- capriccio_steepest_decent.m
    Executes capriccio_BB_one_d_generic.m and optimizes the weighting factors with the steepest-descent algorithm.