Department of Mechanics: Seminar: Abstract Krysl 2019: Difference between revisions

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==== Petr Krysl, University of California, La Jolla, San Diego, USA ====
==== Petr Krysl, University of California, La Jolla, San Diego, USA ====


Modal expansion is a workhorse used in many engineering analysis algorithms.
Metamaterials, with their internal composition carefully designed to feature exotic and often counterintuitive properties such as cloaking or band gaps, are the prime example of a pronounced influence of material’s microstructure on its macroscopic response. Regarding mechanical responses, metamaterials have already delivered high stiffness-to-weight ratio, negative compressibility, and tunable auxetic behaviour. These mechanical metamaterials often rely on internal instability mechanisms that trigger transformation of their periodic microstructure into predefined patterns, which introduces strong kinematic coupling among adjacent periodic metamaterial cells and leads to significant size and boundary effects. As a result, the standard first-order computational homogenization fails to provide an effective model of such metamaterials.
One example is the coupled boundary element-finite element computation of the
This talk presents a micromorphic computational homogenization scheme that has been recently developed specifically for the instability-driven mechanical metamaterials. The scheme introduces characteristic deformation patterns at microscale, whose magnitudes are communicated across adjacent macroscopic material points by scalar modulation fields, which are added to the standard continuum formulation at the macroscale and for which an additional micromorphic-like conservation law emerges at macroscale. Consequently, the presented scheme captures the above-mentioned size effect and boundary layers and accounts for with spatial mixing of multiple patterns. Combined with the bifurcation analysis, the scheme also correctly predicts local to global (i.e. micro vs. macro) buckling transitions.
backscattering target strength of underwater elastic objects. To obtain the modal
Keywords: Mechanical metamaterials, computational homogenization, micromorphic continuum
basis, a free-vibration (generalized eigenvalue) problem needs to be solved. This
 
tends to be expensive when there are many basis vectors to compute. In the above
 
mentioned backscattering example it could be many hundreds or thousands.  
References
Excellent algorithms exist to solve the free-vibration problem, and most use some form of
# Ameen, M.M., Rokoš, O., Peerlings, R.H.J., and Geers, M.G.D. (2018). Size effects in nonlinear periodic materials exhibiting reversible pattern transformations. Mechanics of Materials 124, 55–70.
the Rayleigh-Ritz (RR) procedure. The key to an efficient RR application is
# Rokoš, O., Ameen, M.M., Peerlings, R.H.J., and Geers, M.G.D. (2019). Micromorphic computational homogenization for mechanical metamaterials with patterning fluctuation fields. Journal of the Mechanics and Physics of Solids 123, 119–137.
a low-cost transformation into a reduced basis. In this work we show how a cheap a priori
# Rokoš, O., Ameen, M.M., Peerlings, R.H.J., and Geers, M.G.D. (2020a). Extended micromorphic computational homogenization for mechanical metamaterials exhibiting multiple geometric pattern transformations. Extreme Mechanics Letters 37, 100708.
transformation can be constructed for solid-mechanics finite element models based
# Rokoš, O., Zeman, J., Doškář, M., and Krysl, P. (2020b). Reduced integration schemes in micromorphic computational homogenization of elastomeric mechanical metamaterials. Advanced Modeling and Simulation in Engineering Sciences 7, 19.
on the notion of coherent nodal clusters. The inexpensive RR procedure leads to
# Bree, S.E.H.M., Rokoš, O., Peerlings, R.H.J., Doškář, M., Geers, M.G.D. A Newton solver for micromorphic computational homogenization enabling multiscale buckling analysis of pattern-transforming metamaterials. Under review.
not insignificant speedups of the computation of an approximate solution to the free
# Sperling, S.O., Rokoš, O., Ameen, M.M., Peerlings, R.H.J., Kouznetsova, V.G., and Geers, M.G.D.. Enriched Computational Homogenization Schemes Applied to Pattern-Transforming Elastomeric Mechanical Metamaterials. In preparation.
vibration problem.

Revision as of 11:22, 25 June 2020

Using a priori model reduction for the FEM to quickly approximate free-vibration response of solids

Petr Krysl, University of California, La Jolla, San Diego, USA

Metamaterials, with their internal composition carefully designed to feature exotic and often counterintuitive properties such as cloaking or band gaps, are the prime example of a pronounced influence of material’s microstructure on its macroscopic response. Regarding mechanical responses, metamaterials have already delivered high stiffness-to-weight ratio, negative compressibility, and tunable auxetic behaviour. These mechanical metamaterials often rely on internal instability mechanisms that trigger transformation of their periodic microstructure into predefined patterns, which introduces strong kinematic coupling among adjacent periodic metamaterial cells and leads to significant size and boundary effects. As a result, the standard first-order computational homogenization fails to provide an effective model of such metamaterials. This talk presents a micromorphic computational homogenization scheme that has been recently developed specifically for the instability-driven mechanical metamaterials. The scheme introduces characteristic deformation patterns at microscale, whose magnitudes are communicated across adjacent macroscopic material points by scalar modulation fields, which are added to the standard continuum formulation at the macroscale and for which an additional micromorphic-like conservation law emerges at macroscale. Consequently, the presented scheme captures the above-mentioned size effect and boundary layers and accounts for with spatial mixing of multiple patterns. Combined with the bifurcation analysis, the scheme also correctly predicts local to global (i.e. micro vs. macro) buckling transitions. Keywords: Mechanical metamaterials, computational homogenization, micromorphic continuum


References

  1. Ameen, M.M., Rokoš, O., Peerlings, R.H.J., and Geers, M.G.D. (2018). Size effects in nonlinear periodic materials exhibiting reversible pattern transformations. Mechanics of Materials 124, 55–70.
  2. Rokoš, O., Ameen, M.M., Peerlings, R.H.J., and Geers, M.G.D. (2019). Micromorphic computational homogenization for mechanical metamaterials with patterning fluctuation fields. Journal of the Mechanics and Physics of Solids 123, 119–137.
  3. Rokoš, O., Ameen, M.M., Peerlings, R.H.J., and Geers, M.G.D. (2020a). Extended micromorphic computational homogenization for mechanical metamaterials exhibiting multiple geometric pattern transformations. Extreme Mechanics Letters 37, 100708.
  4. Rokoš, O., Zeman, J., Doškář, M., and Krysl, P. (2020b). Reduced integration schemes in micromorphic computational homogenization of elastomeric mechanical metamaterials. Advanced Modeling and Simulation in Engineering Sciences 7, 19.
  5. Bree, S.E.H.M., Rokoš, O., Peerlings, R.H.J., Doškář, M., Geers, M.G.D. A Newton solver for micromorphic computational homogenization enabling multiscale buckling analysis of pattern-transforming metamaterials. Under review.
  6. Sperling, S.O., Rokoš, O., Ameen, M.M., Peerlings, R.H.J., Kouznetsova, V.G., and Geers, M.G.D.. Enriched Computational Homogenization Schemes Applied to Pattern-Transforming Elastomeric Mechanical Metamaterials. In preparation.
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