arXiv subjects

Martin Vejvoda

Publications and source records attributed to Martin Vejvoda.

3 recordsLinked to original sources

arXiv2026

Discrete versus continuous -- linear lattice models and their exact continuous counterparts

We review and study the correspondence between discrete linear lattice/chain models of interacting particles and their continuous counterparts represented by linear partial differential equations. In particular, we study the correspondence problem for linear nearest neighbour interaction lattice models as well as for linear multiple-neighbour interaction lattice models, while we gradually proceed from infinite lattices to periodic lattices and finally to finite lattices with fixed ends/zero Dirichlet boundary conditions. The whole study is framed as a systematic specialisation of Fourier analysis tools from the continuous to the discrete setting and vice versa, and the correspondence between the discrete and continuous models is examined primarily with regard to the dispersion relation.

physics.class-ph↗

arXiv2025

Modeling metamaterials by second-order rate-type constitutive relations between only the macroscopic stress and strain

We propose a thermodynamically based approach for constructing effective rate-type constitutive relations describing finite deformations of metamaterials. The effective constitutive relations are formulated as \emph{second-order} in time rate-type Eulerian constitutive relations between only the Cauchy stress tensor, the Hencky strain tensor and objective time derivatives thereof. In particular, there is no need to introduce additional quantities or concepts such as ``micro-level deformation'',``micromorphic continua'', ``enriched continua'', or elastic solids with frequency dependent material properties. The linearisation of the proposed fully nonlinear (finite deformations) constitutive relations leads, in Fourier space, to the same constitutive relations as those commonly used in theories based on the concepts of frequency dependent density and/or stiffness. From this perspective the proposed constitutive relations reproduce the behaviour predicted by the frequency dependent density and/or stiffness models, but yet they work with constant -- that is motion independent -- material properties. Finally, we argue that the proposed fully nonlinear (finite deformations) second-order in time rate-type constitutive relations do not fall into traditional classes of models for elastic solids (hyperelastic solids/Green elastic solids, first-order in time hypoelastic solids), and that the proposed constitutive relations embody a \emph{new} class of constitutive relations characterising elastic solids.

cond-mat.mtrl-sci↗

arXiv2024

The conclusion that metamaterials could have negative mass is a consequence of improper constitutive characterisation

The concept of "effective mass" is frequently used for the simplification of complex lumped parameter systems (discrete dynamical systems) as well as materials that have complicated microstructural features. From the perspective of wave propagation, it is claimed that for some bodies described as metamaterials, the corresponding "effective mass" can be frequency dependent, negative or it may not even be a scalar quantity. The procedure has even led some authors to suggest that Newton's second law needs to be modified within the context of classical continuum mechanics. Such absurd physical conclusions are a consequence of appealing to the notion of "effective mass" with a preconception for the constitutive structure of the metamaterial and using a correct mathematical procedure. We show that such unreasonable physical conclusions would not arise if we were to use the appropriate "effective constitutive relation" for the metamaterial, rather than use the concept of "effective mass" with an incorrect predetermined constitutive relation.

cond-mat.mtrl-sci↗