arXiv subjects

Michal Šmejkal

Publications and source records attributed to Michal Šmejkal.

4 recordsLinked to original sources

arXiv2026

Incremental equations in curvature-dependent surface elasticity

We develop a general incremental framework for hyperelastic solids whose surfaces exhibit both stretch-dependent and curvature-dependent elastic behavior. Building upon a variational formulation of curvature-dependent surface elasticity, we derive compact governing equations expressed in a coordinate-free Lagrangian setting that remain valid for arbitrary geometries. Linearization about an arbitrarily large finite deformation yields incremental bulk and surface balance laws that closely resemble the classical small-on-large theory, but are now extended to include surface-curvatureinduced stresses. The applicability of the general theory is demonstrated by analyzing the onset of periodic beading in a soft cylindrical substrate coated with a surface layer exhibiting stretching- or curvature-dependent behavior, illustrating how surface stretching and bending effects influence instability thresholds for both compressible and incompressible bulk. This unified formulation thus provides a foundation for studying stability phenomena in elasto-capillary systems where surface curvature plays a critical mechanical role.

math-ph↗

arXiv2025

Surface-Polyconvex Models for Soft Elastic Solids

Soft solids with surface energy exhibit complex mechanical behavior, necessitating advanced constitutive models to capture the interplay between bulk and surface mechanics. This interplay has profound implications for material design and emerging technologies. In this work, we set up variational models for bulk-surface elasticity and explore a novel class of surface-polyconvex constitutive models that account for surface energy while ensuring the existence of minimizers. These models are implemented within a finite element framework and validated through benchmark problems and applications, including, e.g., the liquid bridge problem and the Rayleigh-Plateau instability, for which the surface energy plays the dominant role. The results demonstrate the ability of surface-polyconvex models to accurately capture surface-driven phenomena, establishing them as a powerful tool for advancing the mechanics of soft materials in both engineering and biological applications.

math-ph↗

arXiv2024

Integral Micromorphic Model Reproducing Dispersion in 1D Continuum

The paper develops a new integral micromorphic elastic continuum model, which can describe dispersion properties of band-gap metamaterials, i.e., metamaterials that inhibit propagation of waves in a certain frequency range. The enrichment consists in nonlocal averaging of three terms in the expression for the potential energy density of the standard micromorphic continuum. After proper calibration, such a formulation can exactly reproduce two given branches of the dispersion curve (acoustic and optical), even in cases with a band gap. The calibration process exploits Fourier images of the unknown weight functions, which are analytically deduced from the dispersion relation of the material of interest. The weight functions are then reconstructed in the spatial domain by numerical evaluation of the inverse Fourier transform. The presented approach is validated on several examples, including a discrete mass-spring chain with two alternating masses, for which the dispersion relation has an explicit analytical form and the optical and acoustic branches are separated by a band gap.

physics.app-ph↗

arXiv2022

Integral Micromorphic Model for Band Gap in 1D Continuum

The design of band-gap metamaterials, i.e., metamaterials with the capability to inhibit wave propagation of a specific frequency range, has numerous potential engineering applications, such as acoustic filters and vibration isolation control. In order to describe the behavior of such materials, a novel integral micromorphic elastic continuum is introduced, and its ability to describe band gaps is studied in the one-dimensional setting. The nonlocal formulation is based on a modification of two terms in the expression for potential energy density. The corresponding dispersion equation is derived and converted to a dimensionless format, so that the effect of individual parameters can be described in the most efficient way. The results indicate that both suggested nonlocal modifications play an important role. The original local micromorphic model reproduces a band gap only in the special, somewhat artificial case, when the stiffness coefficient associated with the gradient of the micromorphic variable vanishes. On the other hand, the nonlocal formulation can provide band gaps even for nonzero values of this coefficient, provided that the penalty coefficient that enforces coupling between the micromorphic variable and nonlocal strain is sufficiently high and the micromorphic stiffness is sufficiently low.

physics.app-ph↗