arXiv subjects

Yury Solyaev

Publications and source records attributed to Yury Solyaev.

6 recordsLinked to original sources

arXiv2026

Identification of the length scale parameter of simplified strain gradient elasticity from standard Mode I fracture tests

Recently, it was shown that additional material constants of strain gradient elasticity (SGE) can be identified for brittle and quasi-brittle materials based on the analysis of experimental data on the crack size effect. In the present paper, we perform precise numerical simulations within SGE and derive regression relations for processing experimental data from standard fracture mechanics tests under pure Mode I loading conditions (CCT, SENT, SENB). We consider the simplified SGE, whose constitutive relations contain a single length scale parameter $\ell$ in addition to the classical elastic constants. We show that, for brittle materials, this parameter can be explicitly identified as $\ell \approx 0.362 (K_{Ic}/\sigma_{ult})^2$. This identification ensures that the fracture loads predicted by classical linear elastic fracture mechanics (LEFM) and by the simplified SGE coincide for relatively long Mode I cracks. However, within the simplified SGE, these fracture loads are evaluated from the nonsingular stress field using the maximum principal stress criterion. For quasi-brittle materials, we derive regression relations that describe the non-classical size effect on strength. This effect is usually treated within nonlinear fracture mechanics but can be naturally captured by SGE. Examples of identification of the length scale parameter $\ell$ based on the established relations and the experimental data for chopped fiber composites and for porous and dense quasi-brittle ceramics are presented.

cond-mat.mtrl-sci↗

arXiv2025

Potential-based formalism for electrodynamics of media with weak spatial dispersion

In this work, we develop a potential-based formalism for Maxwell's equations in isotropic media with weak spatial dispersion within the electric quadrupole-magnetic dipole approximation. We introduce an operator form of the constitutive relations along with a modified Lorenz gauge condition, which enables the derivation of decoupled generalized wave equations for electromagnetic potentials. For time-harmonic processes, we derive the representation of general solution for these equations as a combination of solutions to Helmholtz-type equations, whose parameters are determined by both standard and hyper-susceptibilities of the medium. We show that the proposed approach can be extended to more general constitutive relations and it provides a convenient framework for solving various applied problems. Specifically, using a derived closed-form solution for the problem of plane wave incidence on a planar interface, we demonstrate that a correct definition of the Poynting vector within the multipole theory must incorporate quadrupole effects -- an aspect overlooked in some previous works that has led to inconsistent results. We further establish the necessity of accounting for both propagated and evanescent longitudinal components in reflected and transmitted waves. The presence of these components, which follow directly from the general solution for electromagnetic potentials, is essential for satisfying all classical and additional boundary conditions in media with quadrupolar response (e.g., in metamaterials or quadrupolar liquid mixtures). The complete set of these boundary conditions is derived based on the least action principle, ensuring variational consistency with the field equations and generalizing previously known formulations of multipole theory.

cond-mat.other↗

arXiv2025

Enriched $C^1$ finite elements for crack problems in simplified strain gradient elasticity

We present a new type of triangular $C^1$ finite elements developed for the plane strain crack problems within the simplified strain gradient elasticity (SGE). The finite element space contains a conventional fifth-degree polynomial interpolation that was originally developed for the plate bending problems and subsequently adopted for SGE. The enrichment is performed by adding the near-field analytic SGE solutions for crack problems preserving $C^1$ continuity of interpolation. This allows us an accurate representation of strain and stress fields near the crack tip and also results in the direct calculation of the amplitude factors of SGE asymptotic solution and related value of J-integral (energy release rate). The improved convergence of presented formulation is demonstrated within mode I and mode II problems. Size effects on amplitude factors and J-integral are also evaluated. It is found that amplitude factors of SGE asymptotic solution exhibit a linear dependence on crack size for relatively large cracks.

math.NA↗

arXiv2023

Self-consistent homogenization approach for polycrystals within second gradient elasticity

In this paper, we propose a generalized variant of Kröner's self-consistent scheme for evaluation of the effective standard and gradient elastic moduli of polycrystalline materials within Mindlin-Toupin second-gradient elasticity theory. Assuming random orientation of crystallites (grains) we use an extended Eshelby's equivalent inclusion method and mapping conditions between the prescribed linear distribution of macro-strain and corresponding micro-scale field variables averaged over the volume and all possible orientations of single grain. It is found that developed self-consistent scheme predicts the absence of strong gradient effects at the macro-scale level for the model of spherical grains. However, for the more general shape of the grains, considered approach allows to obtain a set of non-linear relations for determination of all effective standard and gradient elastic moduli of polycrystals.

cond-mat.mtrl-sci↗

arXiv2022

Complete general solutions for equilibrium equations of isotropic strain gradient elasticity

In this paper, we consider isotropic Mindlin-Toupin strain gradient elasticity theory in which the equilibrium equations contain two additional length-scale parameters and have the fourth order. For this theory we developed an extended form of Boussinesq-Galerkin (BG) and Papkovich-Neuber (PN) general solutions. Obtained form of BG solution allows to define the displacement field through the single vector function that obeys the eight-order bi-harmonic/bi-Helmholtz equation. The developed PN form of the solution provides an additive decomposition of the displacement field into the classical and gradient parts that are defined through the standard Papkovich stress functions and modified Helmholtz decomposition, respectively. Relations between different stress functions and completeness theorem for the derived general solutions are established. As an example, it is shown that a previously known fundamental solution within the strain gradient elasticity can be derived by using the developed PN general solution.

physics.class-ph↗

arXiv2019

Analytical solution of a plane strain pure bending problem in second gradient electroelasticity

Semi-inverse analytical solution of a pure bending problem for piezoelectric layer is developed in the framework of linear electroelasticity theory with strain gradient and electric field gradient effects. Two-dimensional solution is derived assuming plane strain state of a layer. It is shown that obtained solution can be used for the validation of size-dependent beam and plate models in second gradient electroelasticity theory.

physics.class-ph↗