arXiv subjects

Dimitris Sfyris

Publications and source records attributed to Dimitris Sfyris.

4 recordsLinked to original sources

arXiv2026

Universal Displacements in Linear Strain-Gradient Elasticity

We study universal displacement fields in three-dimensional linear strain-gradient elasticity within the Toupin-Mindlin first strain-gradient theory. Building on the approach of Yavari (2020), we derive, for each material symmetry class, the universality PDEs obtained by requiring the equilibrium equations (in the absence of body forces) to hold for any material in that class, and we determine the complete set of universal displacements. Using the full symmetry classification together with compact matrix representations of the elasticity tensors, we provide explicit characterizations for all 48 strain-gradient symmetry classes, including centrosymmetric and chiral classes. For several high-symmetry classes, the strain-gradient universality PDEs impose no additional restrictions beyond the classical ones, so the universal displacement families coincide with those of classical linear elasticity (for example, the isotropic classes SO(3) and O(3)). For lower symmetry classes, the strain-gradient universality PDEs can be stricter than their classical counterparts, so the universal displacements form proper subsets of the classical universal displacement families due to additional higher-order differential conditions.

physics.class-ph↗

arXiv2025

Alternative writings of classical elastodynamics equations as a first order symmetric system

We explore alternative writings of the equations of classical elastodynamics as a first order symmetric system. In the one dimensional case we present symmetric writings with respect to: i) the velocity ($u_t$) and the displacement gradient ($u_x$), ii) the velocity and stress ($\sigma$), iii) all three quantities: the velocity, the displacement gradient and the stress, and finally iv) the momentum ($\rho_0 u_t$), the velocity, the displacement gradient and the stress. In the two dimensional case we present similar writings with respect to: i) the velocity (${\bf u}_t$) and the strain tensor ($\bf e$), ii) the velocity and the stress tensor ($\boldsymbol \sigma$), iii) all three variables $({\bf u}_t, {\bf e}, \boldsymbol \sigma)$, and finally iv) one more writing utilizing the momentum as well, i.e. $(\rho_0 {\bf u}_t, {\bf u}_t, {\bf e}, \boldsymbol \sigma)$. We accomplish our goal by judiciously using the compatibility equations as well as the momentum equation and the time differentiated constitutive law. This is done in an inverse way: we start by writing our initial equations as a first order system of the form ($\bf q$ being the vector representing the variables in each writing) $$ A \frac{\partial {\bf q}}{\partial t}+\sum_{i=1}^n B_i \frac{\partial {\bf q}}{\partial x_i}=0, $$ with $n=1, 2$ depending on whether we are in 1 or 2 dimensions. We then check what are the symmetric forms of matrices $B_i$ and which combinations of the compatibility equations, the momentum equations and the time differentiated constitutive law should be used in order the symmetric form of matrices $B_i$ to appear into the system. This "symmetrization" process alters matrix $A$ and if the resulting matrix $A$ is symmetric our goal is accomplished. Our analysis is confined to classical elastodynamics, namely geometrically and materially linear anisotropic elasticity.

physics.class-ph↗

arXiv2024

Universal Displacements in Anisotropic Linear Cauchy Elasticity

Universal displacements are those displacements that can be maintained for any member of a specific class of linear elastic materials in the absence of body forces, solely by applying boundary tractions. For linear hyperelastic (Green elastic) solids, it is known that the space of universal displacements explicitly depends on the symmetry group of the material, and moreover, the larger the symmetry group the larger the set of universal displacements. Linear Cauchy elastic solids, which include linear hyperelastic solids as a special case, do not necessarily have an underlying energy function. Consequently, their elastic constants do not possess the major symmetries. In this paper, we characterize the universal displacements of anisotropic linear Cauchy elasticity. We prove the unexpected result that for each symmetry class, the set of universal displacements of linear Cauchy elasticity is identical to that of linear hyperelasticity.

cond-mat.soft↗

arXiv2016

Failure Processes in Embedded Monolayer Graphene under Axial Compression

Exfoliated monolayer graphene flakes were embedded in a polymer matrix and loaded under axial compression. By monitoring the shifts of the 2D Raman phonons of rectangular flakes of various sizes under load, the critical strain to failure was determined. Prior to loading care was taken for the examined area of the flake to be free of residual stresses. The critical strain values for first failure were found to be independent of flake size at a mean value of -0.60 % corresponding to a yield stress of -6 GPa. By combining Euler mechanics with a Winkler approach, we show that unlike buckling in air, the presence of the polymer constraint results in graphene buckling at a fixed value of strain with an estimated wrinkle wavelength of the order of 1-2 nm. These results were compared with DFT computations performed on analogue coronene/ PMMA oligomers and a reasonable agreement was obtained.

cond-mat.mtrl-sci↗