Related papers: Analytical solution of a plane strain pure bending…
The asymptotic behaviour of the solutions of three-dimensional nonlinear elastodynamics in a thin plate is studied, as the thickness $h$ of the plate tends to zero. Under appropriate scalings of the applied force and of the initial values…
We consider the cylindrical bending problem for an infinite plate as modelled with a family of generalized continuum models, including the micromorphic approach. The models allow to describe length scale effects in the sense that thinner…
The rotational instability of the electric polarization P during phase transformations between ferroelectric phases is of great practical interest, since it may be accompanied by extremely large values of the piezoelectric coefficient, and…
Bragg-edge strain imaging from energy-resolved neutron transmission measurements poses an interesting tomography problem. The solution to this problem will allow the reconstruction of detailed triaxial stress and strain distributions within…
We present the construction and application of a first order stabilization-free virtual element method to problems in plane elasticity. Well-posedness and error estimates of the discrete problem are established. The method is assessed on a…
This is part of a series of papers on the inverse spectral problem for bounded analytic plane domains. Here, we use the trace formula established in the first paper (`Balian-Bloch trace formula') to explicitly calculate wave trace…
The duality approach in 2-{\it dim} two-component regular checkerboards was extended onto piezoelectricity and piezomagnetism problems. There are found a relation for effective piezoelectric and piezomagnetic modules for the checkerboard…
The coherent reflectivity of a dense, relativistic, ultra-thin electron layer is derived analytically for an obliquely incident probe beam. Results are obtained by two-fold Lorentz transformation. For the analytical treatment, a plane…
Crystalline two-dimensional (2D) semiconductors often combine high elasticity and in-plane strength, making them ideal for strain-induced tuning of electronic characteristics, akin to strategies used in silicon electronics. However,…
We investigate a quasi-static-antiplane contact problem, examining a thermo-electro-visco-elastic material with a friction law dependent on the slip rate, assuming that the foundation is electrically conductive. The mechanical problem is…
We investigate the so called Biefeld-Brown effect in terms of dimensional analysis and in the frame of classical electrodynamics.
The inverse problem of antiplane elasticity on determination of the profiles of $n$ uniformly stressed inclusions is studied. The inclusions are in ideal contact with the surrounding matrix, the stress field inside the inclusions is…
We analyze the inverse spectral problem on the half line associated with elastic surface waves. Here, we extend the treatment of Love waves [arXiv: 1908.10529] to Rayleigh waves. Under certain conditions, and assuming that the Poisson ratio…
We propose a model for rate-independent evolution in elastoplastic materials under external loading, which allows large strains. In the setting of strain-gradient plasticity with multiplicative decomposition of the deformation gradient, we…
This is a review of theoretical results from the three-dimensional equations of anisotropic elasticity or linear piezoelectricity on waves and vibrations in quartz crystal plates. It covers both the classical results on acoustic wave…
This work models brittle fracture using a linearized surface-substrate theory in which the crack faces possess surface stresses derived from a surface strain-gradient elastic energy. The model incorporates surface stretching, curvature, and…
Strain can affect the morphology of a crystal surface, and cause modifications of its reconstruction even when weak, as in the case of mechanical bending. We carried out calculations of strain-dependent surface free energy and direct…
Electric double layers (EDL) with counterions only, say electrons with the elementary charge $-e$, in thermal equilibrium at the inverse temperature $\beta$ are considered. In particular, we study the effect of the surface charge modulation…
The non-linear second order Born-Infeld equation is reduced to a simpler first order complex equation, which can be trivially solved for the coordinates as functions of the field. Each solution is determined by the choice of a holomorphic…
The article addresses the mathematical modeling of the folding of a thin elastic sheet along a prescribed curved arc. A rigorous model reduction from a general hyperelastic material description is carried out under appropriate scaling…