相关论文: Measure-valued solutions for models of ferroelectr…
We consider a Kelvin-Voigt model for viscoelastic second-grade materials, where the elastic and the viscous stress tensor both satisfy frame indifference. Using a rigidity estimate by [Ciarlet-Mardare '15], existence of weak solutions is…
We prove that, when linearized, the governing equations of an incompressible elastic continuum yield Maxwell's equations as corollaries. Through judicious distinction between the referential and local descriptions, the principle of material…
In many cases the correct theoretical description of flexoelectricity requires the consideration of the finite size of a body and is reduced to the solution of boundary problems for partial differential equations. Generally speaking, in…
The paper considers the system of pressureless gas dynamics in one space dimension. The question of solvability of the initial-boundary value problem is addressed. Using the method of generalized potentials and characteristic triangles,…
A contact problem of the theory of electroelasticity for piecewise-homogeneous plate of piezo-electric material with infinite cut and elastic finite inclusion of variable bending rigidity is considered. By using methods of the theory of…
Temperature measurements of dielectric permittivity are performed for nonstoichiometric ferroelectric lead germanate Pb$_{4.95}$Ge$_3$O$_{11}$ and multiferroic solid solution [N(C$_2$H$_5$)$_4$]$_2$CoClBr$_3$. Unlike the heat capacity data,…
While crack nucleation and propagation in the brittle or quasi-brittle regime can be predicted via variational or material-force-based phase field fracture models, these models often assume that the underlying elastic response of the…
Emergent functionalities of structural and topological defects in ferroelectric materials underpin an extremely broad spectrum of applications ranging from domain wall electronics to high dielectric and electromechanical responses. Many of…
Based upon elements of the modern Pseudoanalytic Function Theory, we analyse a new method for numerically approaching the solution of the Dirichlet boundary value problem, corresponding to the two-dimensional Electrical Impedance Equation.…
Model-free data-driven computational mechanics replaces phenomenological constitutive functions by numerical simulations based on data sets of representative samples in stress-strain space. The distance of strain and stress pairs from the…
Ferroelectric (FE) size effects against the scaling law were reported recently in ultrathin group-IV monochalcogenides, and extrinsic effects (e.g. defects and lattice strains) were often resorted to. Via first-principles based…
The paper studies the evolution of the thermomechanical and electric state of a thermoviscoelastic thermistor that is in frictional contact with a reactive foundation. The mechanical process is dynamic, while the electric process is…
Incompressible nonlinearly hyperelastic materials are rarely simulated in Finite Element numerical experiments as being perfectly incompressible because of the numerical difficulties associated with globally satisfying this constraint. Most…
In this paper a new integral equation solution to the elastic-plastic problem of functionally graded bars under torsional loading is presented. The formulation is general in the sense that it can be applied to an arbitrary cross-section…
Piezoelectric appliances have become hugely important in the past century and computer simulations play an essential part in the modern design process thereof. While much work has been invested into the practical simulation of piezoelectric…
The conformal formulation of the Einstein constraint equations is first reviewed, and we then consider the design, analysis, and implementation of adaptive multilevel finite element-type numerical methods for the resulting coupled nonlinear…
We investigate the numerical implementation of functionally graded properties in the context of the finite element method. The macroscopic variation of elastic properties inherent to functionally graded materials (FGMs) is introduced at the…
Recent experimental realization of ferroelectric nematic liquid crystalline phases stimulated material development and numerous experimental studies of these new phases, guided by their fundamental and applicative interest. In this…
This paper deals with a parabolic partial differential equation that includes a non-linear nonlocal in time term. This term is the product of a so-called interaction potential and the solution of the problem. The interaction potential…
We study a one-dimensional nonlinear hyperbolic-parabolic initial boundary value problem occurring in the theory of thermoelasticity. We prove existence and uniqueness of the local-in-time strong solution. Also, some global-in-time weak…