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Solutions to the differential equations of linear elasticity in the continuum limit in arbitrary crystal symmetry are known only for steady-state dislocations of arbitrary character, i.e. line defects moving at constant velocity. Troubled…
We present a complete analytical solution for the stress field inside a homogeneous, inside a homogeneous, linearly elastic solid sphere subjected to a concentrated normal load applied on its surface. Starting from the three-dimensional…
We present new analytical three-dimensional solutions of the magnetohydrostatic equations, which are applicable to the co-rotating frame of reference outside a rigidly rotating cylindrical body, and have potential applications to planetary…
The structural relaxations of a dense, binary mixture of charged hard spheres are studied using the Mode Coupling Theory (MCT). Qualitative differences to non--ionic systems are shown to result from the long--range Coulomb interaction and…
Oscillatory shear tests are widely used in rheology to characterize the linear and non-linear mechanical response of complex fluids, including the yielding transition. There is an increasing urge to acquire detailed knowledge of the…
Deformation in the lithosphere-asthenosphere system can be accommodated by faulting and plastic flow. However, incorporating structural data in models of distributed deformation still represents a challenge. Here, I present solutions for…
A discrete model describing defects in crystal lattices and having the standard linear anisotropic elasticity as its continuum limit is proposed. The main ingredients entering the model are the elastic stiffness constants of the material…
In this paper, we present a unit cell showing a band-gap in the lower acoustic domain. The corresponding metamaterial is made up of a periodic arrangement of this unit cell. We rigorously show that the relaxed micromorphic model can be used…
In this paper we propose a nonlinear elasticity model of macromolecular conformational change (deformation) induced by electrostatic forces generated by an implicit solvation model. The Poisson-Boltzmann equation for the electrostatic…
The elastic response of the crystalline sheet to the stretching deformation in the form of wrinkles has been extensively investigated. In this work, we extend this fundamental scientific question to the plastic regime by exploring the…
Flexible mechanical structures can undergo large deformations under small loads, enabling large, complex, and nonlinear wave responses under finite-frequency driving. Here, we study a dynamically driven canonical flexible mechanical…
The paper addresses an important issue of cloaking transformations for fourth-order partial differential equations representing flexural waves in thin elastic plates. It is shown that, in contrast with the Helmholtz equation, the general…
This paper formulates three different analytical solutions to the gravitational field equations in the framework of Rastall theory by taking into account the gravitational decoupling approach. For this, the anisotropic spherical interior…
We study {\it analytically} the characteristic resonance spectrum of charged massive scalar fields linearly coupled to a spherically symmetric charged reflecting shell. In particular, we use analytical techniques in order to solve the…
Achieving strongly symmetric stress approximations for linear elasticity problems in high-contrast media poses a significant computational challenge. Conventional methods often struggle with prohibitively high computational costs due to…
We develop a finite element method for a large deformation membrane elasticity problem on meshed surfaces using a tangential differential calculus approach that avoids the use of classical differential geometric methods. The method is also…
We consider the scalar anisotropic wave equation. Recently a convergence analysis for radial perfectly matched layers (PML) in the frequency domain was reported and in the present article we continue this approach into the time domain.…
The stress fields of dislocations predicted by classical elasticity are known to be unrealistically large approaching the dislocation core, due to the singular nature of the theory. While in many cases this is remedied with the…
Deformations of conventional solids are described via elasticity, a classical field theory whose form is constrained by translational and rotational symmetries. However, flexible metamaterials often contain an additional approximate…
The essential role of long range elastic interactions in recrystallization is demonstrated using a simple analytical model: pileup rearrangements following absorption of leading dislocations by a dislocation-free embryo provides an…