Related papers: Matrix representations for 3D strain-gradient elas…

We establish several sufficient conditions for the strong ellipticity of any fourth-order elasticity tensor in this paper. The first presented sufficient condition is an extension of positive definite matrices, which states that the strong…

The elasticity tensor that describes the elastic response of a material to external forces is among the most fundamental properties of materials. The availability of full elasticity tensors for inorganic crystalline compounds, however, is…

Odd transport phenomena -- defined as a flux response orthogonal to an applied gradient -- have been recently observed in isotropic systems, with a multitude of proposed models and experiments to study these effects. Odd transport manifests…

Third-order tensors are widely used as a mathematical tool for modeling physical properties of media in solid state physics. In most cases, they arise as constitutive tensors of proportionality between basic physics quantities. The…

Finite plasticity theories are still a subject of controversy and lively discussions. Among the approaches to finite elastoplasticity two became especially popular. The first, implemented in the commercial finite element codes, is based on…

We develop a reduced-order model for thin plates made of hard magnetorheological elastomers (hard-MREs), which are materials composed of hard-magnetic particles embedded in a polymeric matrix. First, we propose a new magnetic potential, as…

We formulate effective necessary and sufficient conditions to identify the symmetry class of an elasticity tensor, a fourth-order tensor which is the cornerstone of the theory of elasticity and a toy model for linear constitutive laws in…

In this paper, we investigate the inherent physical and mathematical character of higher gradient theories, in which the strain or distortion gradients are considered as the fundamental measures of deformation. Contrary to common belief,…

For homogeneous higher gradient elasticity models we discuss frame-indifference and isotropy requirements. To this end, we introduce the notions of local versus global SO(3)-invariance and identify frame-indifference (traditionally) with…

Magneto-rheological elastomers (MREs) are functional materials that can be actuated by applying an external magnetic field. MREs comprise a composite of hard magnetic particles dispersed into a nonmagnetic elastomeric matrix. By applying a…

Three-dimensional magnetic metamaterials feature interesting phenomena that arise from a delicate interplay of material properties, local anisotropy, curvature, and connectivity. A particularly interesting magnetic lattice that combines…

In this paper, the modelling strategy of a Cosserat rod element (CRE) is addressed systematically for 3-dimensional dynamical analysis of slender structures. We employ the exact nonlinear kinematic relationships in the sense of Cosserat…

The effects of passive scalar anisotropy on subgrid-scale (SGS) physics and modeling for Large-Eddy Simulations are studied experimentally. Measurements are performed across a moderate Reynolds number wake flow generated by a heated…

The paper addresses the problem of finding the necessary and sufficient conditions to be satisfied by the engineering moduli of an anisotropic material for the elastic energy to be positive for each state of strain or stress. The problem is…

Complementary to the development of highly three-dimensional (3D) integrated circuits in the continuation of Moore's law, there has been a growing interest in new 3D deformation strategies to improve device performance. To continue this…

In this work, dislocation master-equations valid for anisotropic materials are derived in terms of kernel functions using the framework of micromechanics. The second derivative of the anisotropic Green tensor is calculated in the sense of…

We study inverse problems in anisotropic elasticity using tools from algebraic geometry. The singularities of solutions to the elastic wave equation in dimension $n$ with an anisotropic stiffness tensor have propagation kinematics captured…

An analytical expression of the strain distribution due to lattice mismatch is obtained in an infinite isotropic elastic medium (a matrix) with a three-dimensional polyhedron-shaped inclusion (a quantum dot). The expression was obtained…

We give conditions on the strain-energy function of nonlinear anisotropic hyperelastic materials that ensure compatibility with the classical linear theories of anisotropic elasticity. We uncover the limitations associated with the…

We present the results of numerical simulation of magnetodielectric effect (MDE) in magnetorheological elastomers (MRE) - the change of effective permittivity of elastomer placed under the external magnetic field. The computer model of…