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The nonlinear mechanics of a flexible elastic rod constrained at its edges by a pair of sliding sleeves is analyzed. The planar equilibrium configurations of this variable-length elastica are found to have shape defined only by the…
This paper is based on a series of talks given at the ESI program on 'Mathematical Perspectives of Gravitation Beyond the Vacuum Regime' in February 2022. It is meant to be an introduction to the field of relativistic elasticity for readers…
We propose bending energies for isotropic elastic plates and shells. For a plate, we define and employ a surface tensor that symmetrically couples stretch and curvature such that any elastic energy density constructed from its invariants is…
The paper studies the interaction of a longitudinal wave with transverse waves in general isotropic and unconstrained hyperelastic materials, including the possibility of dissipation. The dissipative term chosen is similar to the classical…
The linear response of two-dimensional amorphous elastic bodies to an external delta force is determined in analogy with recent experiments on granular aggregates. For the generated forces, stress and displacement fields, we find strong…
Elastic properties of the solid regions of neutron star crusts and white dwarfs play an important role in theories of stellar oscillations. Matter in compact stars is presumably polycrystalline and, since the elastic properties of single…
A detailed study is carried out for the relativistic theory of viscoelasticity which was recently constructed on the basis of Onsager's linear nonequilibrium thermodynamics. After rederiving the theory using a local argument with the…
Critical collapse is a well-studied subject for a variety of self-gravitating matter. One of the most intensively examined models is that of perfect fluids, which have been used extensively to describe compact objects such as stars, as well…
The modern theory of elasticity and the first law of thermodynamics are cornerstones of engineering science that share the concept of reversibility. Engineering researchers have known for four decades that the modern theory violates the…
We find two new classes of exact solutions to the Einstein-Maxwell system of equations. The matter distribution satisfies a linear equation of state consistent with quark matter. The field equations are integrated by specifying forms for…
We prove the local existence of solutions to the Einstein-Elastic equations that represent self-gravitating, relativistic elastic bodies with compact support.
Most early twentieth century relativists --- Lorentz, Einstein, Eddington, for examples --- claimed that general relativity was merely a theory of the aether. We shall confirm this claim by deriving the Einstein equations using aether…
Aether Scalar-Tensor theory is a relativistic alternative gravity model that behaves like cold dark matter on cosmological scales while predicting the MOND force-law in astrophysical systems. The theory correctly predicts the cosmic…
We extend the theory of structured deformations to the setting of linearized elasticity by providing an integral representation for the underlying energy that features bulk and surface contributions. Our derivation is obtained both via a…
Under the static spherically symmetric Einstein-Maxwell spacetime of embedding class one we explore possibility of electromagnetic mass model where mass and other physical parameters have purely electromagnetic origin (Tiwari 1984, Gautreau…
Among the possible extensions of General Relativity that have been put forward in order to address some long standing issues in our understanding of the Universe, Scalar-Tensor Theories have received a lot of attention for their simplicity.…
We demonstrate a technique to generate new class of exact solutions to the Einstein-Maxwell system describing a static spherically symmetric relativistic star with anisotropic matter distribution. An interesting feature of the new class of…
In the framework of multiple-scattering theory, we show that the dispersion relations of certain electromagnetic (EM) and elastic metamaterials can be obtained analytically in the long-wavelength limit. Specific examples are given to the…
We study the interaction between gravitational waves and elastic bodies within the framework of relativistic elasticity. Starting from the Lagrangian formulation of relativistic elasticity, we derive the linearized equations governing the…
Non-Euclidean plates are a subset of the class of elastic bodies having no stress-free configuration. Such bodies exhibit residual stress when relaxed from all external constraints, and may assume complicated equilibrium shapes even in the…