Revisiting imperfect interface laws for two-dimensional elastodynamics

Kinetic Formulation for Systems of Two Conservation Laws and Elastodynamics

On conservation laws in elastodynamics

The objective of this investigation is the establishment of governing balance and conservation laws in elastodynamics. The feature of the approach employed here consists in placing time on the same level as the space coordinates, as is done in the theory of relativity, i.e., pursuing a 4 · 4 formalism. Both the Lagrangian and the Eulerian descriptions of the postulated Lagrangian function are f...

Self-similar solutions‎ ‎of the Riemann problem for two-dimensional systems of conservation‎ ‎laws

In this paper, a new approach is applied to study the self-similar solutions of 2×2 systems of nonlinear hyperbolic conservation laws. A notion of characteristic directions is introduced and then used to construct local and smooth solutions of the associated Riemann problem

2d Elastodynamics of an Interface Crack

The rapid development of different areas of engineering, creation of new structures make the computational fracture mechanics a topic area. Among the most important applied problems there are structural strength problems, complicated by various flaws (cracks, delaminations, etc). The presence of cracks and delaminations considerably decreases the strength and the lifetime of the composite struc...

Revisiting Batchelor’s theory of two-dimensional turbulence

Recent mathematical results have shown that a central assumption in the theory of two-dimensional turbulence proposed by Batchelor (Phys. Fluids, vol. 12, 1969, p. 233) is false. That theory, which predicts a χ2/3k−1 enstrophy spectrum in the inertial range of freely-decaying turbulence, and which has evidently been successful in describing certain aspects of numerical simulations at high Reyno...