The general relativistic theory of elasticity is reviewed from a Lagrangian, as opposed to Eulerian, perspective. equations motion and stress-energy-momentum tensor for hyperelastic body are derived the gauge-invariant action principle first considered by DeWitt. This natural extension single particle. central object in Lagrangian treatment Landau-Lifshitz radar metric, which version right Cauc...

Abstract In this paper, modelling of the superposition stress-induced and inherent anisotropy soil small strain stiffness is presented in framework hyperelasticity. A simple hyperelastic model, capable reproducing variable stiffness, extended by replacement stress invariant with mixed stress–microstructure to introduce constant cross-anisotropic component. convenient feature new model low numbe...

A plane crack is considered and the influence of local curvature front on mechanical fields studied. The main goal to determine stress intensity factors along a curved planar in linear elasticity with accuracy. This obtained by determination new test use bilinear forms, issued from invariant integrals, which separate modes fracture.

we introduce a general implicit algorithm for finding a common element of‎ ‎the set of solutions of systems of equilibrium problems and the set of common fixed points‎ ‎of a sequence of nonexpansive mappings and a continuous representation of nonexpansive mappings‎. ‎then we prove the strong convergence of the proposed implicit scheme to the unique solution of the minimization problem on the so...

Contrary to what has been often claimed in the literature, we clarify that the hard photongluon cross section ∆σ hard(x) in polarized deep inelastic scattering calculated in the gauge-invariant factorization scheme does not involve any soft contributions and hence it is genuinely hard. We show that the polarized proton structure function g 1(x) up to the next-to-leading order of αs is independe...

A flow invariant is a quantity depending only on the UV and IR conformal fixed points and not on the flow connecting them. Typically, its value is related to the central charges a and c. In classically-conformal field theories scale invariance is broken by quantum effects and the flow invariant aUV − aIR is measured by the area of the graph of the beta function between the fixed points. There e...

A bstract We find the set of generalized symmetries associated with free graviton theory in four dimensions. These are generated by gauge invariant topological operators that violate Haag duality ring-like regions. As expected from general QFT grounds, we a “electric” and dual “magnetic” compute their algebra. To do so, describe using phase space gauge-invariant electric magnetic variables cons...