Nonuniqueness for a hyperbolic system: Cavitation in nonlinear elastodynamics

On Cavitation in Elastodynamics

Motivated by the works of Ball (1982) and Pericak-Spector and Spector (1988), we investigate singular solutions of the compressible nonlinear elastodynamics equations. These singular solutions contain discontinuities in the displacement field and can be seen as describing fracture or cavitation. We explore a definition of singular solution via approximating sequences of smooth functions. We use...

Well-posed Quasi-linear Second-order Hyperbolic Systems with Applications to Nonlinear Elastodynamics and General Relativity

Nonlinear manifold learning for model reduction in finite elastodynamics

Model reduction in computational mechanics is generally addressed with linear dimensionality reduction methods such as Principal Components Analysis (PCA). Hypothesizing that in many applications of interest the essential dynamics evolve on a nonlinear manifold, we explore here reduced order modeling based on nonlinear dimensionality reduction methods. Such methods are gaining popularity in div...

Isogeometric Analysis Applied to Nonlinear Elastodynamics

A numerical investigation is carried out in this work in order to evaluate the computational performance of a numerical model based on isogeometric analysis for applications on geometrically nonlinear elastodynamics. In the FEM (finite element method) practice, it is well known that the Newmark’s method is unconditionally stable for linear structural systems, but this characteristic is frequent...

On the Nonuniqueness of Balanced Nonlinear Realizations

The notion of balanced realizations for nonlinear state space model reduction problems was first introduced by Scherpen in 1993. Analogous to the linear case, the so called singular valuefunctions of a system describe the relative importance of each state component from an input-output point of view. In this paper it is shown that the procedure for nonlinear balancing has some interesting ambig...