Korn's second inequality and geometric rigidity with mixed growth conditions

Geometric rigidity states that a gradient field which is $L^p$-close to the set of proper rotations is necessarily $L^p$-close to a fixed rotation, and is one key estimate in nonlinear elasticity. In several applications, as for example in the theory of plasticity, energy densities with mixed growth appear. We show here that geometric rigidity holds also in $L^p+L^q$ and in $L^{p,q}$ interpolation spaces. As a first step we prove the corresponding linear inequality, which generalizes Korn's inequality to these spaces

Investigation of sandwich material surface created by abrasive water jet (AWJ) via vibration emission

The paper presents research a of abrasive waterjet cutting of heterogeneous “sandwich“ material with different Young modulus of elasticity of the cutted surface geometry by means of vibration emission. In order to confirm hypothetical assumptions about direct relation between vibration emission and surface quality an experiment in heterogeneous material consisting of stainless steel (DIN 1.4006 / AISI 410) and alloy AlCuMg2 has been provided

Eigenvalue problems associated with Korn's inequalities

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46189/1/205_2004_Article_BF00251798.pd