238 citations · 611 across the 32 of their papers we have counts for
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A non-ellipticity result, or the impossible taming of the logarithmic strain measure
Robert J. Martin, Ionel-Dumitrel Ghiba, Patrizio Neff
The logarithmic strain measures , where is the principal matrix logarithm of the stretch tensor corresponding to the deformation grad…
Rank-one convexity implies polyconvexity in isotropic planar incompressible elasticity
Ionel-Dumitrel Ghiba, Robert J. Martin, Patrizio Neff
We study convexity properties of energy functions in plane nonlinear elasticity of incompressible materials and show that rank-one convexity of an objective and isotropic elastic e…
An ellipticity domain for the distortional Hencky-logarithmic strain energy
Ionel-Dumitrel Ghiba, Patrizio Neff, Robert J. Martin
We describe ellipticity domains for the isochoric elastic energy $ F\mapsto \|{\rm dev}_n\log U\|^2=\bigg\|\log \frac{\sqrt{F^TF}}{(\det F)^{1/n}}\bigg\|^2 =\frac{1}{4}\,\bigg\|\lo…
The exponentiated Hencky-logarithmic strain energy. Part II: Coercivity, planar polyconvexity and existence of minimizers
Patrizio Neff, Johannes Lankeit, Ionel-Dumitrel Ghiba +2
We consider a family of isotropic volumetric-isochoric decoupled strain energies $$ F\mapsto W_{\rm eH}(F):=\widehat{W}_{\rm eH}(U):=\left\{\begin{array}{lll} \fracμ{k}\,e^{k\,\|{\…
A Riemannian approach to strain measures in nonlinear elasticity
Patrizio Neff, Bernhard Eidel, Frank Osterbrink +1
The isotropic Hencky strain energy appears naturally as a distance measure of the deformation gradient to the set SO(n) of rigid rotations in the canonical left-invariant Riemannia…