238 citations · 611 across the 32 of their papers we have counts for
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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…
Rank-one convexity implies polyconvexity for isotropic, objective and isochoric elastic energies in the two-dimensional case
Robert J. Martin, Ionel-Dumitrel Ghiba, Patrizio Neff
We show that in the two-dimensional case, every objective, isotropic and isochoric energy function which is rank-one convex on is already polyconvex on $\mathrm{…
Geometry of logarithmic strain measures in solid mechanics
Patrizio Neff, Bernhard Eidel, Robert J. Martin
We consider the two logarithmic strain measures\[ω_{\rm iso}=\|\mathrm{dev}_n\log U\|=\|\mathrm{dev}_n\log \sqrt{F^TF}\|\quad\text{ and }\quad ω_{\rm vol}=|\mathrm{tr}(\log U)|=|\m…