Dr. rer. nat. Robert Martin

Forschungsinteressen

  • Angewandte Mathematik mit Bezug zu Ingenieurwissenschaften
  • Elastizitätstheorie
  • Konstitutive Ungleichungen
  • Geodäten auf Lie-Gruppen

 

Publikationen in referierten Fachzeitschriften

Christian Thiel, Jendrik Voss, Robert J. Martin, Patrizio Neff
Shear, pure and simple
To appear in International Journal of Non-Linear Mechanics
arXiv: 1806.07749pdf

Jendrik Voss, Herbert Baaser, Robert J. Martin, Patrizio Neff
Again anti-plane shear
To appear in Journal of Optimization Theory and Applications
arXiv: 1802.00265 pdf

Ionel-Dumitrel Ghiba, Robert J. Martin, Patrizio Neff
Rank-one convexity implies polyconvexity in isotropic planar incompressible elasticity
Journal de Mathématiques Pures et Appliquées; 2018 Vol. 116, pp. 88-104; DOI: 10.1016/j.matpur.2018.06.009;
arXiv:1609.01339v1 pdf

Robert J. Martin, Ionel-Dumitrel Ghiba, Patrizio Neff
A non-ellipticity result, or the impossible taming of the logarithmic strain measure
International Journal of Non-Linear Mechanics; 2018 Vol. 102, pp. 147-158
arXiv: 1712.04846pdf

Robert J. Martin, Ionel-Dumitrel Ghiba, Patrizio Neff
A polyconvex extension of the logarithmic Hencky strain energy
Analysis and Application; 2017, online first: DOI: 10.1142/S0219530518500173
arXiv: 1712.08864 pdf

Boumediene Nedjar, Herber Baaser, Robert J. Martin, Patrizio Neff
A finite element implementation of the isotropic exponentiated Hencky-logarithmic model and simulation of the eversion of elastic tubes
Computational Mechanics; 2017, online first; DOI:10.1007/s00466-017-1518-9
arXiv:1705.08381 pdf

Robert J. Martin, Ionel-Dumitrel Ghiba, Patrizio Neff
Rank-one convexity implies polyconvexity for isotropic, objective and isochoric elastic energies in the two-dimensional case
Proceedings of the Royal Society of Edinburgh Section A; 2017, Vol. 147 (3), pp. 571-597
arXiv:1507.00266pdf

Patrizio Neff, Ingo Münch, Robert J. Martin
Rediscovering GF Becker's early axiomatic deduction of a multiaxial nonlinear stress-strain relation based on logarithmic strain
Math. Mech. Solids; 2016 Vol. 21, No. 7, pp. 856–911
arXiv: 1403.4675  pdf

Robert J. Martin, Patrizio Neff
Minimal geodesics on GL(n) for left-invariant, right-O(n)-invariant Riemannian metrics
The Journal of Geometric Mechanics; 2016 Vol. 3, pp. 323-357
arXiv:1409.7849 pdf

Patrizio Neff, Bernhard Eidel, Robert J. Martin
Geometry of logarithmic strain measures in solid mechanics
Archive for Rational Mechanics and Analysis; 2016 Vol. 222, pp. 507-572
arXiv:1505.02203 pdf

Patrizio Neff, Ingo Münch, Robert J. Martin
Rediscovering G.F. Becker's early axiomatic deduction of a multiaxial nonlinear stress-strain relation based on logarithmic strain
Mathematics and Mechanics of Solids; 2016 Vol. 21 (7), pp. 856-911
arXiv:1403.4675   abstract  pdf

Ionel-Dumitrel Ghiba, Patrizio Neff, Robert J. Martin
An ellipticity domain for the distortional Hencky logarithmic strain energy
Proceedings A of the Royal Society; 2015 Vol. 471(2184)
arXiv:1507.07388 abstract pdf

Patrizio Neff, Johannes Lankeit, Ionel-Dumitrel Ghiba, Robert J. Martin, David Steigmann
The exponentiated Hencky-logarithmic strain energy. Part II: Coercivity, planar polyconvexity and existence of minimizers
Zeitschrift für angewandte Mathematik und Physik; 2015 Vol. 66(4), pp.1671-1693
arXiv:1408.4430 abstract pdf

Robert J. Martin, Patrizio Neff
Some remarks on the monotonicity of primary matrix functions on the set of symmetric matrices
Archive of Applied Mechanics; 2015 Vol. 85 (12), pp.1761-1778
arXiv:1409.7847 abstract  pdf

Patrizio Neff, Bernhard Eidel, Frank Osterbrink, Robert J. Martin
A Riemannian approach to strain measures in nonlinear elasticity
Comptes Rendus Mécanique; 2014 Volume 342(4), pp. 254–257
arXiv:1305.2393 abstract  pdf

 

Sonstige Publikationen

Robert J. Martin, Ionel-Dumitrel Ghiba, Patrizio Neff
Rank-one convexity implies polyconvexity for isotropic, objective and isochoric elastic energies in the two-dimensional case
PAMM: Proceedings in Applied Mathematics and Mechanics; October 2016, Vol. 16 (1), pp. 659–660
arXiv:1507.00266pdf

Robert J. Martin, Ionel-Dumitrel Ghiba, Patrizio Neff
Rank-one convexity implies polyconvexity for isotropic, objective and isochoric elastic energies in the two-dimensional case
PAMM: Proceedings in Applied Mathematics am Mechanics; 2016 Vol. 16, pp. 659-660
arXiv:1507.00266 pdf

Patrizio Neff, Robert J. Martin, Bernhard Eidel
New thoughts in Nonlinear Elasticity Theory via Hencky’s logarithmic strain tensor
Chapter in book: Mathematical Modelling in Solid Mechanics, pp.165-180
pdf

Ionel-Dumitrel Ghiba, Patrizo Neff, Robert J. Martin
Loss of ellipticity in additive logarithmic finite strain plasticity and related results on Hencky-type energies
PAMM: Proceedings in Applied Mathematics and Mechanics; 2016 Vol. 16 (1), pp. 341-342
pdf

Patrizo Neff, Ionel-Dumitrel Ghiba, Johannes Lankeit, Robert J. Martin
Rank-one convexity and polyconvexity of Hencky-type energies
PAMM: Proceedings in Applied Mathematics and Mechanics; 2014 Vol. 14 (1), pp. 735-736
pdf

Patrizio Neff, Frank Osterbrink, Robert J. Martin
The Hencky strain energy |log U|² measures the geodesic distance of the deformation gradient to SO(n) in the canonical left-invariant Riemannian metric on GL(n)
PAMM, Proceedings in Applied Mathematics and Mechanics; 2013 Vol. 13(1), pp. 369–370
abstract pdf

Patrizio Neff, Bernhard Eidel, Robert J. Martin
The axiomatic deduction of the quadratic Hencky strain energy by Heinrich Hencky
arXiv:1402.4027 pdf

 

Poster

Jendrik Voss, Christian Thiel, Robert J. Martin, Patrizio Neff
Shear in nonlinear elasticity
July 2018 Poster

Jendrik Voss, Robert J. Martin, Herbert Baaser, Patrizio Neff
Anti-plane shear in nonlinear elasticity
February 2018 Poster

Robert J. Martin, Ionel-Dumitrel Ghiba, Patrizio Neff
A Polyconvex extension of the logarithmic Hencky strain energy
January 2018 Poster

Ionel-Dumitrel Ghiba, Robert J. Martin, Patrizio Neff
Rank-one convexitiy implies polyconvexity for isotropic energies on SL(2)
September 2016 Poster

Patrizio Neff, Robert J. Martin, Ingo Münch, Bernhard Eidel
A brief history of logarithmic strain measures in nonlinear elasticity
May 2016 Poster

Patrizio Neff, Bernhard Eidel, Robert J. Martin
Geometry of logarithmic strain measures
May 2016 Poster

Patrizio Neff, Bernhard Eidel, Robert J. Martin
Strain tensors and strain measures in nonlinear elasticity
May 2015 Poster

Robert J. Martin, Ionel-Dumitrel Ghiba, Patrizio Neff
Rank-one convexity vs. polyconvexity for isochoric engergies on GL+(2)
January 2016 Poster