Robert Martin - Publications

Publications in peer-reviewed journals

Robert J. Martin, Jendrik Voss, Ionel-Dumitrel Ghiba, Oliver Sander, Patrizio Neff
The quasiconvex envelope of conformally invariant planar energy functions in isotropic hyperelasticity
Journal of Nonlinear Science; 2020, 30(6), pp. 2885-2923
arXiv: 1901.00058 pdf

Patrizio Neff, Kai Graban, Eva Schweickert, Robert J. Martin
The axiomatic introduction of arbitrary strain tensors by Hans Richter - a commented translation of “Strain tensor, strain deviator and stress tensor for finite deformations”
Mathematics and Mechanics of Solids; 2020, Vol.  25 (5), pp. 1060-1080
arXiv: 1909.05998 pdf

Eva Schweickert, L. Angela Mihai, Robert J. Martin,  Patrizio Neff
A note on non-homogeneous deformation with homogeneous Cauchy stress for a strictly rank-one convex energy in isotropic hyperelasticity
International Journal of Non-Linear Mechanics; 2020, Vol. 119, 103282
abstract arXiv: 1904.11358

Jendrik Voss, Herbert Baaser, Robert J. Martin, Patrizio Neff
More on anti-plane shear
Journal of Optimization Theory and Applications, 2020, Vol. 184 (1), pp. 226-249
abstract
arXiv: 1802.00265 pdf

Mircea Birsan, Ionel-Dumitrel Ghiba, Robert J. Martin, Patrizio Neff
Refined dimensional reduction for isotropic elastic Cosserat shells with initial curvature
Mathematics and Mechanics of solids; 2019, Vol. 24(12), pp. 4000-4019
abstract  arXiv: 1909.12585

Robert J. Martin, Jendrik Voss, Ionel-Dumitrel Ghiba, Patrizio Neff
Quasiconvex relaxation of isotropic functions in incompressible planar hyperelasticity
Proceedings of the Royal Society of Edinburgh Section A Mathematics; (2020) Vol. 150(5), pp. 2620-2631
abstract arXiv: 1903.00508 pdf

Kai Graban, Eva Schweickert, Robert J. Martin, Patrizio Neff
A commented translation of Hans Richter's early work "The isotropic law of elasticity"
Mathematics and Mechanics of solids; 2019, Vol. 24(8), pp. 2649-2660
abstract arXiv: 1904.05164 pdf

Christian Thiel, Jendrik Voss, Robert J. Martin, Patrizio Neff
Shear, pure and simple
International Journal of Non-Linear Mechanics; 2019, Vol. 112, pp. 57-72
abstract arXiv: 1806.07749pdf

Christian Thiel, Jendrik Voss, Robert J. Martin, Patrizio Neff
Do we need Truedell's empirical inequalities? On the coaxiality of stress and stretch
International Journal of Non-Linear Mechanics; 2019, Vol.112, pp. 106-116
abstract  arXiv: 1812.03053 pdf

Robert J. Martin, Ionel-Dumitrel Ghiba, Patrizio Neff
A polyconvex extension of the logarithmic Hencky strain energy
Analysis and Application; 2019, Vol. 17 (3), pp. 349-361
arXiv: 1712.08864 abstract 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; 2018, Vol. 62 (4), pp. 635-654
arXiv:1705.08381abstract 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
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
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

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

 

Other publications

Robert J. Martin, Ingo Münch, Bernhard Eidel, Patrizio Neff
A brief history of logarithmic strain measures in nonlinear elasticity
PAMM: Proceedings in Applied Mathematics and Mechanics; 2018, Vol.18 (1) Special issue: 89th Annual Meeting of the International Association of Applied Mathematics and Mechanics  
abstract 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
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

 

Posters

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 2016 Poster

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

 

PD Dr. rer. nat. habil. Robert Martin

Tel. +49(0)/379-3461 (Duisburg)
robert.martin@uni-due.de

Room WSC-S-4.09 (Essen)
Room ST110 (Duisburg)

Robert Martin

Contact

Universität Duisburg-Essen
Fakultät für Mathematik
Mathematik-Carrée
Thea-Leymann-Straße 9
45127 Essen

 

Office hours

by appointment only