65 citations · 87 across the 15 of their papers we have counts for
13 papers · 1 filter
Vector and matrix monotonicity characterisation of the "load forces" in nonlinear elasticity: compressible versus incompressible response
Jendrik Voss, Ionel-Dumitrel Ghiba, Robert J. Martin +1
In this paper, we study the relation between different notions of monotonicity for isotropic hyperelastic compressible and incompressible materials. We study how to define the mono…
Monotonicity of isotropic tensor functions on the set of symmetric matrices: completing Rodney Hill's generalization of the Chandler Davis convexity theorem
Jendrik Voss, Robert J. Martin, Ionel-Dumitrel Ghiba +2
Motivated by classical constitutive inequalities in isotropic nonlinear elasticity theory, we investigate the monotonicity of isotropic tensor functions of the form \[ Σ_f\colon\ma…
Yet another best approximation isotropic elasticity tensor in plane strain
Jendrik Voss, Panos Gourgiotis, Peter Lewintan +2
For plane strain linear elasticity, given any anisotropic elasticity tensor , we determine a best approximating isotropic counterpart …
Numerical approaches for investigating quasiconvexity in the context of Morrey's conjecture
Jendrik Voss, Robert J. Martin, Oliver Sander +3
Deciding whether a given function is quasiconvex is generally a difficult task. Here, we discuss a number of numerical approaches that can be used in the search for a counterexampl…
Morrey's conjecture for the planar volumetric-isochoric split. Part I: least convex energy functions
Jendrik Voss, Robert J. Martin, Ionel-Dumitrel Ghiba +1
We consider Morrey's open question whether rank-one convexity already implies quasiconvexity in the planar case. For some specific families of energies, there are precise condition…
A rank-one convex, non-polyconvex isotropic function on with compact connected sublevel sets
Jendrik Voss, Ionel-Dumitrel Ghiba, Robert J. Martin +1
According to a 2002 theorem by Cardaliaguet and Tahraoui, an isotropic, compact and connected subset of the group of invertible matrices is ra…
Rank-one convexity vs. ellipticity for isotropic functions
Robert J. Martin, Jendrik Voss, Ionel-Dumitrel Ghiba +1
It is well known that a twice-differentiable real-valued function on the group of invertible ma…
Sharp rank-one convexity conditions in planar isotropic elasticity for the additive volumetric-isochoric split
Jendrik Voss, Ionel-Dumitrel Ghiba, Robert J. Martin +1
We consider the volumetric-isochoric split in planar isotropic hyperelasticity and give a precise analysis of rank-one convexity criteria for this case, showing that the Legendre-H…
Quasiconvex relaxation of isotropic functions in incompressible planar hyperelasticity
Robert J. Martin, Jendrik Voss, Ionel-Dumitrel Ghiba +1
In this note, we provide an explicit formula for computing the quasiconvex envelope of any real-valued function with f…
The quasiconvex envelope of conformally invariant planar energy functions in isotropic hyperelasticity
Robert J. Martin, Jendrik Voss, Ionel-Dumitrel Ghiba +2
We consider conformally invariant energies on the group of -matrices with positive determinant, i.e. $W\colon\operatorname{GL}^+(2)\to\mathbb…
Do we need Truesdell's empirical inequalities? On the coaxiality of stress and stretch
Christian Thiel, Jendrik Voss, Robert J. Martin +1
Truesdell's empirical inequalities are considered essential in various fields of nonlinear elasticity. However, they are often used merely as a sufficient criterion for semi-invert…
Shear, pure and simple
Christian Thiel, Jendrik Voss, Robert J. Martin +1
In a 2012 article in the International Journal of Non-Linear Mechanics, Destrade et al. showed that for nonlinear elastic materials satisfying Truesdell's so-called empirical inequ…
Again anti-plane shear
Jendrik Voss, Herbert Baaser, Robert J. Martin +1
We reconsider anti-plane shear deformations of the form based on prior work of Knowles and relate the existence of anti-plane shear deformations…