Some remarks on the monotonicity of primary matrix functions on the set of symmetric matrices

Abstract

This note contains some observations on primary matrix functions and different notions of monotonicity with relevance towards constitutive relations in nonlinear elasticity. Focussing on primary matrix functions on the set of symmetric matrices, we discuss and compare different criteria for monotonicity. The demonstrated results are particularly applicable to computations involving the true-stress-true-strain monotonicity condition, a constitutive inequality recently introduced in an Arch. Appl. Mech. article by C.S. Jog and K.D. Patil. We also clarify a statement by Jog and Patil from the same article which could be misinterpreted.

References in corpus (5)

• Geometry of logarithmic strain measures in solid mechanics
• The exponentiated Hencky-logarithmic strain energy. Part II: Coercivity, planar polyconvexity and existence of minimizers
• A Riemannian approach to strain measures in nonlinear elasticity
• The exponentiated Hencky-logarithmic strain energy. Improvement of planar polyconvexity
• The axiomatic deduction of the quadratic Hencky strain energy by Heinrich Hencky

Cited by in corpus (5)

• Geometry of logarithmic strain measures in solid mechanics
• An ellipticity domain for the distortional Hencky-logarithmic strain energy
• A non-ellipticity result, or the impossible taming of the logarithmic strain measure
• A commented translation of Hans Richter's early work "The isotropic law of elasticity"
• Commutator calculus and symbolic differentiation of matrix functions