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

摘要

This note contains some observations on primary matrix functions anddifferent notions of monotonicity with relevance towards constitutive relationsin nonlinear elasticity. Focussing on primary matrix functions on the set ofsymmetric matrices, we discuss and compare different criteria for monotonicity.The demonstrated results are particularly applicable to computations involvingthe true-stress-true-strain monotonicity condition, a constitutive inequalityrecently 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 couldbe misinterpreted.