关于对称矩阵集合上初等矩阵函数单调性的若干评注
Some remarks on the monotonicity of primary matrix functions on the set of symmetric matrices
AI总结：
本文研究对称矩阵集合上初等矩阵函数的多种单调性判据，并将结果用于澄清非线性弹性中真应力-真应变单调性条件的相关表述。
摘要：
本札记包含关于初等矩阵函数以及与非线性弹性本构关系相关的不同单调性概念的若干观察。我们聚焦于对称矩阵集合上的初等矩阵函数，讨论并比较了单调性的不同判据。所展示的结果尤其适用于涉及真应力-真应变单调性条件的计算，该本构不等式最近由 C.S. Jog 和 K.D. Patil 在一篇发表于《Arch. Appl. Mech.》的论文中提出。我们还澄清了同一篇论文中 Jog 和 Patil 的一个可能被误解的陈述。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
