Equivalent-Network Representations of the Generalized Hooke's Law for Isotropic Materials

摘要

It is shown that the generalized Hooke's law - the constitutive relation for all solid materials that behave mechanically in a linear fashion - defines the topology of equivalent networks analogous to such solids insofar as mechanical behavior is concerned. Two equivalent networks are reported, one representing each of the two forms in which Hooke's law is usually expressed. Each analog is a six-port network that can be decomposed into a pair of independent three-port networks. One three-port network in each pair reflects the extensional behavior of a material and one its distortional behavior. Elastic moduli and compliances appear as immittances in the networks. Since network topology is determined only by the analytic can be mathematical entities more general than complex quantities. Some results from linear elasticity theory are interpreted using the analog networks, and their application in describing the viscoelastic behavior of materials is considered briefly. The analysis pertains principally to homogeneous isotropic materials.