Multi-Monotonic Constitutive Networks

The purpose of this paper is to present to structural and material engineers a set of recently developed  constitutive tools that give considerable insight into the performance of their materials.  Most, if not all materials, have simple internal structures. Each structure behaves in a monotonic fashion when subjected to stress and strain. Examples of these monotonic responses in some material structures are given.  The Richard-Blacklock constitutive relationship is monotonic. It is modified to use the ultimate stress and strain point and eliminate the asymptotic stress. This change makes it simultaneously applicable to softening and hardening responses, meaning that it becomes invertible and symmetric in stress and unidirectional strain.  A general nonlinear multi-monotonic invertible symmetric system-equation is obtained by using series and parallel spring circuits.  An example is given of a complex stress-strain response that is decomposed into its monotonic constituents.  One of the monotonic constituents is an unwanted test artifact and is removed.  The specific case of linear constituents is discussed and an example is given.

Exactly how the general system works and how to select the appropriate combination for a given stress-strain response is discussed.  Furthermore, how each monotonic type affects unloading behavior is discussed and an example is given.  Next, a relationship between monotonic type and time dependency is conjectured.  A simple modification yields a time asymptote for creep rupture.  A relationship between applied stress and rupture time is proposed, and from that equation, a relationship for residual strength as a function of time, temperature, and load is obtained.  Finally, a general relationship for time dependency is derived and an example is given.  The developed techniques provide the engineer with concepts and tools to better understand material response in loading, unloading, and time dependent situations.