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An interpretation of initial stress and strain methods, and numerical stability
Author(s) -
Stolle Dieter F. E.
Publication year - 1991
Publication title -
international journal for numerical and analytical methods in geomechanics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.419
H-Index - 91
eISSN - 1096-9853
pISSN - 0363-9061
DOI - 10.1002/nag.1610150604
Subject(s) - viscoplasticity , stability (learning theory) , mathematics , plasticity , constitutive equation , matrix (chemical analysis) , simple (philosophy) , finite element method , computer science , structural engineering , materials science , engineering , composite material , philosophy , epistemology , machine learning
This paper explores similarities and differences between initial stress and initial strain methods of analyses. The author takes the position that both methods, although perhaps conceptually different, are actually numerically the same. A simple approach for providing closed‐form stability criteria for explicit and implicit time‐marching procedures is described. For the case of associated, non‐hardening viscoplasticity the approach provides criteria which are identical to those of Cormeau for explicit schemes. An implicit time‐marching scheme which avoids the compliance matrix inversions at the constitutive level is also presented. Like many other implicit methods, this implicit time‐marching scheme is unconditionally stable for θ≥½. The connection between initial strain plasticity and an explicit viscoplastic time‐marching scheme is also addressed.