An interpretation of initial stress and strain methods, and numerical stability

Abstract 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.