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Analysis of the anisotropic viscoplastic‐damage response of composite laminates—continuum basis and computational algorithms
Author(s) -
Saleeb A. F.,
Wilt T. E.
Publication year - 1993
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620361003
Subject(s) - viscoplasticity , inviscid flow , mathematics , composite laminates , constitutive equation , tangent , basis (linear algebra) , algorithm , finite element method , composite number , structural engineering , geometry , classical mechanics , physics , engineering
The mathematical structure underlying the rate equations of a recently‐developed constitutive model for the coupled viscoplastic‐damage response of anisotropic composites is critically examined. In this regard, a number of tensor projection operators have been identified, and their properties were exploited to enable the development of a general computational framework for their numerical implementation using the Euler fully‐implicit integration method. In particular, this facilitated (i) the derivation of explicit expressions of the (consistent) material tangent stiffnesses that are valid for both three‐dimensional as well as subspace (e.g. plane stress) formulations, (ii) the implications of the symmetry or unsymmetry properties of these tangent operators from a thermodynamic standpoint, and (iii) the development of an effective time‐step control strategy to ensure accuracy and convergence of the solution. In addition, the special limiting case of inviscid elastoplasticity is treated. The results of several numerical simulations are given to demonstrate the effectiveness of the schemes developed.