Finite-element implementation of schapery-type constitutive theories based on an internal variable approach

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Proceedings title26th annual technical conference of the American Society for Composites 2011 : the 2nd joint US-Canada conference on composites.
Conference26th Annual Technical Conference of the American Society for Composites 2011 and the 2nd Joint US-Canada Conference on Composites, September 26-28, 2011, Montreal, QC, Canada
Pages22122224; # of pages: 13
SubjectConstitutive theory; Convergence rates; Finite difference; Finite element codes; Integral formulations; Internal variables; Loading history; Original differential equations; Quadratic convergence; Strategy use; Time step; Differential equations; Finite difference method; Loading
AbstractThis paper presents two new strategies for implementing Schapery-type nonlinearly viscoelastic constitutive theories into Finite Element (FE) codes. The first strategy uses the original differential equations that lead to the integral formulation of Schapery-type constitutive theories and Finite Difference (FD) scheme. This strategy is quite different from all the other strategies found in the literature. The second strategy is an improvement of recursive strategies, used by many authors, based on the integral formulation of the constitutive theory. The performances of the new algorithms are compared to that of existing strategies for various loading histories and nonlinearities. It is shown that the newly developed strategy relying on FD schemes can exhibit quadratic convergence rate when one time step is stored and 4th order convergence rate when two time steps are stored, which is a major improvement over the recursive strategies.
Publication date
AffiliationNational Research Council Canada (NRC-CNRC); NRC Institute for Aerospace Research
Peer reviewedYes
NPARC number21271958
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Record identifierbead40bc-ae09-4796-ae9b-dfa6a7024405
Record created2014-05-13
Record modified2016-05-09
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