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Development of a curvilinear viscoelastic constitutive relationship for time dependent materials. Part B: Example problems
Author(s) -
Stephenson M. J.,
Dargush G. F.
Publication year - 2002
Publication title -
polymer engineering and science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.503
H-Index - 111
eISSN - 1548-2634
pISSN - 0032-3888
DOI - 10.1002/pen.10969
Subject(s) - curvilinear coordinates , viscoelasticity , constitutive equation , singularity , finite element method , cauchy elastic material , cauchy stress tensor , boundary value problem , traction (geology) , mechanics , mathematical analysis , materials science , stress (linguistics) , finite strain theory , classical mechanics , geometry , mathematics , structural engineering , physics , mechanical engineering , composite material , engineering , linguistics , philosophy
The boundary value problem of a two‐dimensional viscoelastic beam clamped at two ends and subjected to both a dead load and normal surface traction is solved using a finite element method here in Part B. The constitutive relationship between stress and strain developed in Part A uses a convected coordinate system and body tensor mathematics. Maxwell elements (springs and dashpots) describe the material for both fluid and solid characterizations. The overall finite element results calculated were physically reasonable. However, the assumed boundary conditions produce a stress singularity at the boundary, a singularity that is also seen in small deformation elastic theory.