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Simulation of strength difference in elasto‐plasticity for adhesive materials
Author(s) -
Mahnken Rolf,
Schlimmer Michael
Publication year - 2005
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.1315
Subject(s) - plasticity , tangent , torsion (gastropod) , backward euler method , finite element method , hardening (computing) , cauchy stress tensor , mathematics , materials science , structural engineering , mathematical analysis , euler equations , geometry , engineering , composite material , layer (electronics) , medicine , surgery
Experimental evidence of certain adhesive materials reveals elastic strains, plastic strains and hardening. Furthermore, a pronounced strength difference effect between tension, torsion or combined loading is observed. For simulation of these phenomena, a yield function dependent on the first and second basic invariants of the related stress tensor in the framework of elasto‐plasticity is used in this work. A plastic potential with the same mathematical structure is introduced to formulate the evolution equation for the inelastic strains. Furthermore, thermodynamic consistency of the model equations is considered, thus rendering some restrictions on the material parameters. For evolution of the strain like internal variable, two cases are considered, and the consequences on the thermodynamic consistency and the numerical implementation are extensively discussed. The resulting evolution equations are integrated with an implicit Euler scheme. In particular, the reduction of the resulting local problem is performed, and for the finite‐element equilibrium iteration, the algorithmic tangent operator is derived. Two examples are presented. The first example demonstrates the capability of the model equations to simulate the yield strength difference between tension and torsion for the adhesive material Betamate 1496. A second example investigates the deformation evolution of a compact tension specimen with an adhesive zone. Copyright © 2005 John Wiley & Sons, Ltd.