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On the variationally consistent modeling of material failure
Author(s) -
Mosler Jörn
Publication year - 2010
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201010148
Subject(s) - dissipation , jump , traction (geology) , shear (geology) , state variable , work (physics) , material failure theory , statistical physics , mathematics , computer science , materials science , physics , thermodynamics , engineering , mechanical engineering , composite material , quantum mechanics , finite element method
Abstract Material failure associated with cracks or shear bands is frequently analyzed by utilizing so‐called cohesive models . Such models are based on traction‐separation laws. Within such approaches, the stress vector of the considered crack or shear band is related to its conjugate variable being the respective displacement jump (such as the material separation or the crack opening). In the present work, a framework suitable for the analysis of shear bands is discussed. All models belonging to that framework are consistently derived from thermodynamical principles. Hence, the second law of thermodynamics is automatically fulfilled. Furthermore, a variational principle strongly relying on the postulate of maximum dissipation is elaborated leading finally to a variationally consistent implementation. More precisely, all state variables, together with the unknown deformation mapping, follow naturally from minimizing an incrementally defined potential within the presented algorithmic formulation. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)