NDLI: A Pian–Sumihara type element for modeling shear bands at finite deformation

Content Provider	Springer Nature Link
Author	McAuliffe, Colin Waisman, Haim
Copyright Year	2013
Abstract	A monolithic numerical solution of a partial differential equation (PDE) model for shear bands, which includes a thermal softening rate dependent plastic flow rule and finite thermal conductivity, is presented. The formulation accounts for large deformation kinematics and includes incrementally objective treatment of the hypoplastic constitutive relations. Regularization is achieved by including finite thermal conductivity, which informs the PDE system of a length scale, governed by competition between shear heating and thermal diffusion. The monolithic solution scheme is then used to eliminate splitting errors during the solution of the discretized system. The scheme is presented in a general, mixed formulation, which allows for many choices of shape functions. We study and compare two elements, which have been implemented with the monolithic nonlinear solver: the Irreducible Shear Band Quad (ISBQ) and the Pian Sumihara Shear Band Quad (PSSBQ). ISBQ employs the same interpolation as an irreducible four node quad while PSSBQ is a mixed, assumed stress element. The algorithmic approximations to the Lie derivative and Jaumann rate of Kirchhoff stress are available in the literature for ISBQ type elements, and are derived in this paper for the PSSBQ. These expressions are used to achieve an incrementally objective formulation. It is found that the PSSBQ converges faster than the ISBQ with mesh refinement, and that the convergence of the ISBQ can be improved with a remeshing procedure.
Starting Page	925
Ending Page	940
Page Count	16
File Format	PDF
ISSN	01787675
Journal	Computational Mechanics
Volume Number	53
Issue Number	5
e-ISSN	14320924
Language	English
Publisher	Springer Berlin Heidelberg
Publisher Date	2013-10-22
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Constitutive laws Shear band Instability Large deformation Theoretical and Applied Mechanics Computational Science and Engineering Classical Continuum Physics
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Ocean Engineering Computational Theory and Mathematics Mechanical Engineering Computational Mechanics Computational Mathematics

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