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CivilComp Proceedings
ISSN 17593433 CCP: 93
PROCEEDINGS OF THE TENTH INTERNATIONAL CONFERENCE ON COMPUTATIONAL STRUCTURES TECHNOLOGY Edited by:
Paper 267
Progress in the Formulation of Finite Elements with Embedded Discontinuities to Model Failure in Solids F. Armero and J. Kim
Department of Civil and Environmental Engineering, University of California at Berkeley, United States of America F. Armero, J. Kim, "Progress in the Formulation of Finite Elements with Embedded Discontinuities to Model Failure in Solids", in , (Editors), "Proceedings of the Tenth International Conference on Computational Structures Technology", CivilComp Press, Stirlingshire, UK, Paper 267, 2010. doi:10.4203/ccp.93.267
Keywords: failure and fracture, finite elements, strong discontinuities.
Summary
The lack of smoothness of the solutions involved when modeling failure in solids
leads to difficult and challenging problems as it regards both its theoretical
modeling and its numerical resolution.
This nonsmoothness is reflected by the formation of narrow zones where the strain
is localized (e.g. shear bands) and its limit case consisting of discontinuous
displacements (e.g. cracks), the socalled strong discontinuities.
It is precisely a multiscale treatment of these solutions that allows its
efficient inclusion in general continuum problem and their sharp and efficient
numerical resolution through finite elements with embedded discontinuities.
The multiscale framework developed in this work consists of the standard continuum
mechanical problem as the largescale problem
(possibly considering other physical effects like thermal or porous
fluid flow
couplings and/or based on classical structural theories of beams, plates and shells
rather than the continuum), with the discontinuities
introduced locally in the small scales with a localized model (e.g. cohesive law)
capturing the localized dissipative effects that lead the system to failure.
These ideas lead naturally to the enhancement of the finite elements crossed
by the discontinuity (e.g. crack) by local fields that are eliminated at the
element level through their static condensation, thus resulting in computationally very efficient
numerical techniques that can be easily incorporated in an existing general finite element
code.
We have recently proposed a general strategy for the development of these finite element enhancements, namely, rather that trying to develop local interpolations of discontinuous displacement fields at the element level, the strains are enhanced through the proper modes capturing the separation of the element by the discontinuity. This strategy automatically considers the kinematics of the underlying element (triangular or quadrilateral, basic displacement, mixed or assumed strain formulations), hence leading to enhanced elements avoiding the socalled stress locking by which spurious transfers of stresses lead to an overstiff resolution of the kinematics of the discontinuity. Following these ideas we have already developed new plane quadrilateral finite elements capturing single discontinuities in the infinitesimal and the finite deformation ranges [1,2], as well as several discontinuities branches as needed in the modeling of crack branching in dynamic fracture [3,4]. We focus in this contribution on the development of new threedimensional brick elements, constructing and analyzing the separation modes in this general threedimensional setting. We discuss the details of the propagation and representation of the discontinuity surfaces as well as the numerical integration and other implementation issues that appear in this setting. Several representative numerical simulations are presented to illustrate the use and performance of the newly developed finite element methods. References
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