Strain stiffening of protein networks is explored by means of a finite strain analysis of a two-dimensional network model of cross-linked semiflexible filaments. The results show that stiffening is caused by non-affine network rearrangements that govern a transition from a bending dominated response at small strains to a stretching dominated response at large strains. Thermally-induced filament undulations only have a minor effect; they merely postpone the transition.

A three-dimensional discrete dislocation dynamics plasticity model is presented. The approach allows realistic boundary conditions on the specimen, as both stress and displacement fields of the dislocations are incorporated in the formulation. Emphasis is placed on various technical details in the formulation as well as on the implementation. The current implementation includes features necessary to model conservative motion of dislocations in presence of surfaces. These include details of the discretization of the evolving dislocation structure, the handling of junction formation and destruction, cross-slip and boundary conditions. Special attention is given to the treatment of dislocations that partly glide out of the material, including the treatment of image forces via the finite-element method.

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Comparison of discrete dislocation and continuum plasticity predictions for a composite material Cleveringa, H.H.M.; van der Giessen, E.; Needleman, A. Take-down policy If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim.Downloaded from the University of Groningen/UMCG research database (Pure): http://www.rug.nl/research/portal. For technical reasons the number of authors shown on this cover page is limited to 10 maximum. Download date: 11-04-2019Acfcr maf~r. Vol. 45, No. 8, pp. 3163.-3179, 1997 G (Received 8 October 1996; accepted 18 December 1996) Abstract-A two-dimensional model composite with elastic reinforcements in a crystalline matrix subject to macroscopic shear is analyzed using both discrete dislocation plasticity and conventional continuum slip crystal plasticity. In the discrete dislocation formulation, the dislocations are modeled as line defects in a linear elastic medium. At each stage of loading, superposition is used to represent the solution in terms of the infinite medium solution for the discrete dislocations and a complimentary solution that enforces the boundary conditions, which is non-singular and obtained from a linear elastic, finite element solution. The lattice resistance to dislocation motion, dislocation nucleation, and dislocation annihilation are incorporated into the formulation through a set of constitutive rules. Obstacles leading to possible dislocation pile-ups are also accounted for. Results are presented for materials with a single slip system. A reinforcement size effect is exhibited by the discrete dislocation-based analysis whereas the continuum slip results are size independent. The discrete dislocation results have higher average reinforcement stress levels than do the corresponding continuum slip calculations. Averaging of stress fields over windows of increasing size is used to gain insight into the transition from discrete dislocation-controlled to continuum behavior. IQ 1997 Acta Metallurgica Inc.1997 Acta Metallurgica Inc. Published by Elsevier Science Ltd. All rrghts reserved Printed in Great Britain PII: S1359-6454(97)00011-6 1359

A discrete dislocation analysis of mode I crack growth Cleveringa, H.H.M.; van der Giessen, E.; Needleman, A. Take-down policy If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim.Downloaded from the University of Groningen/UMCG research database (Pure): http://www.rug.nl/research/portal. For technical reasons the number of authors shown on this cover page is limited to 10 maximum. AbstractSmall scale yielding around a plane strain mode I crack is analyzed using discrete dislocation dynamics. The dislocations are all of edge character, and are modeled as line singularities in an elastic material. At each stage of loading, superposition is used to represent the solution in terms of solutions for edge dislocations in a half-space and a complementary solution that enforces the boundary conditions. The latter is non-singular and obtained from a ®nite element solution. The lattice resistance to dislocation motion, dislocation nucleation, dislocation interaction with obstacles and dislocation annihilation are incorporated into the formulation through a set of constitutive rules. A relation between the opening traction and the displacement jump across a cohesive surface ahead of the initial crack tip is also speci®ed, so that crack growth emerges naturally from the boundary value problem solution. Material parameters representative of aluminum are employed. For a low density of dislocation sources, crack growth takes place in a brittle manner; for a low density of obstacles, the crack blunts continuously and does not grow. In the intermediate regime, the average near-tip stress ®elds are in qualitative accord with those predicted by classical continuum crystal plasticity, but with the local stress concentrations from discrete dislocations leading to opening stresses of the magnitude of the cohesive strength. The crack growth history is strongly aected by the dislocation activity in the vicinity of the growing crack tip. #