Interpretation of X-ray Powder Diffraction Patterns . By H. Lipson and H. Steeple. Pp. viii + 335 + 3 plates. (Mac-millan: London; St Martins Press: New York, May 1970.) £4.

X-Ray Diffraction

An overview of the extended/generalized finite element method (GEFM/XFEM) with emphasis on methodological issues is presented. This method enables the accurate approximation of solutions that involve jumps, kinks, singularities, and other locally non-smooth features within elements. This is achieved by enriching the polynomial approximation space of the classical finite element method. The GEFM/XFEM has shown its potential in a variety of applications that involve non-smooth solutions near interfaces: Among them are the simulation of cracks, shear bands, dislocations, solidification, and multi-field problems. Copyright © 2010 John Wiley & Sons, Ltd.

The extended/generalized finite element method: An overview of the method and its applications

The cohesive zone model: advantages, limitations and challenges

Unperturbed dimensions of stereoregular polymers.- Reinforcement of rubber by carbon black.- Transformations of phenolic antioxidants and the role of their products in the long-term properties of polyolefins.

Properties of polymers

The extended and generalized finite element methods are reviewed with an emphasis on their applications to problems in material science: (1) fracture, (2) dislocations, (3) grain boundaries and (4) phases interfaces. These methods facilitate the modeling of complicated geometries and the evolution of such geometries, particularly when combined with level set methods, as for example in the simulation growing cracks or moving phase interfaces. The state of the art for these problems is described along with the history of developments.

/pdf/a-review-of-extended-generalized-finite-element-methods-for-1uqjazt5n2.pdf

A review of extended/generalized finite element methods for material modeling

T hree-dimensional molecular network theories are studied which use a non-Gaussian statistical mechanics model for the large strain extension of molecules. Invoking an affine deformation assumption, the evolution of the network — consisting of a large number of molecular chains per unit volume, which are initially randomly oriented in space — is shown to be governed by a balance equation in orientation space. Eulerian and Lagrangian type formulations of these balance equations are given, and the closed-form analytical solution for the so-called Chain Orientation Distribution Function is derived. This full network model is then used to describe the large strain inelastic behaviour of rubber-like materials. Detailed comparisons with experimental results and with two approximate models, namely the classical three-chain model and a very recently proposed eight-chain model, are provided for different types of deformation and rubbers. Finally, the network model is applied to describe the orientational hardening in amorphous glassy polymers, and confronted with experimental data for polycarbonate. The inherent physical limitations of the network theory for both applications are discussed.

On Improved Network Models for Rubber Elasticity and Their Applications to Orientation Hardening in Glassy Polymers

A two-dimensional nonlocal version of continuum crystal plasticity theory is proposed, which is based on a statistical-mechanics description of the collective behavior of dislocations coupled to standard small-strain crystal continuum kinematics for single slip. It involves a set of transport equations for the total dislocation density field and for the net-Burgers vector density field, which include a slip system back stress associated to the gradient of the net-Burgers vector density. The theory is applied to the problem of shearing of a two-dimensional composite material with elastic reinforcements in a crystalline matrix. The results are compared to those of discrete dislocation simulations of the same problem. The continuum theory is shown to be able to pick up the distinct dependence on the size of the reinforcing particles for one of the morphologies being studied. Also, its predictions are consistent with the discrete dislocation results during unloading, showing a pronounced Bauschinger effect. None of these features are captured by standard local plasticity theories.

https://pure.rug.nl/ws/files/6676754/2004JMechPhysSolYefimov.pdf

A comparison of a statistical-mechanics based plasticity model with discrete dislocation plasticity calculations

SUMMARY We present a Generalized Finite Element Method for the analysis of polycrystals with explicit treatment of grain boundaries. Grain boundaries and junctions, understood as loci of possible displacement discontinuity, are inserted into finite elements by exploiting the partition of unity property of finite element shape functions. Consequently, the finite element mesh does not need to conform to the polycrystal topology. The formulation is outlined and a numerical example is presented to demonstrate the potential and accuracy of the approach. The proposed methodology can also be used for branched and intersecting cohesive cracks, and comparisons are made to a related approach (Int. J. Numer. Meth. Engng. 2000; 48:1741). Copyright 2006 John Wiley & Sons, Ltd.

/pdf/a-generalized-finite-element-method-for-polycrystals-with-4jcl425e7q.pdf

A Generalized Finite Element Method for polycrystals with discontinuous grain boundaries

https://pure.rug.nl/ws/files/3629647/2000MechMaterTijssens.pdf

Modeling of crazing using a cohesive surface methodology

http://www-mech.eng.cam.ac.uk/profiles/vsd/papers/acta_short.pdf

E. van der Giessen

Papers

On Improved Network Models for Rubber Elasticity and Their Applications to Orientation Hardening in Glassy Polymers

A comparison of a statistical-mechanics based plasticity model with discrete dislocation plasticity calculations

A Generalized Finite Element Method for polycrystals with discontinuous grain boundaries

Modeling of crazing using a cohesive surface methodology

Discrete dislocation plasticity modeling of short cracks in single crystals