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1. On the computational solution of vector-density based continuum dislocation dynamics models: a comparison of two plastic distortion and stress update algorithms

   https://doi.org/https://doi.org/10.1016/j.ijplas.2021.102943  

   P. Lin, V. Vivekanandan. (January 2021, International journal of plasticity)

   null (Ed.)

   Continuum dislocation dynamics models of mesoscale plasticity consist of dislocation transport-reaction equations coupled with crystal mechanics equations. The coupling between these two sets of equations is such that dislocation transport gives rise to the evolution of plastic distortion (strain), while the evolution of the latter fixes the stress from which the dislocation velocity field is found via a mobility law. Earlier solutions of these equations employed a staggered solution scheme for the two sets of equations in which the plastic distortion was updated via time integration of its rate, as found from Orowan’s law. In this work, we show that such a direct time integration scheme can suffer from accumulation of numerical errors. We introduce an alternative scheme based on field dislocation mechanics that ensures consistency between the plastic distortion and the dislocation content in the crystal. The new scheme is based on calculating the compatible and incompatible parts of the plastic distortion separately, and the incompatible part is calculated from the current dislocation density field. Stress field and dislocation transport calculations were implemented within a finite element based discretization of the governing equations, with the crystal mechanics part solved by a conventional Galerkin method and the dislocation transport equations by the least squares method. A simple test is first performed to show the accuracy of the two schemes for updating the plastic distortion, which shows that the solution method based on field dislocation mechanics is more accurate. This method then was used to simulate an austenitic steel crystal under uniaxial loading and multiple slip conditions. By considering dislocation interactions caused by junctions, a hardening rate similar to discrete dislocation dynamics simulation results was obtained. The simulations show that dislocations exhibit some self-organized structures as the strain is increased. 

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2. Strain predictions at unmeasured locations of a substructure using sparse response-only vibration measurements

   https://doi.org/10.1007/s13349-021-00476-x  

   Tchemodanova, Sofia Puerto; Sanayei, Masoud; Moaveni, Babak; Tatsis, Konstantinos; Chatzi, Eleni (June 2021, Journal of Civil Structural Health Monitoring)

   null (Ed.)

   Structural health monitoring of complex structures is often limited by restricted accessibility to locations of interest within the structure and availability of operational loads. In this work, a novel output-only virtual sensing scheme is proposed. This scheme involves the implementation of the modal expansion in an augmented Kalman filter. Performance of the proposed scheme is compared with two existing methods. Method 1 relies on a finite element model updating, batch data processing, and modal expansion (MUME) procedure. Method 2 employs a recursive sequential estimation algorithm, which feeds a substructure model of the instrumented system into an Augmented Kalman Filter (AKF). The new scheme referred to as Method 3 (ME-AKF), implements strain estimates generated via Modal Expansion into an AKF as virtual measurements. To demonstrate the applicability of the aforementioned methods, a rollercoaster connection was instrumented with accelerometers, strain rosettes, and an optical sensor. A comparison of estimated dynamic strain response at unmeasured locations using three alternative schemes is presented. Although acceleration measurements are used indirectly for model updating, the response-only methods presented in this research use only measurements from strain rosettes for strain history predictions and require no prior knowledge of input forces. Predicted strains using all methods are shown to sufficiently predict the measured strain time histories from a control location and lie within a 95% confidence interval calculated based on modal expansion equations. In addition, the proposed ME-AKF method shows improvement in strain predictions at unmeasured locations without the necessity of batch data processing. The proposed scheme shows high potential for real-time dynamic estimation of the strain and stress state of complex structures at unmeasured locations. 

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3. A discrete dislocation analysis of size-dependent plasticity in torsion

   https://doi.org/10.1016/j.jmps.2024.105709  

   Cruzado, A; Ariza, MP; Needleman, A; Ortiz, M; Benzerga, AA (September 2024, Journal of the Mechanics and Physics of Solids)

   A method for solving three dimensional discrete dislocation plasticity boundary-value problems using a monopole representation of the dislocations is presented. At each time step, the displacement, strain and stress fields in a finite body are obtained by superposition of infinite body dislocation fields and an image field that enforces the boundary conditions. The three dimensional infinite body fields are obtained by representing dislocations as being comprised of points, termed monopoles, that carry dislocation line and Burgers vector information. The image fields are obtained from a three dimensional linear elastic finite element calculation. The implementation of the coupling of the monopole representation with the finite element method, including the interaction of curved dislocations with free surfaces, is presented in some detail because it differs significantly from an implementation with a line based dislocation representation. Numerical convergence and the modeling of dislocation loop nucleation for large scale computations are investigated. The monopole discrete dislocation plasticity framework is used to investigate the effect of size and initial dislocation density on the torsion of wires with diameters varying over three orders of magnitude. Depending on the initial dislocation source density and the wire diameter, three regimes of torsion–twist response are obtained: (i) for wires with a sufficiently small diameter, plastic deformation is nucleation controlled and is strongly size dependent; (ii) for wires with larger diameters dislocation plasticity is dislocation interaction controlled, with the emergence of geometrically necessary dislocations and dislocation pile-ups playing a key role, and is strongly size dependent; and (iii) for wires with sufficiently large diameters plastic deformation becomes less heterogeneous and the dependence on size is greatly diminished. 

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4. Computational 3-dimensional dislocation elastodynamics

   https://doi.org/10.1016/j.jmps.2019.02.008  

   Cui, Yinan; Po, Giacomo; Pellegrini, Yves-Patrick; Lazar, Markus; Ghoniem, Nasr (February 2019, Journal of the mechanics and physics of solids)

   Understanding the mechanical behavior of solids at extremely high strain rates is of great scientific and technical interest. Current dislocation-based model of plasticity are typically implemented as quasi-static method. Their applicability to high strain rate condition is limited, because the influence of the elastodynamic stress field at extreme strain rates on the collective behavior of 3-dimensional (3D) dislocations is not clear, and the time-dependent nature is very important when the strain rate is higher than 1e6 /s (e.g. laser shock loading). To overcome this limitation, we present here the first computational procedure for 3D discrete dislocation elastodynamics (DDE). A novel computational method is developed for calculations of the fully-resolved elastodynamic field of non-uniformly moving dislocation loops. The developed method here extends the technique of retarded potentials, which was originally used to describe the electrodynamics of charged particles moving near the speed of light. Comparison with independent 2D calculations establish the accuracy and convergence of the numerical scheme. It is shown that dislocation loop motion near the sound speed results in significant restructuring of the emitted elastodynamic fields. New insights on short-time dislocation interactions during shock loading are also revealed through a study of the forces between rapidly-moving shear dislocation loops. 

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5. Deep learning predicts path-dependent plasticity

   https://doi.org/10.1073/pnas.1911815116  

   Mozaffar, M.; Bostanabad, R.; Chen, W.; Ehmann, K.; Cao, J.; Bessa, M. A. (December 2019, Proceedings of the National Academy of Sciences)

   Plasticity theory aims at describing the yield loci and work hardening of a material under general deformation states. Most of its complexity arises from the nontrivial dependence of the yield loci on the complete strain history of a material and its microstructure. This motivated 3 ingenious simplifications that underpinned a century of developments in this field: 1) yield criteria describing yield loci location; 2) associative or nonassociative flow rules defining the direction of plastic flow; and 3) effective stress–strain laws consistent with the plastic work equivalence principle. However, 2 key complications arise from these simplifications. First, finding equations that describe these 3 assumptions for materials with complex microstructures is not trivial. Second, yield surface evolution needs to be traced iteratively, i.e., through a return mapping algorithm. Here, we show that these assumptions are not needed in the context of sequence learning when using recurrent neural networks, diverting the above-mentioned complications. This work offers an alternative to currently established plasticity formulations by providing the foundations for finding history- and microstructure-dependent constitutive models through deep learning. 

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