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The spontaneous emergence of heterogeneous dislocation patterns is a conspicuous feature of plastic deformation and strain hardening of crystalline solids. Despite long-standing efforts in the materials science and physics of defect…

Materials Science · Physics 2015-05-22 Stefan Sandfeld , Michael Zaiser

We present a dislocation density-based strain hardening model for single crystal copper through a systematic coarse-graining analysis of more than 200 discrete dislocation dynamics (DDD) simulations of plastic deformation under uniaxial…

Materials Science · Physics 2020-10-28 Sh. Akhondzadeh , Ryan B. Sills , Nicolas Bertin , Wei Cai

In this study, we employ high-energy X-ray characterization to examine the role of relatively large amounts of intragranular lattice misorientation -- present after many thermomechanical processes -- on the micromechanical response of…

A systematic study on the different roles of the governing components of a well-defined finite-deformation gradient crystal-plasticity model proposed by (Gurtin, 2008b) is carried out, in order to visualize the capability of the model in…

Computational Physics · Physics 2017-09-13 Habib Pouriayevali , Bai-Xiang Xu

We rigorously derive a strain-gradient model of plasticity as a $\Gamma$-limit of continuum bodies containing finitely-many edge-dislocations (in two dimensions). The key difference from previous such derivations is the elemental notion of…

Analysis of PDEs · Mathematics 2026-03-03 Raz Kupferman , Cy Maor

When metals are plastically deformed, the total density of dislocations increases with strain as the microstructure is continuously refined, leading to the strain hardening behavior. Here we report the fundamental role played by the…

Materials Science · Physics 2018-08-29 Ryan B. Sills , Nicolas Bertin , Amin Aghaei , Wei Cai

Deformation band patterning in single crystals is investigated using a finite strain crystal viscoplasticity model based on the evolution of dislocation densities. In the presence of strong latent hardening and weak rate dependence, the…

Materials Science · Physics 2025-07-02 Jean-Michel Scherer

The strength of the lithosphere is typically modelled based on constitutive equations for steady-state flow. However, models of lithospheric flexure reveal differences in lithospheric strength that are difficult to reconcile based on such…

In this paper a geometric field theory of dislocation dynamics and finite plasticity in single crystals is formulated. Starting from the multiplicative decomposition of the deformation gradient into elastic and plastic parts, we use…

Materials Science · Physics 2023-08-02 Fabio Sozio , Arash Yavari

A simple analytical model of intergranular normal stresses is proposed for a general elastic polycrystalline material with arbitrary shaped and randomly oriented grains under uniform loading. The model provides algebraic expressions for the…

Materials Science · Physics 2023-04-21 Samir El Shawish , Timon Mede

We present a novel approach to understand geometric-incompatibility-induced rigidity in under-constrained materials, including sub-isostatic 2D spring networks and 2D and 3D vertex models for dense biological tissues. We show that in all…

Soft Condensed Matter · Physics 2023-01-18 Matthias Merkel , Karsten Baumgarten , Brian P. Tighe , M. Lisa Manning

The yield surface in crystal plasticity can be approached from various directions during mechanical loading. We consider the competition between nanoindentation and tensile loading towards plastic yielding. For this purpose, we develop a…

Materials Science · Physics 2017-07-14 Hengxu Song , Hakan Yavas , Erik Van der Giessen , Stefanos Papanikolaou

Thermodynamic dislocation theory incorporating dislocation impediment by the grain boundaries is developed to analyze the shear test of polycrystals. With a small set of physics based material parameters, we are able to simulate the…

Materials Science · Physics 2021-04-13 Yinguang Piao , Khanh Chau Le

We derive strain-gradient plasticity from a nonlocal phase-field model of dislocations in a plane. Both a continuous energy with linear growth depending on a measure which characterizes the macroscopic dislocation density and a nonlocal…

Analysis of PDEs · Mathematics 2020-09-08 Sergio Conti , Adriana Garroni , Stefan Muller

The granular microstructure of metals evolves significantly during thermomechanical processing through viscoplastic deformation and recrystallization. Microstructural features such as grain boundaries (GBs), subgrains, localized deformation…

Materials Science · Physics 2025-06-11 Izzet Tarik Tandogan , Michael Budnitzki , Stefan Sandfeld

External magnetic fields influence the microstructure of polycrystalline materials. We explore the influence of strong external magnetic fields on the long time scaling of grain size during coarsening in thin films with an extended…

Materials Science · Physics 2020-03-04 Rainer Backofen , Axel Voigt

Dislocations are the carriers of plasticity in crystalline materials. Their collective interaction behavior is dependent on the strain rate and sample size. In small specimens, details of the nucleation process are of particular importance.…

Materials Science · Physics 2020-11-05 Jianqiao Hu , Hengxu Song , Zhanli Liu , Zhuo Zhuang , Xiaoming Liu , Stefan Sandfeld

The common practice of ignoring the elastic strain gradient in measurements of geometrically necessary dislocation (GND) density is critically examined. It is concluded that the practice may result in substantial errors. Our analysis points…

Materials Science · Physics 2013-01-08 Amit Acharya , Robin J. Knops

We develop and demonstrate the first general computational tool for finite deformation static and dynamic dislocation mechanics. A finite element formulation of finite deformation (Mesoscale) Field Dislocation Mechanics theory is presented.…

Materials Science · Physics 2020-06-24 Rajat Arora , Xiaohan Zhang , Amit Acharya

In this work, the influence of the plastic size effect on the fracture process of metallic materials is numerically analyzed using the strain-gradient plasticity (SGP) theory established from the Taylor dislocation model. Since large…

Materials Science · Physics 2017-10-17 E. Martínez-Pañeda , C. Betegón