Related papers: Consistent determination of geometrically necessar…
In this work hydrogen diffusion towards the fracture process zone is examined accounting for local hardening due to geometrically necessary dislocations (GNDs) by means of strain gradient plasticity (SGP). Finite element computations are…
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…
Dislocations are at the heart of the plastic behavior of crystalline materials yet it is notoriously difficult to perform quantitative, non-intrusive, measurements of their single or collective properties. Dislocation density is a critical…
A procedure based on a Mixture Density Model for correcting experimental data for distortions due to finite resolution and limited detector acceptance is presented. Addressing the case that the solution is known to be non-negative, in the…
Accurate prediction of springback and formability in sheet metal forming requires understanding reverse loading behavior under complex loading path changes, such as tension followed by compression. However, for ultra-thin sheets…
We provide a minimal continuum model for mesoscale plasticity, explaining the cellular dislocation structures observed in deformed crystals. Our dislocation density tensor evolves from random, smooth initial conditions to form self-similar…
When a material is subjected to an applied stress, the material will experience recoverable elastic deformation followed by permanent plastic deformation at the point when the applied stress exceeds the yield stress of the material.…
Mechanical and elastic properties of materials are among the most fundamental quantities for many engineering and industrial applications. Here, we present a formulation that is efficient and accurate for calculating the elastic and bending…
We investigate the T(3)-gauge theory of static dislocations in continuous solids. We use the most general linear constitutive relations bilinear in the elastic distortion tensor and dislocation density tensor for the force and pseudomoment…
Understanding lattice deformations is crucial in determining the properties of nanomaterials, which can become more prominent in future applications ranging from energy harvesting to electronic devices. However, it remains challenging to…
The Tangential-Displacement Normal-Normal-Stress (TDNNS) method is a finite element method for mixed elasticity. As the name suggests, the tangential component of the displacement vector as well as the normal-normal component of the stress…
The computational method of discrete dislocation dynamics (DDD), used as a coarse-grained model of true atomistic dynamics of lattice dislocations, has become of powerful tool to study metal plasticity arising from the collective behavior…
The present paradigm in design and modelling of lattice architected mechanical metamaterials is mostly limited to traditional numerical methods like finite element analysis. Recently, the use of machine learning and artificial intelligence…
Nonnegative Tucker decomposition (NTD) is a powerful tool for the extraction of nonnegative parts-based and physically meaningful latent components from high-dimensional tensor data while preserving the natural multilinear structure of…
This article attempts to clarify an issue regarding the proper definition of plastic dislocation density tensor. This study shows that the Ortiz's and Berdichevsky's plastic dislocation density tensors are equivalent with each other, but…
In dislocation-free martensites the components of the elastic strain tensor are constrained by the Saint-Venant compatibility condition which guarantees continuity of the body during external loading. However, in dislocated materials the…
This paper deals with the solution of delay differential equations describing evolution of dislocation density in metallic materials. Hardening, restoration, and recrystallization characterizing the evolution of dislocation populations…
We derive general relations between grain boundaries, rotational deformations, and stress-free states for the mesoscale continuum Nye dislocation density tensor. Dislocations generally are associated with long-range stress fields. We…
The decentralized gradient descent (DGD) algorithm, and its sibling, diffusion, are workhorses in decentralized machine learning, distributed inference and estimation, and multi-agent coordination. We propose a novel, principled framework…
Quantifying the degree of dissimilarity between two probability distributions on a finite metric space is a fundamental task in Computer Science and Computer Vision. A natural dissimilarity measure based on optimal transport is the Earth…