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Related Concept Videos

General State of Stress01:21

General State of Stress

179
The general state of stress within a material can be accurately depicted using a stress tensor. This tensor encapsulates the internal forces distributed within a material subjected to external forces or deformations.
Specifically, consider a tetrahedral element where one face, labeled XYZ, is perpendicular to the line OA, and the remaining faces align with the coordinate axes with point O as the origin. At any point, such as point O, the stress tensor can be used to determine the stress...
179
Stress: General Loading Conditions01:15

Stress: General Loading Conditions

305
To grasp the intricacy of real-world conditions where multiple loads are applied simultaneously to a structure, one might visualize a section passing through a specific point within a body, aligned parallel to the xy plane. This section is subjected to various forces, including original loads, normal forces, and shearing forces.
The shearing force, possessing potential directionality within the plane of the section, is simplified into two component forces running parallel to the x and y axes....
305
Stresses under Combined Loadings01:23

Stresses under Combined Loadings

148
When analyzing a bent tube with a circular cross-section subjected to multiple forces, it is crucial to determine the stress distribution in order to maintain structural integrity under varied load conditions.
The process begins by slicing the tube at critical points and analyzing the internal forces and stress components at these sections, focusing on the centroid. Normal stresses, generated by axial forces and bending moments, are either compressive or tensile and vary across the section from...
148
Transformation of Plane Stress01:18

Transformation of Plane Stress

218
Studying stress transformation is essential in understanding how stress components within a material, like a cube under plane stress, change with rotation. This change is analyzed by considering a prismatic element within the cube. As the element rotates, the stress components acting on it—both normal and shearing stresses—change in magnitude and orientation. This change is quantified using trigonometric functions of the rotation angle, relating the forces acting on the rotated element's...
218
Flexural Stress01:16

Flexural Stress

238
When analyzing bending in symmetric members, it's crucial to understand how stresses distribute when subjected to bending moments. This stress distribution is effectively described by applying fundamental mechanics and material science principles, particularly Hooke's Law for elastic materials.
Hooke's Law states that within the material's elastic limits, stress is directly proportional to strain. In a member experiencing a bending moment, the strain at any point is relative to...
238
Elastic Strain Energy for Shearing Stresses01:20

Elastic Strain Energy for Shearing Stresses

173
As discussed in previous lessons, strain energy in a material is the energy stored when it is elastically deformed, a concept crucial in materials science and mechanical engineering. This energy results from the internal work done against the cohesive forces within the material. When a material undergoes shearing stress and corresponding shearing strain, the strain energy density, which is the energy stored per unit volume, is calculated. Within the elastic limit, where the stress is...
173

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Force and stress calculations with a neural-network wave function for solids.

Yubing Qian1,2, Xiang Li2, Ji Chen1,3

  • 1School of Physics, Peking University, Beijing 100871, People's Republic of China.

Faraday Discussions
|July 26, 2024
PubMed
Summary
This summary is machine-generated.

A new method improves interatomic force and stress tensor calculations for real solids using neural network variational Monte Carlo (VMC). This enhances accuracy and efficiency in materials modeling.

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Area of Science:

  • Computational materials science
  • Quantum chemistry
  • Condensed matter physics

Background:

  • Accurate ab initio calculations are crucial for understanding chemistry, phases, and materials science.
  • Neural network (NN) based variational Monte Carlo (VMC) offers a promising approach to overcome challenges in ab initio calculations.

Purpose of the Study:

  • To develop and assess a novel neural network-based VMC method for calculating interatomic forces and stress tensors in real solids.
  • To enhance the accuracy, efficiency, and robustness of ab initio calculations for materials modeling.

Main Methods:

  • Implementation of a neural network-based variational Monte Carlo (VMC) framework.
  • Development of a new scheme for computing interatomic forces using space-warp coordination transformation.
  • Design of novel periodic features for neural networks to improve robustness across different crystal lattices.

Main Results:

  • The proposed space-warp coordination transformation method demonstrates superior accuracy, efficiency, and robustness compared to existing force calculation techniques.
  • The new periodic features enhance the reliability of force calculations for diverse lattice structures.
  • The study validates the effectiveness of NN-VMC for calculating forces and stress tensors in real solids.

Conclusions:

  • The developed NN-VMC method with the space-warp transformation and periodic features significantly advances the capability for accurate ab initio calculations of real solids.
  • This work facilitates the broader application of machine learning quantum Monte Carlo methods in materials science and condensed matter physics.
  • The improved computational efficiency and robustness pave the way for more complex materials modeling and discovery.