Related Experiment Video
Updated: Aug 12, 2025
10:36
Stress Distribution During Cold Compression of Rocks and Mineral Aggregates Using Synchrotron-based X-Ray Diffraction
Published on: May 20, 2018
9.8K
A perspective on the microscopic pressure (stress) tensor: History, current understanding, and future challenges
Kaihang Shi1, Edward R Smith2, Erik E Santiso1
1Department of Chemical and Biomolecular Engineering, North Carolina State University, Raleigh, North Carolina 27695, USA.
The Journal of Chemical Physics
|February 1, 2023
Summary
This perspective reviews methods for calculating the microscopic pressure tensor, crucial for engineering and science. It highlights challenges and suggests future research directions for this fundamental concept.
Area of Science:
- Physics
- Engineering
- Thermodynamics
- Biophysics
Background:
- The pressure tensor is fundamental to fluid dynamics, solid mechanics, and thermodynamics.
- Understanding microscopic pressure tensor is key across multiple scientific disciplines.
Purpose of the Study:
- To review methods for calculating the microscopic pressure tensor.
- To establish connections between different pressure forms for equilibrium and nonequilibrium systems.
- To identify challenges and suggest future directions in the field.
Main Methods:
- Review of existing literature on microscopic pressure tensor calculation methods.
- Analysis of theoretical frameworks for equilibrium and nonequilibrium systems.
- Identification of computational and experimental limitations.
Main Results:
- Established connections between various pressure tensor formulations.
- Highlighted difficulties with many-body and long-range potentials.
- Identified insufficiency of current software and computational tools.
Conclusions:
- The microscopic pressure tensor is vital but faces definition controversies and computational challenges.
- Lack of experimental nanoscale probing methods hinders progress.
- Future research should address these limitations and explore new avenues.
Related Concept Videos
01:21General State of Stress
270
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...
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...
270
01:20Stress
7.7K
When a force is applied on a body, it undergoes deformation. In order to restore the body to its original shape and/or size, an opposite or restoring force is generated within the body. This restoring force is equal to the magnitude of the applied force, but acts in the opposite direction. The amount of this restoring force developed per unit area of the body is called stress. Stress is a tensor quantity and has the SI unit pascal. Stress can be separated into four broad categories depending...
7.7K
01:15Stress: General Loading Conditions
358
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....
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....
358
01:23Components of Stress
256
Stress analysis under multiple loading conditions is intricate, necessitating a comprehensive grasp of normal and shearing stresses. Consider a small cube at point O, subjected to stress on all six faces, visible or not. Normal stress components σx, σy, σz act perpendicularly to the x, y, and z axes. Shearing stress components τxy and τxz are exerted on faces perpendicular to these axes.
Interestingly, the hidden cube faces also experience these stresses, equal and...
Interestingly, the hidden cube faces also experience these stresses, equal and...
256
01:18Transformation of Plane Stress
323
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...
323
01:15Concept of Pressure at a Point
342
The concept of pressure at a point in a fluid establishes that pressure within a fluid is uniform in all directions at a specific location. This uniformity occurs because fluid molecules exert force evenly across any point due to their random motion and continuous collisions within the fluid. Pressure at a point is determined by the surrounding fluid molecules and is influenced by factors like depth and density, rather than by shape or orientation.
In a fluid at rest, pressure acts equally in...
In a fluid at rest, pressure acts equally in...
342