Search results for keyword: cauchy
Lagrangian stress tensor
Lagrange Strain Tensor
The Lagrange strain tensor is a mathematical concept used to describe the strain on an object due to a force in a given direction. This idea is commonly used in engineering to analyze materials and structures for their strength and possible failure points. In this article, ......
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Sophia
Solow residual method
Introduction
The cauchy-Euler Method (or cauchy-Euler Residual Method) is an iterative numerical method used in the solution of various linear systems of equations. The method is based on the notion that approximate solutions to the system of equations can be found which are close to the exact so......
HO theorem
This article is a summary of the proof of the Ky Fan Theorem. In the article, we will look at the history and background of the theorem, the statement of the theorem and its proof.
The Ky Fan Theorem was developed by the mathematician Ky Fan in 1954. He proved that any reasonable measure can be ......
spherical stress tensor
A tensor is a mathematical object which describes how a physical system changes shape when that system is stressed. Tensors are used in the analysis of a variety of physical systems, such as continuum mechanics and solid mechanics. A stress tensor, often referred to as a cauchy Stress tensor, is u......
cauchy stress tensor
Introduction
cauchy Stress Tensor is an important concept used in the field of continuum mechanics, particularly in the study of stress caused by mechanical loads on material. When a material is under stress, cauchy Stress Tensor helps in understanding the resultant strain or deformation along wi......
Rigid-Plastic Variational Principle
Introduction
In recent years the plastic deformation theory (PDT) has become an important topic in mechanics research. It is a basic theory that uses continuum mechanics to describe the plastic deformation of materials. It is based on the idea that when a material is subjected to large enough loa......
Kirchhoff stress tensor
The von Mises-Hencky–von Kármán tensor is a mathematical model that is used to describe the stress–strain field in an elastic body. It involves several properties, such as the principal stresses, strain invariants, and overall isotropy which a material may possess. The von Mises-Hencky–von K......
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