Continuum Mechanics Chadwick Pdf.zip

If one studies the behavior of a solid material, and the material is divided into small elements, so that the element is in practice assumed to be homogeneous and isotropic, one can associate each element to a point in a three-dimensional Euclidean space and each mechanical property of an element to a vector in that space. The mechanical properties of the solid material can then be regarded as arising from the superposition of the mechanical properties of each of its elements. This process of homogenization is used in continuum mechanics, and is based on the concept of a continuous field of materials having mechanical properties. These properties can be described by the vector field of mechanical properties of the material, and this vector field can be found from the properties of each of the elements in the material.

In a continuum the material properties of each element can be represented by a vector field in some space. The vectors in this space may be considered as the values of the mechanical properties of the material at the various points in the body. The values of these fields at a point are denoted by the vectors in the vector space, and are usually written in bold italics to distinguish them from the vector values. The components of the mechanical property vectors are functions of space. The functions are continuous over an element. The vector field for the mechanical property of the material is called the stress field.

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