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The Description of Strain in Biological Materials The third type of anatomical movement involves changes in the internal structure of biological materials. These changes are called strain. This collection of essays explores the description of strain in terms of quaternions. The first essays consider more theoretical aspects of stain and the later essays work through a series of calculations of strain is special circumstances. These essays are still an exploration of the concepts, therefore are somewhat unfinished and tentative. They will likely to be changed or updated to reflect changes in thinking and notation. |
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Strain in Distorted Boxes The analysis of strain starts with the concept of boxes, hypothetical unit cubes that lie within the medium and suffer distortion by the strain. It is the changes in the relations between the edges of the box that are the measures of strain in the medium. [ Word | PDF ] |
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Diagonal Vectors One of the most useful indices of distortion of a box is the change in the diagonal vector of the box. In this essay the diagonal is examined and several secondary measures are explored. [ Word | PDF ] |
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Strain and Triple Vector Products At the center of the analysis are the concepts of volumetric strain versus shear strain. These two types of strain are components of the quaternion strain. In this essay the two types of strain are derived from the triple vector product of the edge vectors of a distorted unit cube. [ Word | PDF ] |
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Analysis of Strain This is a more general examination of the types of strain, including types that are more complex than a linear strain. It is often difficult to determine how the strain is to be viewed in terms of internal distortion of the material matrix of the anatomical substance. [ Word | PDF ] |
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Distorted Boxes This is a consideration of the concept of a box. It is argued that a box is actually an oriented point in the strained medium. The image of a complete unit cubical box may lead one astray, if it is taken too literally when considering strain. [ Word | PDF ] |
Calculations of Strain in Special Circumstances These essays consider a set of calculations in situations in which the matrix is distorted in standard ways, such as compression between two flat plates, shearing between plates, twisting about an axis, and depression by a probe. |
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Definitions of Shear This essay takes a very general approach to strain and differentiates between location shear and orientation shear. [ Word | PDF ] |
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Extension and Orientation Strain This essay considers the strain produced by changing the physical dimensions of a block of material or it orientation. |
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Compression In these calculations, the matrix is compressed between two flat plates, causing it to spread laterally. [ Word | PDF ] |
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Shear Displacement In these calculations, the matrix is sheared by moving one plate parallel with another with the matrix confined between them. [ Word | PDF ] |
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Torsion In these calculations, one plate is rotated about an axis with the matrix confined between the two plates. [ Word | PDF ] |
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Depression In these calculations the matrix is displaced by a probe that pushes into it. [ Word | PDF ] |