Mechanics of Solids 2 min read
Finite deformation and strain tensors
In the theory of finite deformations, extension and rotations of line elements are unrestricted as to size. For an infinitesimal…
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Small-strain tensor
The small strains, or infinitesimal strains, εij are appropriate for situations with |∂uk/∂Xl|<< 1 for all k and l. Two…
Mechanics of Solids 3 min read
Geometry of deformation
Strain and strain-displacement relations The shape of a solid or structure changes with time during a deformation process. To characterize…
Mechanics of Solids 3 min read
Equations of motion
Now the linear momentum principle may be applied to an arbitrary finite body. Using the expression for Tj above and…
Mechanics of Solids 4 min read
Stress
Assume that F and M derive from two types of forces, namely, body forces f, such as gravitational attractions—defined such…
Mechanics of Solids 3 min read
Linear and angular momentum principles: stress and equations of motion
Let x denote the position vector of a point in space as measured relative to the origin of a Newtonian…
Mechanics of Solids 4 min read
Basic Principles
In addressing any problem in continuum or solid mechanics, three factors must be considered: (1) the Newtonian equations of motion,…
Mechanics of Solids 2 min read
Computational mechanics
The digital computer revolutionized the practice of many areas of engineering and science, and solid mechanics was among the first…
Mechanics of Solids 3 min read
Viscoelasticity
The German physicist Wilhelm Weber noticed in 1835 that a load applied to a silk thread produced not only an…
Mechanics of Solids 6 min read
Dislocations
The Italian elastician and mathematician Vito Volterra introduced in 1905 the theory of the elastostatic stress and displacement fields created…
Mechanics of Solids 3 min read
Stress concentrations and fracture
In 1898 G. Kirsch derived the solution for the stress distribution around a circular hole in a much larger plate…
Mechanics of Solids 4 min read
The general theory of elasticity
Linear elasticity as a general three-dimensional theory began to be developed in the early 1820s based on Cauchy’s work. Simultaneously,…