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The basic stress analysis problem is therefore a boundary-value problem. Stress analysis for elastic structures is based on the theory of elasticity and infinitesimal strain theory. When the applied loads cause permanent deformation, one must use more complicated constitutive equations, that can account for the physical processes involved ...
There are also fluids whose strain rate is a function of time. Fluids that require a gradually increasing shear stress to maintain a constant strain rate are referred to as rheopectic. An opposite case of this is a fluid that thins out with time and requires a decreasing stress to maintain a constant strain rate (thixotropic).
Stress–strain analysis (or stress analysis) is an engineering discipline that uses many methods to determine the stresses and strains in materials and structures subjected to forces. In continuum mechanics , stress is a physical quantity that expresses the internal forces that neighboring particles of a continuous material exert on each other ...
A starting point for solving contact problems is to understand the effect of a "point-load" applied to an isotropic, homogeneous, and linear elastic half-plane, shown in the figure to the right. The problem may be either plane stress or plane strain. This is a boundary value problem of linear elasticity subject to the traction boundary conditions:
The (infinitesimal) strain tensor (symbol ) is defined in the International System of Quantities (ISQ), more specifically in ISO 80000-4 (Mechanics), as a "tensor quantity representing the deformation of matter caused by stress. Strain tensor is symmetric and has three linear strain and three shear strain (Cartesian) components."
Displacements (,) can be obtained from the Michell solution by using the stress-strain and strain-displacement relations. A table of displacement components corresponding the terms in the Airy stress function for the Michell solution is given below.
In continuum mechanics an eigenstrain is any mechanical deformation in a material that is not caused by an external mechanical stress, with thermal expansion often given as a familiar example. The term was coined in the 1970s by Toshio Mura , who worked extensively on generalizing their mathematical treatment. [ 1 ]
For example, moderate creep in concrete is sometimes welcomed because it relieves tensile stresses that might otherwise lead to cracking. Unlike brittle fracture, creep deformation does not occur suddenly upon the application of stress. Instead, strain accumulates as a result of long-term stress. Therefore, creep is a "time-dependent" deformation.