| Solid mechanics |
Solid mechanics
Solid mechanics is the branch of
mechanics,
physics, and
mathematics that concerns the behavior of solid matter under external
actions (e.g., external
forces,
temperature changes, applied displacements, etc.). It is part of a broader study
known as
continuum mechanics.
A material has a rest shape and its shape departs away from the rest shape
due to stress. The amount of departure from rest shape is called
deformation, the proportion of deformation to original size is called
strain. If the applied stress is sufficiently low (or the imposed strain is
small enough), almost all solid materials behave in such a way that the strain
is directly proportional to the stress; the coefficient of the proportion is
called the
modulus of elasticity or
Young's modulus. This region of deformation is known as the linearly elastic
region.
Major topics
There are several standard models for how solid materials respond to stress:
-
Elastic � Linearly elastic materials can be described by the
linear elasticity equations. A spring obeying
Hooke's law is a one-dimensional linear version of a general elastic
body. By definition, when the stress is removed, elastic deformation is
fully recovered.
-
Viscoelastic � a material that is elastic, but also has
damping:
on loading, as well as on unloading, some work has to be done against the
damping effects. This work is converted in heat within the material. This
results in a
hysteresis loop in the stress�strain curve.
-
Plastic � a material that, when the stress exceeds a threshold (yield
stress), permanently changes its rest shape in response. The material
commonly known as "plastic"
is named after this property. Plastic deformation is not recovered on
unloading, although generally the elastic deformation up to yield is.
One of the most common practical applications of Solid Mechanics is the
Euler-Bernoulli beam equation.
Solid mechanics extensively uses
tensors to
describe stresses, strains, and the relationship between them.
Typically, solid mechanics uses
linear models
to relate stresses and strains (see
linear elasticity). However, real materials often exhibit
non-linear behavior.
For more specific definitions of stress, strain, and the relationship between
them, see
strength of materials.
|
