MANE-6940
Jonathan Gomez-Leon
Homework #1
Linear Elasticity
It is said that materials undergo elasticity when an external force is applied to it temporarily deforming it
and, when this external forces are removed, the material returns to its original shape. The unloading
path is the same as the loading path. The term linear means that the stresses and strains are linearly
related. The assumption of isotropic materials is usually taken, where elastic properties are the same in
all directions of the body, as it has been verified for most metallic materials.
Thermo-elasticity
In addition to the explained above regarding elasticity, thermo-elasticity introduces the temperature
variable when studying the deformation of materials. This is introduces when the external loads applied
to a body have a variation in temperature. The increase in temperature on a material means that the
vibration in its atomic structure will increase, making the material deform and expand. In the same
manner, the material will compress when their temperature decreases. The deformation of a material is
a relationship between its coefficient of thermal expansion, the change in temperature, and the change
in dimension as a function of temperature.
Viscoelasticity
Similarly as explained previously, a material will deform elastically when external forces are applied to it.
However, viscoelasticity as the name indicates, deals with materials that are relatively viscous. When a
uniform load is applied instantly to a material, the strain response of the material does not occur
instantly, but rather as a function of time. When analyzing a material under viscoelasticity, one can
observe the resistance of a material under rapid changes in shape, or forces applied in a rapid manner.
This phenomenon is usually observed in polymers
Plasticity and Elasto-Plasticity
As opposed to elasticity, a material is said to be plastic when external forces are applied to it but the
material does not return to its original shape after the forces are removed. These materials would
initially deform elastically, but after reaching a yield stress it will deform plastically. The study of
plasticity is used to calculate the irreversible deformation of materials as well as calculating the forces
required to deform a material for manufacturing purposes.
Viscoplasticity/Creep
Viscoplasticity is an extension of the plasticity study. The difference is that plasticity is rate independent,
whereas viscoplasticity deals with the plastic deformation of materials depending on the rate at which
the loads are applied. A more notable difference is that viscoplastic model continues to undergo a creep
flow as a function of time under the influence of the applied load. In other words, a material will deform
permanently under as a result of long-term exposure to high levels of stress that are still below the yield
strength of the material.
Damage/Fracture/Fatigue
Damage failure deals with the deformation of materials to a point where macroscopic cracks and
cavities start to form, represented by surface or volume discontinuities. This way, this study is
commonly used to predict crack propagation and initiation as well as fracture of materials. Along the
same lines of Damage failure, Fatigue failure can also be discussed under the same context. Fatigue
failure is when a material fractures under repeated stress cycles. The intensity of each of these stress
cycles would be below the normal strength of the material.