ICME Course: Constitutive Behavior
Classification of Stress-Strain Response in Materials
Elastic
Linear elasticity
Non-linear elasticity
Viscoelastic(rate dependent)
Creep
Stress Relaxation
Strain-Rate Dependency
Perfectly Plastic
Elasto-plastic (rate independent)
Elasto-Perfectly Plastic
Elasto-Linear Plastic
Elasto-Non Linear Plastic
Elasto-viscoplastic(rate dependent)
Creep in Metals
6) Thermoelsticity
7) Thermoviscoelastcity
8) Thermoplasticity
1.a. Linear Elastic:
1.b. Non-linear elasticity:
2. Viscoelastic (rate or time dependent elasticity):1
Viscoelastic materials are those for which the relationship between stress and strain depends on time.
2.1. Characteristics of a Viscoelastic Material2
Just like for elastic models, there are specific characteristics for viscoelastic models. These characteristics set viscoelastic models distinctly apart from elastic models. Most notably, we know that elastic materials store 100% of the energy due to deformation. However, viscoelastic materials do not store 100% of the energy under deformation, but actually lose or dissipate some of this energy. This dissipation is also known as hysteresis. Hysteresis explicitly requires that the loading portion of the stress strain curve must be higher than the unloading curve. Thus, from a stress-strain curve we can see the hysteresis as the area between the loading and unloading curve:
The ability to dissipate energy is one of the main reasons for using viscoelastic materials for any application to cushion shock, from running shoes to packing materials.
Some phenomena in viscoelastic materials are:
if the stress is held constant, the strain increases with time (creep);
if the strain is held constant, the stress decreases with time (relaxation);
the effective stiffness depends on the rate of application of the load;
All materials exhibit some viscoelastic response. In common metals such as steel or aluminum, as well as in quartz, at room temperature and at small strain, the behavior does not deviate much from linear elasticity. Synthetic polymers, wood, and human tissue as well as metals at high temperature display significant viscoelastic effects.
§1.3.1 Viscoelastic functions
Creep is a slow, progressive deformation of a material under constant stress.
Fig.
1.1 Creep and recovery. Stress
and strain
vs. time t.
Stress relaxation is the gradual decrease of stress when the material is held at constant strain.
Strain rate dependency: the effective stiffness depends on the rate of application of the load;
Plasticity3
Perfectly Plastic:
Elasto-Perfectly Plastic:
Elasto-Linear Plastic:
Elasto-Non Linear Plastic:
Elasto-Viscoplastic (rate dependent):
Creep
Creep curves may exhibit three regions (Fig. 1.2), primary creep in which the curve is concave down, secondary creep in which deformation is proportional to time, and tertiary creep in which deformation accelerates until creep rupture occurs. Tertiary creep is always a manifestation of nonlinear viscoelasticity, and secondary creep is usually nonlinear as well. Although secondary creep is represented by a straight line in a plot of strain vs. time, that straight line has nothing whatever to do with linear viscoelasticity.
Fig.
1.2 Regions of creep behavior. Strain
vs. time t, for different load levels.
1 http://silver.neep.wisc.edu/~lakes/VEnotes.html
2 http://www.engin.umich.edu/class/bme456/ch7consteqviscoelasticity/bme456consteqviscoelasticity.htm
3 http://web.mit.edu/course/3/3.11/www/modules/ss.pdf#search=%22stress%20strain%20curve%22
AVIS DE COURSE TROPHEE JL BONNAFOUS CLUB NAUTIQUE
CHALLENGE COURSE SKILLS SELFASSESSMENT N AME DATE A
COURSE TITLE BUS030150FINANCIAL ACCOUNTING BRIEF DESCRIPTION
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