ICME COURSE CONSTITUTIVE BEHAVIOR CLASSIFICATION OF STRESSSTRAIN RESPONSE IN

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ICME Course: Constitutive Behavior

Classification of Stress-Strain Response in Materials

  1. Elastic

    1. Linear elasticity

    2. Non-linear elasticity

  2. Viscoelastic(rate dependent)

    1. Creep

    2. Stress Relaxation

    3. Strain-Rate Dependency

  3. Perfectly Plastic

  4. Elasto-plastic (rate independent)

    1. Elasto-Perfectly Plastic

    2. Elasto-Linear Plastic

    3. Elasto-Non Linear Plastic

  5. Elasto-viscoplastic(rate dependent)

    1. Creep in Metals

6) Thermoelsticity

7) Thermoviscoelastcity

8) Thermoplasticity


1.a. Linear Elastic:

ICME COURSE CONSTITUTIVE BEHAVIOR CLASSIFICATION OF STRESSSTRAIN RESPONSE IN

1.b. Non-linear elasticity:


ICME COURSE CONSTITUTIVE BEHAVIOR CLASSIFICATION OF STRESSSTRAIN RESPONSE IN

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:

ICME COURSE CONSTITUTIVE BEHAVIOR CLASSIFICATION OF STRESSSTRAIN RESPONSE IN

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:

  1. if the stress is held constant, the strain increases with time (creep);

  2. if the strain is held constant, the stress decreases with time (relaxation);

  3. 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.


ICME COURSE CONSTITUTIVE BEHAVIOR CLASSIFICATION OF STRESSSTRAIN RESPONSE IN
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.

ICME COURSE CONSTITUTIVE BEHAVIOR CLASSIFICATION OF STRESSSTRAIN RESPONSE IN

Strain rate dependency: the effective stiffness depends on the rate of application of the load;

ICME COURSE CONSTITUTIVE BEHAVIOR CLASSIFICATION OF STRESSSTRAIN RESPONSE IN



Plasticity3


Perfectly Plastic:


ICME COURSE CONSTITUTIVE BEHAVIOR CLASSIFICATION OF STRESSSTRAIN RESPONSE IN

Elasto-Perfectly Plastic:

ICME COURSE CONSTITUTIVE BEHAVIOR CLASSIFICATION OF STRESSSTRAIN RESPONSE IN


Elasto-Linear Plastic:


ICME COURSE CONSTITUTIVE BEHAVIOR CLASSIFICATION OF STRESSSTRAIN RESPONSE IN



Elasto-Non Linear Plastic:

ICME COURSE CONSTITUTIVE BEHAVIOR CLASSIFICATION OF STRESSSTRAIN RESPONSE IN



ICME COURSE CONSTITUTIVE BEHAVIOR CLASSIFICATION OF STRESSSTRAIN RESPONSE IN ICME COURSE CONSTITUTIVE BEHAVIOR CLASSIFICATION OF STRESSSTRAIN RESPONSE IN





Elasto-Viscoplastic (rate dependent):

ICME COURSE CONSTITUTIVE BEHAVIOR CLASSIFICATION OF STRESSSTRAIN RESPONSE IN









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.

ICME COURSE CONSTITUTIVE BEHAVIOR CLASSIFICATION OF STRESSSTRAIN RESPONSE IN
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


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