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Material Behavior

 

Dr. Layer 1.0
Lesson 10- Non-linear Material Behavior

Introduction

Introduction

Background

The numerical formulation used in Dr. Layer requires the idealization of the material stress-strain behavior. The current Dr. Layer implementation uses two of such idealizations: a)linearly elastic law, and b)nonlinear model. The linearly elastic model assumes a constant variation of stress and strain according to Hooke's law with no permanent deformations after the applied stresses is removed, Figure 1. The shear modulus G1 specifies the material stiffness.
Figure 1

The nonlinear (varying stress- strain relationship) model can be used to simulate the soil behavior during cyclic loading. In Dr. Layer, the nonlinear behavior of soils is represented by a bilinear model with the following characteristics:

1. An initial yield shear stress tY0
2. An initial shear modulus G1 valid until the yield stress tY is reached.
3. A hardening shear modulus G2 activated after the yield stress tY is reached.

When the direction of the applied loading is reversed, behavior is again determined by the modulus G1 until a stress change of 2tY is obtained and then the modulus G2 takes control of the behavior, Figure 2. Every time the yield stress is reached a new value is calculated based on plastic shear strain. This pattern is continuously repeated upon loading, unloading and reloading. An option to select different material properties is included in Dr. Layer which provides the opportunity to play with different yield stresses and hardening conditions.


Figure 2

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Objective

After this exercise you will have a better understanding of the phenomenon of wave propagation in nonlinear materials. The effect of material nonlinearity on permanent deformations and energy loss are graphicaly explained.

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Things to Do

  1. Open the Dr. Layer program. By default we get twelve layers. The top six layers are hardwired into the system with a velocity specified as very fast. The bottom six layers are hardwired with a velocity of very slow.

  2. Select all (Edit menu) the layers to all have "very fast" wave speed values.

  3. Select the top four or five layers and assign them a "very slow" wave speed.

  4. Select a pulse load from the loading window. Using the frequency bar select a high frequency (i.e 80% of max value). Keep default amplitude.

  5. On the menu listings choose options and material model by default we have a linearly elastic model.

  6. Create two stress-strain plot boxes near the interface between two materials, Figure 3. To create a stress-strain plot box select the plot box tool, , and pushing the Ctrl and Alt keys select the layer position where you want the box.

  7. Return to zero time by pushing the reset button, . Start loading by pushing the time forward button, . Observe the pulse load as it travels along the layer. As soon as the perturbation reaches the interface between the two materials the stress-strain plots will show some change. Explain the characteristics of this change. Can you identify plastic deformations? How are the slopes of the stress-strain plots? Are these slopes consistent with the selected wave speed? Why?


    FIgure 3

  8. On the menu listings choose options and material model. Select the Bilinear option and choose a Low yield stress and the hardening option.
  9. Repeat step No. 7 and observe the deformed shape and the stress-strain curves as the wave travels along the layer, Figure 4.



    Figure 4

  10. Can you identify any permanent deformations??
                                                  

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Observation

  • The material models employed show marked differences when turned on. The stress-strain curves obtained are different for each case. Turning on strain hardening causes permanent irreversible deformation with a decrease in load applied.

  • Observe that most of the irreversible deformation is concentrated at the interface between the two materials.

  • Observe that after the wave reaches the interface between the two materials, the perturbation vanishes almost completely. This damping effect can be attributed to the loss of energy during the nonlinear cycle. This form of damping is usually referred to as material damping. In contrast, no energy is lost in the elastic case. Therefore, multiple reflections are observed as time increases.

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On Your Own

  1. Repeat the exercise using one single material with "very fast" wave speed. Do you observe any permanent deformations?? Describe location.

  2. Repeat the exercise using different wave speed and layer thickness combinations.

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 Last Updated:
 12/27/00

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