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Material Behavior

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

Introduction

Introduction

### Background

The analysis employed by DR. Layer required an appropriate idealization of the stress-strain relationship. Two such idealizations were used- linearly elastic and bilinear models. 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. This holds true until the yield point followed by an unrestricted plastic strain after yield.
A nonlinear (varying stress- strain relationship) model may also be used for soils from the beginning of loading. For our analysis this is implemented as a bilinear model with the following characteristics
1. Strain E1
2. An initial shear modulus G1 until a limiting strain E1
3. A Shear modulus G2 after the strain E1

When the direction of the applied loading is reversed, behavior is again determined by the modulus G1 until a strain change of 2E1 is obtained and then the modulus G2 takes control of the behavior. This pattern is continuously repeated. An option to include strain hardening is included which provides the opportunity to play with the possibility of including permanent deformation.

### Objective

After this exercise you will have a better understanding of two idealized models used to obtain stress-strain curves in practice.

### 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 slow values or any combination you desire.

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

4. Push the ctrl key and apply the label tool at the mid layer level. You should get a stress-strain plot with origin in the middle of the plot area. A combination of different layer types can give you plots like that shown below in Fig. 8.1

5. Return to zero time by pushing bottom left button and try many combinations as possible varying as many parameters as you desire.

6. Next we will change the to a bilinear, medium stressed and strain hardened material model. This can be achieved in the options menu and material model. To get a reasonable visual effect you need to increase the amplitude to its maximum value. Also apply a very low damping value to the layers and with strain hardening you will obtain the permanent deformation shown below.

### 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.