i. Draw 4 graphs that qualitatively show the shear strain response, y, versus time for: A. a purely viscous material B. a purely elastic (ideal rubber) material C. a polymer that follows the Maxwell model of spring and dashpot in series D. a more realistic viscoelastic polymer

Elements Of Electromagnetics
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**Transcription and Explanation for Educational Website**

---

**Title: Analyzing Viscoelastic Polymer Behavior Using Shear Stress**

**Section 15.1: Mechanical Experiment on a Viscoelastic Polymer**

In this section, we explore a mechanical experiment conducted on a viscoelastic polymer. The input shear stress, denoted as τ (in MPa), is applied to the polymer as documented in the graph below.

**Graph Explanation:**

- **Axes:** 
  - The vertical axis represents the input shear stress (τ) measured in MPa (MegaPascals).
  - The horizontal axis represents time in seconds.

- **Shear Stress Pattern:**
  - The input shear stress is shown to vary over time. 
  - The stress is initially at zero, then it rises immediately to a certain level, holds steady for a duration, drops back to zero, and then repeats the rise-and-fall cycle after some time.

**Task i: Visualization of Shear Strain Response**

The following task involves drawing four graphs that qualitatively depict the shear strain response, γ, versus time for various materials:

**A. Purely Viscous Material**
- Expect a linear, time-dependent increase in shear strain with the application and release of stress, reflecting permanent deformation.

**B. Purely Elastic (Ideal Rubber) Material**
- The shear strain demonstrates an immediate response to stress application and returns to zero upon stress removal, illustrating perfect elasticity.

**C. Polymer Following the Maxwell Model (Spring and Dashpot in Series)**
- Anticipate a combination of viscous flow and elastic recovery, where shear strain exhibits both immediate and time-dependent behavior.

**D. More Realistic Viscoelastic Polymer**
- Illustrate a complex time-dependent shear strain response that doesn’t immediately revert to the initial state upon stress removal, capturing both viscous and elastic characteristics.

Each graph should distinctly highlight the unique mechanical behavior of the material type it represents, providing insight into their elastic and viscous properties.

---
Transcribed Image Text:**Transcription and Explanation for Educational Website** --- **Title: Analyzing Viscoelastic Polymer Behavior Using Shear Stress** **Section 15.1: Mechanical Experiment on a Viscoelastic Polymer** In this section, we explore a mechanical experiment conducted on a viscoelastic polymer. The input shear stress, denoted as τ (in MPa), is applied to the polymer as documented in the graph below. **Graph Explanation:** - **Axes:** - The vertical axis represents the input shear stress (τ) measured in MPa (MegaPascals). - The horizontal axis represents time in seconds. - **Shear Stress Pattern:** - The input shear stress is shown to vary over time. - The stress is initially at zero, then it rises immediately to a certain level, holds steady for a duration, drops back to zero, and then repeats the rise-and-fall cycle after some time. **Task i: Visualization of Shear Strain Response** The following task involves drawing four graphs that qualitatively depict the shear strain response, γ, versus time for various materials: **A. Purely Viscous Material** - Expect a linear, time-dependent increase in shear strain with the application and release of stress, reflecting permanent deformation. **B. Purely Elastic (Ideal Rubber) Material** - The shear strain demonstrates an immediate response to stress application and returns to zero upon stress removal, illustrating perfect elasticity. **C. Polymer Following the Maxwell Model (Spring and Dashpot in Series)** - Anticipate a combination of viscous flow and elastic recovery, where shear strain exhibits both immediate and time-dependent behavior. **D. More Realistic Viscoelastic Polymer** - Illustrate a complex time-dependent shear strain response that doesn’t immediately revert to the initial state upon stress removal, capturing both viscous and elastic characteristics. Each graph should distinctly highlight the unique mechanical behavior of the material type it represents, providing insight into their elastic and viscous properties. ---
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