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Related Concept Videos

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Thermal Strain

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Thermal strain is a concept that arises when we consider how temperature changes affect structures. Unlike the conventional assumption that structures remain constant under load, real-world scenarios often involve temperature fluctuations that can significantly impact these structures. Consider a homogeneous rod with a uniform cross-section resting freely on a flat horizontal surface. If the rod's temperature increases, the rod elongates. This elongation is proportional to the temperature...
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Thermal expansion and Thermal stress: Problem Solving01:27

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San Francisco's Golden Gate Bridge is exposed to temperatures ranging from -15 °C to 40 °C. At its coldest, the main span of the bridge is 1275 m long. Assuming that the bridge is made entirely of steel, what is the change in its length between these temperatures?
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In a nonhomogeneous rod made up of steel and brass, restrained at both ends and subjected to a temperature change, several steps are involved in calculating the stress and compressive load. Due to the problem's static indeterminacy, one end support is disconnected, allowing the rod to experience the temperature change freely. Next, an unknown force is applied at the free end, triggering deformations in the rod's steel and brass portions. These deformations are then calculated and added...
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If the temperature of an object is changed while it is prevented from expanding or contracting, the object is subjected to stress. The stress is compressive if the object expands in the absence of constraint and tensile if it contracts. This stress resulting from temperature change is known as thermal stress. It can be quite large and can cause damage. To avoid this stress, engineers may design components so they can expand and contract freely. For instance, on highways, gaps are deliberately...
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Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
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Elastic Strain Energy for Shearing Stresses01:20

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As discussed in previous lessons, strain energy in a material is the energy stored when it is elastically deformed, a concept crucial in materials science and mechanical engineering. This energy results from the internal work done against the cohesive forces within the material. When a material undergoes shearing stress and corresponding shearing strain, the strain energy density, which is the energy stored per unit volume, is calculated. Within the elastic limit, where the stress is...
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On nonlinear thermo-electro-elasticity.

Markus Mehnert1, Mokarram Hossain2, Paul Steinmann1

  • 1Department of Applied Mechanics , University of Erlangen-Nuremberg , Paul-Gordan Strasse 3, 91052 Erlangen, Germany.

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Summary
This summary is machine-generated.

This study introduces a new model for electro-active polymers (EAPs) that accounts for temperature changes during operation. The framework helps predict material behavior under combined electrical, mechanical, and thermal loads.

Keywords:
electro-active polymerselectro-mechanical problemnonlinear elasticitythermo-electro-mechanical couplingthermo-mechanical problem

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Area of Science:

  • Materials Science
  • Polymer Physics
  • Thermodynamics

Background:

  • Electro-active polymers (EAPs) are widely used in sensors and actuators.
  • Polymeric materials are sensitive to temperature variations.
  • Maintaining constant temperature during EAP characterization is challenging due to internal heating under electrical loads.

Purpose of the Study:

  • To develop a constitutive framework for modeling thermo-electro-mechanical couplings in EAPs.
  • To ensure thermodynamic consistency in the constitutive equations.

Main Methods:

  • A constitutive framework based on the total energy approach was formulated.
  • Thermodynamically consistent constitutive equations were derived from fundamental laws of thermodynamics.
  • An analytical solution was obtained for the extension and inflation of a cylindrical tube.

Main Results:

  • The proposed framework successfully models the behavior of EAPs under coupled loads.
  • The results demonstrate the significant influence of thermo-electro-mechanical couplings on EAP performance.
  • The analytical solution provides insights into the complex interactions within the material.

Conclusions:

  • The developed thermo-electro-mechanically coupled framework is effective for analyzing EAP behavior.
  • Understanding these couplings is crucial for designing reliable EAP-based devices.
  • This work provides a foundation for further research into advanced EAP modeling.