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Related Concept Videos

Thermal Strain01:19

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?
To solve the problem, first, identify the known and unknown quantities. The initial length (L) of the bridge is 1275 m, the coefficient of linear expansion (α) for steel is 12 x 10-6/°C, and the change in...
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Thermal Stress01:09

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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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Thermal Expansion01:22

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The expansion of alcohol in a thermometer is one of many commonly encountered examples of thermal expansion, which is the change in size or volume of a given system as its temperature changes. The most visible example is the expansion of hot air. When air is heated, it expands and becomes less dense than the surrounding air, which then exerts an upward force on the hot air to, for example, make steam and smoke rise, and hot air balloons float. The same behavior happens in all liquids and gases,...
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The work done by a thermodynamic system depends not only on the initial and final states but also on the intermediate states—that is, on the path. Like work, when heat is added to a thermodynamic system, it undergoes a change of state, and the state attained depends on the path from the initial state to the final state. Consider an ideal gas cylinder fitted with a piston. When the cylinder is heated at a constant temperature, the gas molecules absorb energy and expand slowly in a...
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Temperature Dependent Deformation01:12

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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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Generic Elasticity of Thermal, Underconstrained Systems.

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Athermal systems gain rigidity from strain, a phenomenon extended to finite temperatures. This study reveals how entropic and energetic rigidity interact, explaining temperature-dependent elastic properties in diverse materials.

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Area of Science:

  • Soft matter physics
  • Materials science
  • Statistical mechanics

Background:

  • Athermal (zero-temperature) underconstrained systems exhibit unique mechanical properties, becoming rigid under external strain.
  • Existing theories well-explain the strain-induced rigidity at zero temperature.
  • Extending these theories to finite temperatures is crucial for understanding real-world material behavior.

Purpose of the Study:

  • To extend the theory of underconstrained systems from athermal to finite temperatures.
  • To derive first-principles expressions for elastic properties (tension and shear modulus) as functions of temperature and strain.
  • To provide a unified theoretical framework for diverse underconstrained systems.

Main Methods:

  • Theoretical derivation from first principles near the athermal transition point.
  • Numerical confirmation of derived expressions.
  • Analysis of system microstructure to determine key parameters.

Main Results:

  • Derived expressions for isotropic tension (t) and shear modulus (G) dependent on temperature (T), isotropic strain (ϵ), and shear strain (γ).
  • Identified three key parameters: entropic rigidity (κS), energetic rigidity (κE), and a strain interaction parameter (bϵ).
  • Demonstrated that entropic and energetic rigidity act in series, explaining the observed scaling relation t∼G∼T^{1/2} at zero strain.

Conclusions:

  • The developed theory successfully unifies the physics of various underconstrained systems, including polymer networks, membranes, and biological tissues.
  • The findings provide a simple explanation for the temperature dependence of elastic properties in these systems.
  • The three-parameter model offers a powerful tool for predicting and understanding the mechanical behavior of underconstrained materials.