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Related Concept Videos

Elasticity01:12

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Elasticity is the ability of an object to withstand the effects of distortion and to return to its original size and shape once the forces causing deformation are removed. When an elastic material deforms under the action of an external force, it experiences internal resistance to the deformation. However, if no external force is applied, it returns to its original state.
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Upon subjecting concrete to moderate or high uniaxial compressive or tensile stresses, the strain response is non-linear relative to the stress applied. As the stress is removed, the resulting stress-strain curve deviates from the original path traced during loading, creating a hysteresis loop, indicative of the concrete's non-linear and non-elastic properties. Typically, a material's modulus of elasticity, which is a measure of the material's stiffness, is inferred from the linear...
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Elastic Potential Energy01:01

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Elastic potential energy is the energy stored as a result of the deformation of an elastic object, such as the stretching of a spring. An object is elastic if it returns to its original shape and size after being deformed. 
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The quantity that describes the deformation of a body under stress is known as strain. Strain is given as a fractional change in either length, volume, or geometry under tensile, volume (also known as bulk), or shear stress, respectively, and is a dimensionless quantity. The strain experienced by a body under tensile or compressive stress is called tensile or compressive strain, respectively. In contrast, the strain experienced under bulk stress and shear stress is known as volume and shear...
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The concept of curvature in plane curves, crucial in structural engineering, defines how sharply a beam bends under load. This curvature is determined using the curve's first and second derivatives.
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Elastic Collisions: Introduction01:00

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An elastic collision is one that conserves both internal kinetic energy and momentum. Internal kinetic energy is the sum of the kinetic energies of the objects in a system. Truly elastic collisions can only be achieved with subatomic particles, such as electrons striking nuclei. Macroscopic collisions can be very nearly, but not quite, elastic, as some kinetic energy is always converted into other forms of energy such as heat transfer due to friction and sound. An example of a nearly...
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Deterministic interrelation between elastic moduli in critically elastic materials.

Hongryol Jeon1, Mahdi Sadjadi2, Varda F Hagh3

  • 1University of Illinois Urbana-Champaign, Department of Materials Science and Engineering, Urbana, Illinois 61801, USA.

Physical Review. E
|January 21, 2026
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Summary
This summary is machine-generated.

Critically elastic materials are created by removing constraints from parent systems. Their elastic moduli are universally related, allowing for deterministic selection of mechanical properties in simulations.

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Area of Science:

  • Materials Science
  • Solid Mechanics
  • Computational Physics

Background:

  • Critically elastic materials possess a single state of self-stress, distinguishing them from other materials.
  • Understanding the relationship between parent systems and critically elastic daughter systems is crucial for material design.

Purpose of the Study:

  • To demonstrate that critically elastic materials can be derived from parent systems with two states of self-stress through constraint removal.
  • To establish a universal functional form relating the elastic moduli of daughter systems to parent system properties.
  • To provide a framework for the deterministic selection of mechanical properties in critically elastic materials.

Main Methods:

  • Simulations of spring networks.
  • Simulations of soft sphere packings.
  • Analysis of constraint removal effects on material properties.

Main Results:

  • A universal functional form interrelates the elastic moduli of homogeneous and isotropic daughter systems.
  • The functional form is parametrized by the properties of the parent system.
  • Judicious selection of parent systems and constraint removal enables the tuning of moduli and Poisson's ratios.

Conclusions:

  • Critically elastic materials can be deterministically engineered by modifying parent systems.
  • The discovered universal relationship offers a powerful tool for designing materials with specific mechanical responses.
  • This framework facilitates the creation of versatile critically elastic materials with tailored properties.