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Solids in which the atoms, ions, or molecules are arranged in a definite repeating pattern are known as crystalline solids. Metals and ionic compounds typically form ordered, crystalline solids. A crystalline solid has a precise melting temperature because each atom or molecule of the same type is held in place with the same forces or energy. Amorphous solids or non-crystalline solids (or, sometimes, glasses) which lack an ordered internal structure and are randomly arranged. Substances that...
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Particles in a solid are tightly packed together (fixed shape) and often arranged in a regular pattern; in a liquid, they are close together with no regular arrangement (no fixed shape); in a gas, they are far apart with no regular arrangement (no fixed shape). Particles in a solid vibrate about fixed positions (cannot flow) and do not generally move in relation to one another; in a liquid, they move past each other (can flow) but remain in essentially constant contact; in a gas, they move...
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Printing Non-Euclidean Solids.

Giuseppe Zurlo1, Lev Truskinovsky2

  • 1School of Mathematics, Statistics and Applied Mathematics, NUI Galway, University Road, Galway, Ireland.

Physical Review Letters
|January 18, 2018
PubMed
Summary
This summary is machine-generated.

Geometrically frustrated solids, crucial in biology and technology, can be precisely engineered through surface growth. This method ensures specific system behaviors under physiological conditions, with applications in 3D printing arteries and explosive plants.

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Area of Science:

  • Solid Mechanics
  • Materials Science
  • Biophysics

Background:

  • Geometrically frustrated solids with non-Euclidean metrics are common in nature and technology.
  • Surface mass accretion is a key mechanism for achieving targeted configurations of incompatibility in these solids.

Purpose of the Study:

  • To investigate how incompatible surface growth mechanics can fine-tune geometrical frustration.
  • To demonstrate the potential for controlling system behavior under physiological or working conditions.

Main Methods:

  • Utilizing the mechanics of incompatible surface growth.
  • Developing explicit 3D printing protocols for biological and engineered systems.

Main Results:

  • Geometrical frustration can be precisely controlled during deposition to achieve desired system behaviors.
  • An explicit 3D printing protocol for arteries ensures stress uniformity under inhomogeneous loading.
  • A protocol for explosive plants allows complete release of residual elastic energy via a single cut.
  • Topological (global) components of incompatibility are essential for achieving physiological targets in both examples.

Conclusions:

  • Incompatible surface growth offers a powerful method for engineering geometrically frustrated solids.
  • This approach has significant implications for designing functional biological constructs and advanced materials.