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Relation between Poisson's ratio, Modulus of Elasticity and Modulus of Rigidity01:15

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Deformation occurs in axial and transverse directions when an axial load is applied to a slender bar. This deformation impacts the cubic element within the bar, transforming it into either a rectangular parallelepiped or a rhombus, contingent on its orientation. This transformation process induces shearing strain. Axial loading elicits both shearing and normal strains. Applying an axial load instigates equal normal and shearing stresses on elements oriented at a 45° angle to the load axis.
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The bulk modulus is a scientific term used to describe a material's resistance to uniform compression. It is the proportionality constant that links a change in pressure to the resulting relative volume change.
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The fineness modulus (FM) of aggregate is a numerical index that measures the coarseness or fineness of the particles. It is calculated by adding the cumulative percentages of aggregate retained on each of a specified series of sieves and dividing the sum by 100.
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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 dynamic modulus of elasticity assesses how a concrete structure deforms under impact or dynamic loads. It is typically higher than the static modulus of elasticity, measured under slow, steady loading conditions.
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Vertical Curve: Problem Solving01:23

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Vertical curves provide the transition between two roadway grades, ensuring safety, comfort, and functionality. Calculating elevations at specific stations along the curve involves several systematic steps based on the curve's geometry and provided design parameters.The vertical curve is defined by its length, grades, Point of Vertical Intersection (P.V.I.) location, and P.V.I. elevation. The stations of the Point of Vertical Curvature (P.V.C.), where the curve begins, and the Point of Vertical...
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Modulus Engineered Substrate With Vertical Soft Interconnects for Ultra-Stable Stretchable Multilayer Electronic

Wenbo Zhao1,2, Yifan Deng1, Binlong Deng3

  • 1Institute of Flexible Electronics, Northwestern Polytechnical University, Xi'an, China.

Advanced Materials (Deerfield Beach, Fla.)
|January 27, 2026
PubMed
Summary
This summary is machine-generated.

Engineered stretchable multilayer electronics overcome interfacial mismatch for enhanced wearable devices and soft robotics. This novel design achieves 800% strain and 4000 cycles, enabling advanced electronic skin and haptic systems.

Keywords:
modulus‐engineered substratesstabilitystretchabilitystretchable multilayer electronic systemsvertical interconnects

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Area of Science:

  • Materials Science
  • Mechanical Engineering
  • Electrical Engineering

Background:

  • Stretchable multilayer electronic systems are crucial for advanced wearable electronics, soft robotics, and human-machine interfaces.
  • Interfacial mechanical and electrical mismatch between components limits the stretchability and stability of current systems.

Purpose of the Study:

  • To develop a stretchable multilayer electronic system design that overcomes interfacial mismatch for high stretchability and stability.
  • To demonstrate the system's performance in practical applications like electronic skin and haptic systems.

Main Methods:

  • Combined modulus-engineered substrate with vertical soft interconnects.
  • Utilized homologous soft-bridge and rigid-island design to reduce modulus mismatch and improve interfacial bonding.
  • Employed raw/hybrid liquid metal-based vertical interconnects to mitigate Poisson effect and ensure stable connections.

Main Results:

  • Achieved a high stretchability limit of 800% strain.
  • Demonstrated high stability with over 4000 cycles at 100% strain.
  • Outperformed previously reported multilayered flexible electronic devices in stretchability and stability.

Conclusions:

  • The developed multilayer electronic system design offers significant improvements in stretchability and stability.
  • The system shows promise for applications in electronic skin for soft robots and wireless battery-integrated intelligent haptic systems.