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Related Concept Videos

Transformation of Plane Strain01:12

Transformation of Plane Strain

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When analyzing elongated structures like bars subjected to uniformly distributed loads, it is essential to understand the transformation of plane strain when coordinate axes are rotated. This transformation helps to assess how material deformation characteristics vary with orientation, which is crucial in materials science and structural engineering.
Under plane strain conditions, typical for members where one dimension significantly exceeds the others, deformations and resultant strains are...
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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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Elastic Strain Energy for Normal Stresses01:22

Elastic Strain Energy for Normal Stresses

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Strain energy quantifies the energy stored within a material due to deformation under loading conditions, a fundamental concept in materials science and engineering. The strain energy can be modeled when a material is subjected to axial loading with uniformly distributed stress. In this scenario, the stress experienced by the material is the internal force divided by the cross-sectional area, and the strain induced is directly proportional to this stress through the modulus of elasticity.
If...
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Plastic Deformations01:14

Plastic Deformations

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It is essential to understand how structural members behave under plastic deformation when the bending stress exceeds the material's yield strength. This state of deformation permanently alters the shape of the member, in contrast to the linear elastic behavior observed before yielding. The strain at any point in the member is expressed in terms of maximum strain. Notably, the neutral axis, which coincides with the centroid during elastic bending, shifts away from the centroid under plastic...
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Three-Dimensional Analysis of Strain01:29

Three-Dimensional Analysis of Strain

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Three-dimensional strain analysis is crucial for understanding how materials deform under stress, particularly in elastic, homogeneous materials. This method employs principal stress axes to simplify complex stress states into more understandable forms. Subjected to stress, a small cubic element within a material either expands or contracts along these axes, transforming into a rectangular parallelepiped. This transformation effectively illustrates the material's deformation. The principal...
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Measurements of Strain01:27

Measurements of Strain

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Strain quantifies the deformation of a material under force, typically measured as normal strain, which represents the change in length when compared with the original length. Electrical strain gauges are used for enhanced accuracy. These devices consist of a conductive wire mounted on a paper backing that adheres to the material's surface. These gauges operate on the piezoresistive effect, where the wire's electrical resistance changes in response to mechanical deformation. The strain...
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Updated: Jan 5, 2026

Measuring Local Tissue Strains in Tendons via Open-Source Digital Image Correlation
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Geometric localization in supported elastic struts.

T C T Michaels1, R Kusters2,3, A J Dear1

  • 1Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, USA.

Proceedings. Mathematical, Physical, and Engineering Sciences
|October 16, 2019
PubMed
Summary
This summary is machine-generated.

Localized deformations emerge in semi-flexible filaments on shearable substrates due to growth and shear. This study quantifies how mechanics and growth control these patterns, with applications in materials science.

Keywords:
elasticitylocalizationpattern formation

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Area of Science:

  • Mechanics of Materials
  • Materials Science
  • Biophysics
  • Morphogenesis

Background:

  • Localized deformation patterns are crucial in biological development (morphogenesis).
  • These patterns have emerging applications in materials science and engineering, such as in mechanical memories.
  • Understanding the fundamental principles governing localized deformations is key for designing advanced materials.

Purpose of the Study:

  • To investigate the emergence of spatially localized deformations in a minimal mechanical system.
  • To explore the impact of growth and shear on the conformation of a semi-flexible filament attached to a shearable substrate.
  • To quantify the interplay between geometry, mechanics, and growth in creating localized structures.

Main Methods:

  • Numerical simulations using a discrete rod model.
  • Theoretical analysis of differential equations in the continuum limit.
  • Experimental validation using a 3D-printed multi-material model system.

Main Results:

  • Spatially localized deformations arise along the filament under conditions of intermediate shear modulus and increasing growth.
  • Scaling laws were derived to quantify the relationship between system parameters and deformation patterns.
  • Experimental results confirmed the ability to regulate localized strain texture by controlling shear and growth.

Conclusions:

  • Growth and shear are critical factors in generating localized deformations in filament-substrate systems.
  • The findings provide quantitative insights into the mechanics of localized pattern formation.
  • This research offers a pathway for externally controlling strain localization in engineered materials.