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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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Related Experiment Video

Updated: Mar 6, 2026

The Mechanics of Poro-Elastic Contractile Actomyosin Networks As a Model System of the Cell Cytoskeleton
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Effective equations governing an active poroelastic medium.

J Collis1, D L Brown1, M E Hubbard1

  • 1School of Mathematical Sciences , University of Nottingham , University Park, Nottingham NG7 2RD, UK.

Proceedings. Mathematical, Physical, and Engineering Sciences
|March 16, 2017
PubMed
Summary
This summary is machine-generated.

This study derives effective equations for active poroelastic media, modeling coupled flow, deformation, and transport. The model captures finite growth and deformation at the pore scale, relevant for biological and industrial applications.

Keywords:
fluid–structure interactiongrowing mediamultiscale asymptoticsporoelasticity

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Area of Science:

  • Multiphysics
  • Continuum Mechanics
  • Chemical Engineering

Background:

  • Poroelastic media exhibit complex coupled phenomena.
  • Active materials respond to chemical stimuli with morphoelastic effects.
  • Understanding transport and deformation in these media is crucial for various applications.

Purpose of the Study:

  • To derive a homogenized model for active poroelastic media.
  • To develop effective equations for coupled flow, elastic deformation, and solute transport.
  • To incorporate microscopic structural details into macroscale models.

Main Methods:

  • Spatial homogenization of a coupled transport and fluid-structure interaction model.
  • Derivation of a Biot-type system augmented with growth terms.
  • Coupling the system with an advection-reaction-diffusion equation.

Main Results:

  • A system of homogenized partial differential equations for macroscale growth and transport.
  • Explicit incorporation of microscopic structure and dynamics.
  • The model admits finite growth and deformation at the pore scale.

Conclusions:

  • The derived effective model accurately describes active poroelastic behavior.
  • The model offers a unified framework for diverse applications including tissue growth and industrial processes.
  • Comparison with existing models under asymptotic limits validates the approach.