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Related Concept Videos

Space Trusses01:25

Space Trusses

A space truss is a three-dimensional counterpart of a planar truss. These structures consist of members connected at their ends, often utilizing ball-and-socket joints to create a stable and versatile framework. The space truss is widely used in various construction projects due to its adaptability and capacity to withstand complex loads.
At the core of a space truss lies the fundamental unit known as the tetrahedron. This structure is composed of six members that form a three-dimensional shape...
Space Trusses: Problem Solving01:29

Space Trusses: Problem Solving

A space truss is a three-dimensional counterpart of a planar truss. These structures consist of members connected at their ends, often utilizing ball-and-socket joints to create a stable and versatile framework. Due to its adaptability and capacity to withstand complex loads, the space truss is widely used in various construction projects.
Consider a tripod consisting of a tetrahedral space truss with a ball-and-socket joint at C. Suppose the height and lengths of the horizontal and vertical...
Relation between Poisson's ratio, Modulus of Elasticity and Modulus of Rigidity01:15

Relation between Poisson's ratio, Modulus of Elasticity and Modulus of Rigidity

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.
Simple Trusses01:21

Simple Trusses

A truss is a structural framework consisting of slender members connected at joints, designed to support external loads while minimizing material usage and weight. Simple trusses are a type of planar truss where all members lie within a single two-dimensional plane.
The most basic planar truss is a simple truss with three members arranged in a triangular formation. This triangular truss is inherently stable and rigid due to its geometry, making it an ideal starting point for creating more...
Stress: General Loading Conditions01:15

Stress: General Loading Conditions

To grasp the intricacy of real-world conditions where multiple loads are applied simultaneously to a structure, one might visualize a section passing through a specific point within a body, aligned parallel to the xy plane. This section is subjected to various forces, including original loads, normal forces, and shearing forces.
The shearing force, possessing potential directionality within the plane of the section, is simplified into two component forces running parallel to the x and y axes.
Stability of structures01:14

Stability of structures

In mechanical engineering, the stability of systems under various forces is critical for designing durable and efficient structures. One fundamental way to explore these concepts is by analyzing systems like two rods connected at a pivot point, O, with a torsional spring of spring constant k at the pivot point. This system is similar in appearance to a scissor jack used to change tires on a car. In this case, the arms of the linkage (equivalent to the rods in this system) are entirely vertical,...

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Subject-specific Musculoskeletal Model for Studying Bone Strain During Dynamic Motion
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Published on: April 11, 2018

Stress-dependent morphogenesis: continuum mechanics and truss systems.

José J Muñoz1, Vito Conte, Mark Miodownik

  • 1Department of Applied Mathematics III, Universitat Polit. Catalunya, Barcelona, Spain. j.munoz@upc.edu

Biomechanics and Modeling in Mechanobiology
|January 14, 2010
PubMed
Summary

Cell shape changes are controlled by internal remodeling and growth, driven by stress. This model explains how cellular stress alone can drive complex processes like embryonic development.

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Area of Science:

  • Biophysics
  • Cell Biology
  • Developmental Biology

Background:

  • Cellular shape and internal architecture are crucial for biological functions.
  • Existing models often overlook the role of internal stress in cell remodeling and growth.

Purpose of the Study:

  • To derive equilibrium equations for stress-controlled cell shape change.
  • To model the interplay between active growth and passive hyperelasticity in cells.
  • To investigate the role of internal stress in embryonic development, specifically ventral furrow invagination.

Main Methods:

  • Decomposition of the deformation gradient into active (growth) and passive (hyperelastic) components.
  • Coupling of these components via a feedback control function.
  • Derivation of balance equations for general continua using a variational approach.
  • Application to a truss system simulating cytoskeletal networks (myosin microfilaments and microtubules).
  • Simulation of multicellular shape changes during Drosophila melanogaster ventral furrow invagination.

Main Results:

  • The derived equilibrium equations accurately describe stress-controlled cell shape changes.
  • The model confirms that ventral furrow invagination can occur solely through stress control, independent of other signaling mechanisms.
  • The yolk's role in invagination is clarified, highlighting its incompressibility constraint and feedback-generated pressure in the ventral epithelium.
  • Thermodynamic consistency conditions for the formulation were investigated.

Conclusions:

  • Cellular shape changes can be effectively modeled and understood through stress control mechanisms.
  • Internal cellular stress plays a significant role in developmental processes like embryonic invagination.
  • The model provides new insights into the biomechanics of cell remodeling and embryonic development.