Related Experiment Video
Updated: May 19, 2026
06:07
Studying Large Amplitude Oscillatory Shear Response of Soft Materials
Published on: April 25, 2019
Morpho-elastodynamics: the long-time dynamics of elastic growth
Rebecca Vandiver1, Alain Goriely
1Program in Applied Mathematics, BIO5 Institute, University of Arizona, Tucson, AZ, USA.
Journal of Biological Dynamics
|August 14, 2012
Summary
Elastic tissues grow and remodel, influencing their own mechanical states and further growth. This study models this complex feedback loop using nonlinear elasticity and dynamical systems theory for morphoelasticity.
Area of Science:
- Biomechanics
- Continuum Mechanics
- Mathematical Biology
Background:
- Elastic tissues exhibit complex growth and remodeling behaviors.
- Mechanical stresses significantly influence tissue development and shape.
- Existing models often simplify the dynamic interplay between growth and stress.
Purpose of the Study:
- To review theoretical results on growth laws in elastic tissues.
- To present a novel dynamical systems approach to morphoelasticity.
- To model the continuous evolution of growth and stress.
Main Methods:
- Review of existing theoretical frameworks for tissue growth.
- Formulation of morphoelasticity as a continuous dynamical process.
- Application of dynamical systems theory to analyze evolution laws.
Main Results:
- Established a theoretical basis for understanding stress-induced tissue growth.
- Developed a new dynamical model for morphoelastic evolution.
- Demonstrated the applicability of dynamical systems theory to these models.
Conclusions:
- Morphoelasticity can be effectively modeled as a dynamic process.
- The proposed dynamical systems approach offers new insights into tissue remodeling.
- This framework facilitates the study of complex feedback mechanisms in biological growth.
More Related Videos
Related Concept Videos
01:19Members Made of Elastoplastic Material
The behavior of elastoplastic materials under bending stresses, particularly in structural members with rectangular cross-sections, is crucial for predicting material responses and understanding failure modes. Initially, when a bending moment is applied, the stress distribution across the section follows Hooke's Law and is linear and elastic. This distribution means the stress increases from the neutral axis to the maximum at the outer fibers, up to the elastic limit.
As the bending moment...
As the bending moment...
01:18Residual Stresses in Bending
In the study of elastoplastic members subjected to bending moments, understanding the loading and unloading phases is crucial for assessing material behavior and structural integrity. During the loading phase, as the bending moment increases, the material initially responds elastically, adhering to Hooke's Law, where stress is directly proportional to strain. When the load exceeds the yield strength, plastic deformation occurs, resulting in permanent strain and deformation that remains even...
01:15Relation 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.
01:21Plastic Behavior
A material's elastic behavior is characterized by the disappearance of stress once the load is removed, allowing the material to return to its original state. However, when stress surpasses the yield point, yielding commences, marking the onset of plastic deformation or permanent set. This change from elastic to plastic behavior is influenced by the peak stress value and the duration before the load is removed. An intriguing observation occurs when a specimen is loaded, unloaded, and reloaded.
01:12Elasticity
Elasticity is the ability of an object to withstand the effects of distortion and to return to its original size and shape once the forces causing deformation are removed. When an elastic material deforms under the action of an external force, it experiences internal resistance to the deformation. However, if no external force is applied, it returns to its original state.
The elasticity of an object can be described by a stress-strain curve, which represents the relationship between stress...
The elasticity of an object can be described by a stress-strain curve, which represents the relationship between stress...
01:20Elastic Strain Energy for Shearing Stresses
As discussed in previous lessons, strain energy in a material is the energy stored when it is elastically deformed, a concept crucial in materials science and mechanical engineering. This energy results from the internal work done against the cohesive forces within the material. When a material undergoes shearing stress and corresponding shearing strain, the strain energy density, which is the energy stored per unit volume, is calculated. Within the elastic limit, where the stress is...