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Upon subjecting concrete to moderate or high uniaxial compressive or tensile stresses, the strain response is non-linear relative to the stress applied. As the stress is removed, the resulting stress-strain curve deviates from the original path traced during loading, creating a hysteresis loop, indicative of the concrete's non-linear and non-elastic properties. Typically, a material's modulus of elasticity, which is a measure of the material's stiffness, is inferred from the linear...
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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 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.
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Viscoelasticity using reactive constrained solid mixtures.

Gerard A Ateshian1

  • 1Columbia University, Department of Mechanical Engineering, 500 West 120th Street, MC4703, New York, NY 10027, USA.

Journal of Biomechanics
|March 12, 2015
PubMed
Summary
This summary is machine-generated.

This study introduces a new viscoelasticity framework using bond dynamics. It models how strong and weak bonds break and reform, offering a new way to understand material behavior under stress.

Keywords:
Mixture theoryReaction kineticsSoft tissue mechanicsViscoelasticity

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Area of Science:

  • Continuum Mechanics
  • Materials Science
  • Biophysics

Background:

  • Viscoelasticity describes materials exhibiting both viscous and elastic characteristics.
  • Modeling nonlinear viscoelasticity, especially in biological tissues, remains a challenge.
  • Existing models often lack a clear link between microscopic bond behavior and macroscopic response.

Purpose of the Study:

  • To develop a novel constitutive framework for viscoelasticity based on bond dynamics.
  • To incorporate the breaking and reformation of weak bonds into a free energy density function.
  • To provide a model applicable to large deformations in soft biological tissues.

Main Methods:

  • Formulating free energy density based on strong and weak bond energies.
  • Treating weak bond dynamics as a reaction governed by mass balance.
  • Using evolving weak bond mass content as observable state variables.
  • Ensuring thermodynamic consistency via the Clausius-Duhem inequality.

Main Results:

  • The framework yields a strain energy density function dependent only on observable variables.
  • It allows separation of contributions from strong and weak bonds.
  • The model reduces to classical linear viscoelasticity in the limit of small strains.
  • For large strains, it offers distinct predictions compared to classical quasilinear viscoelasticity.

Conclusions:

  • The proposed reactive framework provides a unified approach to viscoelasticity.
  • It accurately models nonlinear behavior and large deformations in soft tissues.
  • This formulation enhances the understanding and prediction of complex material responses.