A non-second-gradient model for nonlinear elastic bodies with fibre stiffness.

Area of Science:

• Continuum Mechanics
• Solid Mechanics
• Material Science

Background:

• Previous models for finite-radius fiber stiffness relied on non-linear strain-gradient or Kirchhoff rod theories.
• These models often assumed zero-radius, flexible fibers and introduced couple stresses, which are not present in real non-polar solids.

Purpose of the Study:

• To develop a constitutive equation for non-linear non-polar elastic solids reinforced by embedded finite-radius fibers.
• To model fiber bending stiffness using classical continuum mechanics, avoiding second-gradient theory.

Main Methods:

• Developed a constitutive equation based on non-polar material theory.
• Modeled fiber bending resistance within the framework of classical continuum mechanics.
• Avoided the use of couple stresses and non-symmetric Cauchy stresses.

Main Results:

• Successfully developed a constitutive equation for non-linear non-polar elastic solids with embedded finite-radius fibers.
• The proposed model simplifies the mechanical behavior of fiber-reinforced composites.
• The model avoids the complexities and limitations of second-gradient theories.

Conclusions:

• The new model provides a more realistic and simpler approach to incorporating fiber bending stiffness.
• It offers an alternative to existing models that rely on more complex and potentially less applicable theories.
• This work advances the understanding of mechanical behavior in fiber-reinforced non-polar elastic materials.