Effective Properties of Homogenised Nonlinear Viscoelastic Composites

Area of Science:

• Composite Materials Science
• Nonlinear Mechanics
• Viscoelasticity Theory

Background:

• Calculating effective properties of composite materials is crucial for predicting their behavior.
• Nonlinear viscoelasticity presents significant challenges due to time-dependent and strain-dependent responses.
• Existing methods often struggle with the complexity of nonlinear viscoelastic composite systems.

Purpose of the Study:

• To develop a general and robust computational approach for effective properties of nonlinear viscoelastic composites.
• To adapt the asymptotic homogenization technique for nonlinear viscoelastic materials.
• To provide a framework for analyzing fiber-reinforced composites with memory effects.

Main Methods:

• Utilized asymptotic homogenization to decouple equilibrium equations into local problems.
• Specialized the theoretical framework for Saint-Venant strain energy density and a memory contribution in the stress tensor.
• Employed the Laplace transform and correspondence principle for infinitesimal displacements.
• Derived classical cell problems and sought analytical solutions for anti-plane problems.

Main Results:

• Obtained classical cell problems applicable to linear viscoelastic composites.
• Developed analytical solutions for anti-plane cell problems in fiber-reinforced composites.
• Computed effective coefficients by defining various constitutive laws for memory terms.

Conclusions:

• The developed method offers a general approach for computing effective properties of nonlinear viscoelastic composites.
• The study successfully adapted asymptotic homogenization for nonlinear viscoelasticity, yielding analytical solutions for specific cases.
• Results were validated against existing data, confirming the method's efficacy.