A method for calculating differential constitutive equation of linear viscoelastic composite model

Area of Science:

• Materials Science
• Mechanical Engineering
• Rheology

Background:

• Viscoelastic materials exhibit time-dependent stress-strain behavior.
• Modeling these materials often involves combinations of springs and dampers.
• Accurate constitutive equations are crucial for simulating material responses.

Purpose of the Study:

• To develop a systematic method for deriving differential constitutive equations for complex viscoelastic models.
• To provide a framework for accurately simulating the behavior of engineering materials.

Main Methods:

• Representing general viscoelastic models as combinations of Kelvin units.
• Transforming the viscoelastic model into a digraph.
• Utilizing digraph properties (independent paths, closed enclosures) and incidence matrices.
• Applying block matrix operations to obtain constitutive equation coefficients.

Main Results:

• A method to derive the differential constitutive equation for any spring-damper viscoelastic model.
• The derivation process is transformed into incidence matrix operations.
• Coefficients of the linear differential operator are obtainable via block matrix operations.

Conclusions:

• The proposed method offers a systematic approach to constructing accurate viscoelastic models.
• This technique is suitable for computer programming, aiding in engineering applications.
• The method enhances the precision of simulating engineering material viscoelasticity.