The Laplace Virtual Fields Method for the direct extraction of viscoelastic properties of materials

Abstract

This work proposes a new method aiming at the direct identification of viscoelastic properties of materials with a Laplace formalism implemented in the Virtual Fields Method and named L-VFM. Using a single test, this formalism allows for a direct extraction of the different viscoelastic properties without any parametric description of their time dependency. The Laplace transform enables the use of theory of elasticity in the Laplace domain. The constitutive equations are expressed in the plane stress framework with the 2D plane stress stiffness coefficients. The conversion from the 2D plane stress stiffness coefficients to the bulk and shear moduli as well as Poisson’s ratio and Young’s modulus is realised in the Laplace domain. The inverse Laplace transform is then applied to these functions in order to obtain the temporal evolution of the material properties. The L-VFM changes the viscoelastic identification from a non-linear to a linear process.

Keywords

• Identification
• Virtual Fields Method
• Linear viscoelasticity
• Laplace transform
• Inverse Laplace transform