Extracting elastic constitutive parameters using the VFM within peridynamics

Abstract

This paper implements the Virtual Fields Method within the ordinary state based peridynamic framework to identify material properties. The key equations derived in this approach are based on the principle of virtual works written under the ordinary state based peridynamic formalism for two-dimensional isotropic linear elasticity. In-house codes including a minimization process have also been developed to implement the method. A three-point bending test and two independent virtual fields arbitrarily chosen are used as a case study throughout the paper. The numerical validation of the virtual fields method has been performed on the case study by simulating the displacement field by finite element analysis. This field has been used to extract the elastic material properties and compared them to those used as input in the finite element model, showing the robustness of the approach. Noise analysis and the effect of the missing displacement fields on the specimen’s edges to simulate digital image correlation limitations have also been studied in the numerical part. This work focuses on pre-damage properties to demonstrate the feasibility of the method and provides a new tool for using full-field measurements within peridynamics with a reduced calculation time as there is no need to compute the displacement field. Future works will deal with damage properties which is the main strength of peridynamics.

Extracting Constitutive Mechanical Parameters in Linear Elasticity Using the Virtual Fields Method Within the Ordinary State-Based Peridynamic Framework

“…The VFM within PD has been derived to extract the elastic properties of a linearly isotropic material. Open-source python codes [18,19] including a minimization process have also developed to implement the PD-VFM. Contrary to most other approaches existing in the PD literature, one of the benefits of the PD-VFM is that no computation of the displacement field during the minimization process is required.…”

“…Several algorithms were evaluated [46] to improve the accuracy of the discretization using partial areas taking into account the fraction that is outside the horizon. The most common is the PA-PDLAMMPS algorithm [42] which has been implemented in the code [19] presented in Section 5.…”

“…21a using the trial material properties and u. For this step, the in-house state-based PD code PeriPyDIC [19] is used with the 2D constitutive modeling described in Section 2.2.3). Note that instead of solving a direct problem in which the displacement field is computed from the boundary conditions, here the dual force density f v is evaluated from a provided displacement field.…”