Constructing Continuous Strain and Stress Fields from Spatially Discrete Displacement Measurements in Soft Materials

Abstract

Recent studies show that particle tracking together with moving least-square (MLS) method is capable to interpolate displacement field and to determine strain and stress fields from discrete displacement measurements in soft materials. The goal of this study is to evaluate of the numerical accuracy of MLS in determining the displacement, strain and stress fields in soft materials. Using an indentation example as the benchmark, we extracted the discrete displacements data from a finite element model and used it as the input to MLS. We assessed the accuracy of MLS by comparing displacement, strain and stress fields from MLS with the corresponding results from finite element analysis (FEA). For the indentation model, we also finished a parametric study and had some understanding towards how the parameters affect the accuracy of MLS. Based on the guideline about the effect of parameters, we applied the MLS method to two other cases with stress concentration: a plate with a circular cavity subjected to large uni-axial stretch and a plane stress crack under large Mode-I loading. The results demonstrated the capability of MLS to measure large deformation and stress concentration within soft materials.