A Novel Mass Spring Model for Simulating Transversely Isotropic Materials Under In-plane Loading


ABSTRACT

Mass spring system (MSS) is a physically based spring network model consisting of point-masses or nodes for simulating deformable objects. Due to its simplicity and well understood dynamics, MSS has been extensively used for simulations in variety of applications such as cloth and soft tissue simulations, and simulation of crack propagation and fracture. Though MSS is approximate, it is computation-ally less taxing and hence, attractive for designing real-time simulations.
One of the major challenges in using MSS is determination of system parameters such as masses, spring stiffness, spring damping coefficients and mesh topology. Most of the proposed approaches presented in the literature, to address this issue are applicable to specific problems, or to a specific choice of system parameters. Also, MSS does not guarantee convergence to the correct solution with mesh refinement and fails to capture the shear deformation.

We present a novel square MSS topology that addresses these issues. The unit cell of the proposed MSS comprises of a square element with edge and diagonal springs. Additionally, we have incorporated shear springs to adequately capture the element deformation under shear loading.
The mesh parameters are determined based upon material properties, and are derived analytically through comparison of the deformation of the unit cell with a corresponding continuum element. We have verified our model using simulations of a beam and a plate under tensile and transverse loading for transversely isotropic materials. We have further obtained displacement and stress fields for beam and plate using the MSS model and observed that the results are in good agreement with finite element method (FEM) results under same boundary conditions.

This MSS model has been used to carry out the following investigations:

• Stress near crack tip and determination of SIF: The MSS was used to model a pre-cracked compact tension (C(T)) test specimen with homogenized properties for a glass/epoxy lamina and comparison of the results with FEM and QFM shows that the MSS model is capable of predicting stress situationnear the singularities such as the crack tip. Further, we applied the MSS model to determine the stress intensity factor (SIF) for a thin cracked plate subjected to tensile load using dimensionless compliance. We have shown that our model closely approximate the experimental and analytical results presented in literature.
• Modeling damage and crack propagation: We have proposed two damage criteria in order to simulate crack propagation in the proposed MSS, namely the maximum potential energy criteria and the maximum deformation criteria. We have experimentally determined fracture energy of buffalo cortical bone using Double cantilever beam (DCB) test and Compliance based beam method (CBBM). We have predicted the fracture energy using the MSS model for DCB and CBBM and observed that the results are in good agreement with the experimental results.
• Modeling of local material heterogeneity: The MSS model is further used to study the effect of local material heterogeneity wherein we have mod- eled in-plane tensile test specimen for glass/epoxy as a lamina with homogenized properties, and a fiber/matrix lamina with individual constituent mate- rial properties. We have shown that the MSS model is capable of predicting bulk behavior as well as local effects (such as stress concentration) due to presence of heterogeneities.