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A novel mass spring model for simulating deformable objects

Pradeepkumar Suryawanshi and Abhishek Gupta

Vol. 18 (2023), No. 2, 143–168

Mass-spring system (MSS) and finite element method (FEM) are extensively used methods for simulating deformable objects. Though MSS is approximate, it is computationally less taxing and hence attractive for performing real-time simulations. One of the major challenges in using MSS is the determination of system parameters such as node mass, spring stiffness, spring damping coefficients and mesh topology. Most of the proposed approaches to determine MSS model parameters are either application specific or limited to a specific choice of material properties. In this work, we present a square MSS topology that incorporates additional springs to ensure physically realistic simulations of orthotropic materials for plane stress (strain) problems. We provide a method to compute model parameters analytically using the properties of the material. The spring stiffnesses are determined by comparing the nodal displacements of a single MSS element with points of a corresponding continuum element. We have verified our model using simulations of a beam and a plate under different in–plane loading conditions. The displacement field obtained through these simulations is used to obtain the stress fields. To show its utility, the MSS is used to estimate dimensionless compliance and stress intensity factor for a compact tension specimen.

MSS, simulations, fracture, compliance, stress intensity factor
Received: 28 August 2021
Revised: 20 April 2022
Accepted: 21 May 2022
Published: 18 April 2023
Pradeepkumar Suryawanshi
Department of Mechanical Engineering
Don Bosco Institute of Technology
Abhishek Gupta
Department of Mechanical Engineering
Indian Institute of Technology