October 22, 2024

Strain Limiting and Linear Model for Fracture in Elastic Body using Finite Element Method

This talk presents a mathematical description of the mode-I fracture boundary value problem in a relatively new class of elastic bodies. After introducing some basic notions about elasticity, a new nonlinear constitutive relation between stress and strain is derived. The balance of linear momentum yields a second-order quasilinear elliptic partial differential equation system.  A well-posed boundary value problem (BVP) will be derived for the case of an elastic body containing a single plane-strain fracture.  The BVP is discretized by a continuous Galerkin-type finite element method coupled with a Picard-type linearization. Finally, we present some interesting simulation results that show contrasts in the crack-tip strain singularity compared with the classical elasticity model. 

About the speaker

Mr. Saugata Ghosh has completed his masters from Indian Institute of Engineering Science and Technology (IIEST) in India. He has joined University of Texas Rio Grande Valley (UTRGV) this fall as a PhD Student, based out of the Edinburg campus. He has received the Presidential Research Fellowship starting in Fall 2023. His research interests are focused on computational mathematics.