Fundamental formulation for residual stress and inhomogeneous inclusion problems

Part of Lunchtime School of Engineering Seminar Series

Abstract of the talk:

Residual stress phenomena and inclusions are found in almost all engineering materials, including composites, alloys, biomaterials, and they are essential to ensure good strength and toughness, so it’s very important to understand how they work. This talk is comprised of two parts:

1. The residual-stress-toughening problem, one of typical residual stress problems, is addressed in the framework of plane strain. In this part, the fundamental solution for a concentrated strain nucleus located in an infinite plane is derived and its applications for residual stress problems are demonstrated. This part is directly related to homogenous inclusion problems.
2. Based on this first part, we propose the principle of equivalent eigenstrain for inhomogeneous inclusion problems. It allows calculating the elastic deformation of an arbitrarily connected and shaped inhomogeneous inclusion, by replacing it with an equivalent homogeneous inclusion problem. The approach allows solving the problems about inclusions of arbitrary shape, multiple inclusion problems, and lends itself to residual stress analysis in non-uniform, heterogeneous media.

The fundamental formulation introduced here have applications in the mechanics of composites, inclusions, phase transformation analysis, plasticity, fracture mechanics and many other areas.

Speaker

Professor Lifeng Ma, Department of Mechanics, Xi'an Jiaotong University

Hosted by

School of Engineeering

Venue

FN185, Fraser Noble building