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Free Boundary Problems in Mechanics
October 23 - October 31
The course will cover basic principles behind the modeling and simulation of (coupled) free boundary problems. Free boundary problems (FBPs) form a coherent branch of science. They describe phenomena where interfaces or boundaries are free to move and they are ubiquitous in nature, engineering and science: crack growth, macroscopic phase changes are only a few examples. Most phenomena of practical engineering interest or of scientific relevance require addressing the behaviour of systems over a range of spatial and temporal scales. At some scale, materials become heterogeneous, or even discrete, and cannot be considered as continua. Evolving interfaces such as dislocations, cracks, contact surfaces, often associated with discontinuities, in the field of interest or its derivatives, have to be treated, usually in a multi-field/physics setting, including various unknown quantities such as temperature, pore pressure and mechanical fields. We attempt to provide a unified framework, to facilitate progress in this field of fundamental scientific importance and growing industrial relevance.
The intended learning outcomes of the course are such that the students will be:
- able to critically assess discretization schemes for free boundary problems
- able to implement simple error estimators for free boundary problems
- familiar with basic interface update and tracking methods
- able to follow basic literature in extended finite element methods, collocation methods and isogeometric discretization techniques
- aware of industrial applications based on real-world examples
About IIT Madras:
Indian Institute of Technology Madras is one among the foremost institutes of national importance in higher technological education, basic and applied research. In 1956, the German Government offered technical assistance for establishing an institute of higher education in engineering in India. The first Indo-German agreement in Bonn, West Germany for the establishment of the Indian Institute of Technology at Madras was signed in 1959.
The Institute was formally inaugurated in 1959 by Prof. Humayun Kabir, Union Minister for Scientific Research and Cultural Affairs. The IIT system has sixteen Institutes of Technology. The first of these to be instituted are at Kharagpur (estb. 1951), Mumbai (estb. 1958), Chennai (estb. 1959), Kanpur (estb. 1959), Delhi (estb. 1961), Guwahati (estb. 1994) and Roorkee (estb. 1847, joined IITs in 2001).
IIT Madras is a residential institute with nearly 550 faculty, 8000 students and 1250 administrative & supporting staff and is a self-contained campus located in a beautiful wooded land of about 250 hectares. It has established itself as a premier centre for teaching, research and industrial consultancy in the country.
The Institute has sixteen academic departments and a few advanced research centres in various disciplines of engineering and pure sciences, with nearly 100 laboratories organised in a unique pattern of functioning. A faculty of international repute, a brilliant student community, excellent technical & supporting staff and an effective administration have all contributed to the pre-eminent status of IIT Madras. The campus is located in the city of Chennai, previously known as Madras. Chennai is the state capital of Tamilnadu, a southern state in India.