What is Modulus of Resilience - Definition

The modulus of resilience, Ur, which is defined as the maximum energy that can be absorbed per unit volume without creating a permanent distortion.

In materials science, resilience is the ability and the capacity of a material to absorb energy when it is deformed elastically and then, upon unloading, to recover this amount of energy. The maximum energy that can be absorbed up to the elastic limit, without creating a permanent deformation is known as proof resilience. In the stress-strain curve, it is given by the area under the portion of a stress–strain curve (up to yield point).

Under assumption of linear elasticity or up to proportional limit, resilience can be calculated by integrating the stress–strain curve from zero to the proportional limit.

The associated property is the modulus of resilience, Ur, which is defined as the maximum energy that can be absorbed per unit volume without creating a permanent distortion. It is the strain energy per unit volume required to stress a material from an unloaded state up to the point of yielding. This analysis is not valid for non-linear elastic materials like rubber, for which the approach of area under the curve till elastic limit must be used.

Thus, resilient materials are those having high yield strengths and low moduli of elasticity such alloys are used in spring applications. The energy expended in deforming the spring is stored in it and can be recovered when the spring returns to its original shape.

References:

Materials Science:

U.S. Department of Energy, Material Science. DOE Fundamentals Handbook, Volume 1 and 2. January 1993.
U.S. Department of Energy, Material Science. DOE Fundamentals Handbook, Volume 2 and 2. January 1993.
William D. Callister, David G. Rethwisch. Materials Science and Engineering: An Introduction 9th Edition, Wiley; 9 edition (December 4, 2013), ISBN-13: 978-1118324578.
Eberhart, Mark (2003). Why Things Break: Understanding the World by the Way It Comes Apart. Harmony. ISBN 978-1-4000-4760-4.
Gaskell, David R. (1995). Introduction to the Thermodynamics of Materials (4th ed.). Taylor and Francis Publishing. ISBN 978-1-56032-992-3.
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J. R. Lamarsh, A. J. Baratta, Introduction to Nuclear Engineering, 3d ed., Prentice-Hall, 2001, ISBN: 0-201-82498-1.

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Resilience

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