Soft elasticity by domain formation in reinforced and magneto-active composites

Add to your list(s) Download to your calendar using vCal

• Pedro Ponte Castañeda, Department of Mechanical Engineering and Applied Mechanics and Graduate Program in Applied Mathematics and Computational Science, University of Pennsylvania,
• Friday 27 October 2023, 14:00-15:00
• Department of Engineering - LR5.

If you have a question about this talk, please contact Hilde Hambro.

Reinforced elastomeric composites with periodic microstructures can undergo both microscopic (pattern changing) and macroscopic (long wavelength) instabilities. This presentation is concerned with the response of magneto-active elastomeric composites after the possible development of a macroscopic instability, which have been previously characterized in terms of loss of strong ellipticity of the incremental homogenized response of the composite material and can also occur when the microstructures are random. Building on earlier work in the purely mechanical context, it is shown by means of a generalized Maxwell construction that the composite loses stability by the formation of lamellar domains, on a scale much larger than that of the fibers, and where the orientation of the fibers changes abruptly from domain to domain in a chevron-type pattern. Mathematically, this corresponds to the relaxation or quasiconvexification of the principal solution for the homogenized energy function and is associated with soft modes of deformation that can be controlled by externally applied magnetic fields. For analytical ease, we consider the application to simple laminate composites consisting of two isotropic neo-Hookean phases with linear magnetic responses and obtain estimates for the homogenized relaxed response under combined magneto-mechanical loadings. One important finding is that an externally applied magnetic field can be used to trigger the instability without the application of mechanical loads. Another very interesting finding is that there are perfectly soft modes of deformation where the deformation can be accommodated purely by appropriate changes in the domain microstructures — without changes in the applied stress. At the more theoretical level, it is found that strict global rank-one convexity of the principal solution is generally lost prior to local rank-one convexity, or strong ellipticity. This suggest a new definition of macroscopic instabilities in terms of loss of global rank-one convexity.

This talk is part of the Engineering - Mechanics Colloquia Research Seminars series.

This talk is included in these lists:

• All Talks (aka the CURE list)
• Cambridge University Engineering Department Talks
• Cambridge talks
• Centre for Smart Infrastructure & Construction
• Civil Engineering Talks
• Computational Continuum Mechanics Group Seminars
• Department of Engineering - LR5
• Engineering - Dynamics and Vibration Tea Time Talks
• Engineering - Mechanics Colloquia Research Seminars
• Engineering - Mechanics and Materials Seminar Series
• Engineering - Mechanics, Materials and Design (Div C) - talks and events
• Featured lists
• Interested Talks
• Lennard-Jones Centre external
• School of Technology
• Trust & Technology Initiative - interesting events
• bld31

Note that ex-directory lists are not shown.