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Title: On a new variational and computational framework for polyconvex nonlinear continuum mechanics and convex multi-variable nonlinear electro-elasticity
Author: Ortigosa Martinez, Rogelio
ISNI:       0000 0004 6497 9991
Awarding Body: Swansea University
Current Institution: Swansea University
Date of Award: 2016
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The world of smart materials has experienced a dramatic revolution in the last decades. Electro Active and Magneto Active Materials are some of the most iconic of these, among which, dielectric and magnetostrictive elastomers are becoming extremely popular due to their outstanding actuation capabilities, and in lesser degree, to their energy harvesting capabilities. A clear example illustrating these extraordinary capabilities has been reported in the experimental literature, which has shown unprecedented extreme electrically induced deformations for the most representative dielectric elastomer, namely the acrylic elastomer VHB 4910.This thesis is focused on the development of well-posed constitutive models for nonlinear electro-elasticity in scenarios characterised by extreme deformations and extreme electric fields. This fundamental objective represents the underlying ingredient for the novel variational and computational frameworks developed hereby in the context of electro-elasticity. Very remarkably, the similarity between the equations in both electro-elasticity and magneto-elasticity, enables the variational and computational frameworks developed to be extended to the latter scenario, characterised by magnetomechanical interactions. Despite the enormous interest of the experimental and computational scientific community, the definition of suitable constitutive models is still at its early stages for both electro and magneto active materials. In the more specic context of elasticity, considerable effort has been devoted to the denition of polyconvex energy functionals, which entail the most widely accepted constitutive restriction, namely the ellipticity or Legendre-Hadamard condition. This condition, strongly related to the material stability of the constitutive equations, ensures the well-posedness of the governing equations. An extension of the ellipticity condition to the context of nonlinear electro-elasticity and hence, magneto-elasticity, is proposed in this work, ensuring the well-posedness of the equations for the entire range of deformations and electric or magnetic fields. It is important to emphasise that in this work, the extension of the ellipticity condition to the field of electro-elasticity is exclusively based on material stability considerations. The energy functional encoding the constitutive response of the electro active material is defined according to a novel convex multi-variable representation in terms of an extended set of arguments which ensures material stability. The extended set of arguments, including those characterising the concept of polyconvexity in the more specic scenario of nonlinear elasticity, is further enriched with additional electromechanical entities. Unfortunately, proof of sequential weak lower semicontinuity of the proposed definition of multi-variable convexity is not provided in this work. This condition, and the additional requirement of appropriate coercivity conditions on the energy functional, would ensure the existence of minimisers. Nevertheless, although of extreme relevance and scientific interest, this topic is not in the scope of the thesis and could be the objective of further research.
Supervisor: Gil, Antonio J. Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral