On Modeling, Analytical Study and Homogenization for Smart Materials

Timofte, Aida

doi:10.1142/9789812706874_0017

Topics on Mathematics for Smart Systems 2007

DOI: 10.1142/9789812706874_0017

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On Modeling, Analytical Study and Homogenization for Smart Materials

Aida Timofte¹

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2011

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A doubly nonlinear problem associated with a mathematical model for piezoelectric material behavior

Kraynyukova

Alber

2011

Z Angew Math Mech

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We consider a mathematical model, which describes piezoelectric material behavior. This model is similar to models of plasticity theory. However, piezoelectric models describe coupled mechanical and electrical material behavior. Therefore they contain additional nonlinearities in the piezoelectric tensor and in the enthalpy function, which is non quadratic. These nonlinearities cause difficulties in the proof of existence theorems. Under the assumption that the piezoelectric tensor is constant (i.e. independent of P ), we show how the system of model equations can be reduced to a doubly nonlinear evolution equation of the form zt ∈ G(−Mz − Φ(z) + f ), which contains a composition of two monotone operators. The monotone mapping G is a subdifferential of the indicator function of some convex set while the second monotone mapping Φ is the Nemyckii operator of a monotone function. We prove existence of strong solutions, if Φ is replaced by a regularization. If in addition Φ is Lipschitz continuous we can show that the solution is unique.

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A doubly nonlinear problem associated with a mathematical model for piezoelectric material behavior

Kraynyukova

Alber

2011

Z Angew Math Mech

View full text Add to dashboard Cite

show abstract

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On Modeling, Analytical Study and Homogenization for Smart Materials

Cited by 1 publication

References 17 publications

A doubly nonlinear problem associated with a mathematical model for piezoelectric material behavior

A doubly nonlinear problem associated with a mathematical model for piezoelectric material behavior

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