On constitutive equations for anisotropic nonlinearly piezoelectric materials
type: Item
instance of: scholarly article
title: On constitutive equations for anisotropic nonlinearly piezoelectric materials
zbMATH Open document ID: 1222.80018
author: Melek Usal
author: Lokman Yünlü
published in: Mathematical \& Computational Applications
publication date: 2011-08-16T00:00:00Z
review text: Summary: The elastic-piezoelectric continuum is investigated theoretically and its non-linear constitutive equations are defined. The theory is formulated in the context of continuum electrodynamics. The solid medium is assumed to be nonlinear, homogeneous, compressible and isothermal, and to have elastic and piezoelectric anisotropy. Basic principles of modern continuum mechanics and balance equations of electrostatics have provided guidance and are determining in the process of this study. From the formulation belonging to the constitutive equations, it is observed that the symmetric stress and polarization are derived from a scalar-valued thermodynamic potential defined in calculations. As a result of thermodynamic constraints, it is determined that the free energy function is dependent on a symmetric tensor and a vector. The free energy function is represented by a power series expansion, and the type and number of terms taken into consideration in this series expansion determine the nonlinearity of the medium. Finally, the quasi-linear constitutive equations are substituted in the balance equations to obtain the field equations.
Mathematics Subject Classification ID: 80A20
Mathematics Subject Classification ID: 78A30
Mathematics Subject Classification ID: 74F15
zbMATH DE Number: 5939118
zbMATH Keywords: piezoelectric
zbMATH Keywords: continuum electrodynamics
zbMATH Keywords: constitutive equations
zbMATH Keywords: anisotropy
MaRDI profile type: Publication
full work available at URL: mca16040839
OpenAlex ID: W2367635474
DOI: 10.3390/MCA16040839
description: scientific article; zbMATH DE number 5939118