Porosity strongly influences the electromechanical properties of Barium Titanate (BaTiO3, BTO) ceramics. Although porosity is generally associated with performance degradation, controlled nanoscale porosity can be exploited to tailor or even enhance specific functional properties. However, establishing a quantitative relationship between pore architecture and the macroscopic electromechanical response remains challenging. In this work, we developed a multiscale computational framework that combines molecular dynamics (MD) simulations with Mori–Tanaka (MT) micromechanical homogenization to directly link pore architecture to macroscopic electromechanical properties. First, MD simulations were performed to determine the effective elastic, piezoelectric, and dielectric tensors of nanoporous BTO with varying pore configurations and porosity levels. These atomistically derived properties were subsequently incorporated into the MT homogenization model to predict the macroscopic electromechanical behaviour. The results show that increasing porosity systematically reduces elastic stiffness. However, the dielectric and piezoelectric responses exhibit a non-monotonic dependence on pore architecture. A more uniform distribution of smaller nanopores not only mitigates stiffness degradation by more than a factor of three but also enhances the dielectric and piezoelectric responses. In particular, the piezoelectric stress coefficient e33 can be increased by up to 24% at 5% porosity, while the average relative dielectric permittivity εavgr can be increased by up to 31% at 10% porosity compared with dense BTO. Overall, the proposed multiscale framework provides a systematic route for establishing quantitative structure–property relationships in nanoporous BTO, thereby guiding the design of porous piezoelectric materials for sensing, actuation, and energy-harvesting applications.

In this paper, mathematical modeling and numerical formulations are developed to predict the overall behavior of fractional visco-electroelastic composites. The modeling is based on Riemann-Liouville's fractional derivative formulation, Carson-Laplace transform, the frequency Green's functions, and integral equation formulations. The micro-macro modeling is elaborated for various heterogeneous visco-electroelastic composites. The inclusion problem and a micromechanical method are used to obtain the localization and the concentration tensors expressions. The block decomposition procedure is used to address the draw-back of the ill-conditioned problem caused by the localization tensor inverses. The effective fractional visco-electroelastic behavior is expressed based on the regularized concentration tensor and the Mori-tanaka method. Numerical results of effective fractional visco-electroelastic properties are obtained and examined for various fractional parameter, volume fraction and shapes of inclusions in frequency domain.

In this paper, a mathematical modeling of energy harvesting obtained from the dynamic response of a beam with an homogenized piezoelectric composite patch subjected to a moving load is investigated. A micromechanical model is used to predict the piezoelectric composites with optimized homogenized properties to be used in the considered energy harvester. The differential quadratic method (DQM) coupled with an implicit time scheme are elaborated for the spatial and time discretizations to numerically solve the resulting partial differential equations. The generated electric power from the homogeneous piezo-composite patches is evaluated based on the root mean square (RMS). The numerical results demonstrate the effect of piezo-composite material on the RMS estimated.

In this paper, integral equation formulations and field-dependent micromechanical modeling of global nonlinear magneto-mechanical behavior of magneto-elastic composites under high strain and magnetic field are elaborated. The modeling is obtained based on an extension of micro–macro transition inclusion problem to nonlinear behavior using field-dependent and highly nonlinear localization tensors. A methodological procedure is elaborated based on newly introduced strain and magnetic field-dependent Green tensors, strain and magnetic field-dependent integral equations linked to tensors of Eshelby and micromechanical approaches. The field-dependent global moduli are predicted based on the Mori–Tanaka approach and self-consistent method. Iterative incremental schemes based on the Newton–Raphson and fixed-point algorithms are examined and established precise semi-analytic equations of the effective magneto-elastic properties of composites that are dependent on the magnetic-strain field for different types of inclusions. A numerical code is elaborated for numerical predictions and the obtained field-dependent effective magneto-elastic coefficients are obtained and presented for various volume fractions of inclusion, types and shapes of the reinforced nonlinear composites.

This paper presents mathematical modeling and predictions of effective nonlinear electro-mechanical behavior of piezoelectric materials under large deformation and high electric field. The heterogeneous inclusion problem is extended to investigate the fields dependent electro-elastic behaviors under high fields. The associated strain field dependent Green tensors are introduced. The field dependent interaction tensors, related to Eshelby’s tensors, are explicitly formulated and used to derive micromechanical models based on the Mori–Tanaka approach and the self-consistent model. Due to electric-strain field dependence nonlinear algebraic tensors equations are resulted. Iterative incremental schemes based on the Newton–Raphson algorithm are elaborated and explicit semi-analytical formulations of electric-strain field dependent effective electro-elastic moduli of piezoelectric multi-phase composites are obtained for various inclusion types. Strain and electric field’s effects on effective properties can be analyzed for various electro-elastic composites. Numerical results of field dependent effective electro-mechanical properties are given for several inclusion’s volume fraction and shapes as well as types of matrix and inclusions phases.

This paper deals with a mathematical modeling of fully coupled reinforced magneto-electro-thermo-mechanical behaviors. The modeling is based on micro–macro transition inclusion problem using the localization and concentration tensors. Various micromechanical modelings are elaborated mainly the Mori–Tanaka, self-consistent, incremental self consistent and the differential approaches. The higher dispersion between the magneto-electro-elastic properties leads to ill-conditioned concentration tensors. This drawback is point out here and a remedy based on block matrix formulations leading to well-conditioned tensors is proposed. The effective magneto-electro-thermo-elastic moduli are derived as a function of the resulting well-conditioned magneto-electro-thermo-mechanical concentration tensors. These properties are derived for different inclusion's volume fraction, types, and shapes, and compared with the existing results.

In this paper, the effective electro-elastic (EE) behavior of piezoelectric composite is predicted and analyzed based on a regularized micromechanical modeling. The mathematical modeling is based on Green’s function approach to derive the localization equation coupled with regularization and conditioned procedure. The ill-conditioned problem is present when going through the inversion of the localization tensor due to the large dispersion between elastic, dielectric, and piezoelectric coefficients. This problem is addressed using the Tikhonov regularization method. The choice of the regularization parameter is studied to be optimal and to assure the solution stability, and the convergence to the desired solution. The Homogenization of effective properties is obtained through the averaged procedure and a regularized Mori-Tanaka model. The effective electro-elastic properties are predicted with respect to the shape of constituents as well as to the volume fraction of inclusions.

In the present paper, a mathematical modeling of effective properties of fully coupled thermo-electro-mechanical heterogeneous materials is elaborated. Constitutive equations combined with equilibrium equations lead to a coupled partial differential system. A methodological procedure is elaborated based on thermo-electro-elastic Green's functions, integral equations, and a micro-macro approach. Localization tensors are derived using the Mori-Tanaka mean-field assumptions and the fully coupled effective behavior is obtained through averaging techniques. Due to the large dispersion between elastic, dielectric, and piezoelectric coefficients ill-conditioned localization tensors are resulted. Block matrix decomposition is elaborated to overcome this drawback and the so-regularized localization tensor's inverses are used to get a well conditioned problem. Numerical computations are done in the general case of ellipsoidal inclusions and anisotropic behavior. Effective thermal conductivity and heat capacity coefficients are obtained with and without the heat strain effect for various volume fractions and types of inclusions. The global properties of thermo-electro-elastic reinforced composites are presented with respect to shape and volume fractions of inclusions. (c) 2021 Elsevier Inc. All rights reserved.

In this paper, the non-ageing effective behavior of fractional viscoelastic reinforced composites is predicted based on the Mori-Tanaka approach. The mathematical modeling is based on the Carson-Laplace transform, the dynamic Greens function and the integral equations. Various fractional viscoelastic models can be easily considered. The localization tensors relating local fields and macroscopic ones are derived based on the equivalence inclusion of Eshelby. The Homogenization of the effective behavior is obtained as a function of volume fractions of the constituents and their properties as well as of the volume fraction of reinforcements in the Carson domain.

In this paper, mathematical modeling for the identification of effective electro-mechanical properties of homogeneous piezoelectric plate composites is proposed. The effective properties are investigated using micromechanical models based on the heterogeneous inclusion problem of Eshelby. The concentration and localization tensors are used attributed to the Mori-Tanaka micromechanical approach. The homogenized coefficients for both electro-elastic and piezoelectric plates are then used to analyze the response of the polarized piezoelectric plate in z-direction. The influence of the direction of polarization in addition to the concentration of the fiber inclusion is analysed using the exact solution from the Stroh-like formalism. The Stroh-like formalism solution demonstrate the effect of the polarization direction of Epoxy/PZT-5 and PZT-C91/PZT-5 on the eletromechanical response of piezoelectric composite.