### Proyecto de investigación

##### Integridad de Materiales Multicampo y Funcionalmente Variables (FGM): Simulación Numérica y Experimental

Responsable: Andrés Sáez Pérez

Tipo de Proyecto/Ayuda: Plan Nacional del 2010

Referencia: DPI2010-21590-C02-02

Fecha de Inicio: 01-01-2011

Fecha de Finalización: 30-09-2014

**Empresa/Organismo financiador/es:**

- Ministerio de Ciencia e Innovación

**Equipo:**

- Investigadores:
- Pedro Alba de la Rubia (alta: 01/03/2012)
- Federico Carlos Buroni Cúneo
- Felipe García Sánchez
- Gabriel Hattori Da Silva
- María Esperanza Rodríguez Mayorga (alta: 01/03/2012)
- Ramón Rojas Díaz
- Chuanzeng Zhang

**Resumen del proyecto:**

**Project ****summary**

The increasing demand for high performance control design of engineering devices together with recent advances in material science have given rise to the so-called smart or adaptive systems. Intelligent structures whose dynamics may be monitored and modified by distributed or continuous sensors and actuators are finding wider applications in many industrial fields like aerospace, aeronautic, automotive, biomedical, and micro- (MEMS) and nano-systems (NEMS) design.

Such applications rely on the use of smart materials showing multifield coupling properties. This project focuses on piezoelectric (PE) and magnetoelectroelastic (MEE) multiphase composite materials that exhibit an inherent coupling among the mechanical, electric and magnetic fields. Understanding and properly modeling the failure mechanisms of these materials is crucial to the advancement of the modern intelligent systems. Fracture mechanics plays therefore a key role, since defects such as cracks will inevitably appear in the material either during manufacturing or in service, leading not only to a decrease in the structural component strength and service life but also modifying the transfer between mechanical and non-mechanical energy (electrical, magnetic).

More specifically, the objectives of the project focus on the formulation, implementation and validation of numerical tools for the analysis and simulation of fracture problems in PE and MEE solids, as well as the use of Artificial Neural Networks (ANN) for damage detection problems in MEE solids.

For the type of applications considered herein, the Boundary Element Method (BEM) has been shown as a powerful and effective tool when compared to other computational techniques. Among its advantages one may cite that 1) only discretization of the boundary is required (thus simplifying pre-processing and remeshing); 2) it shows improved accuracy in stress concentration problems (like fracture problems), since there are no approximations imposed on the stress solution in interior domain points.; or 3) modeling of problems involving infinite and semi-infinite domains (like in wave propagation phenomena) is simple and accurate, since the radiation conditions at infinity are automatically satisfied. A basic feature of BEM is the use of fundamental solutions, which are analytically free space solutions of the governing differential equation under the action of a point source. The fact that they are exact solutions accounts for some of the advantages of the BEM, but it accounts as well for some of the method limitations that this project tackles: the knowledge of suitable fundamental solutions and the numerical treatment of integrations associated to these solutions.

**Keywords:** Smart Structures, Multifield Materials (Piezoelectric, Magnetoelectroelastic), Cracks, Thermal Loads, Fracture Parameters, Wave Propagation, Boundary Element Method, Neural Networks.

**List of some publications related to the project**

Hattori, G., Sáez, A. Crack identification in magnetoelectroelastic materials using neural networks, self-organizing algorithms and boundary element method

(2013) Computers and Structures, 125, pp. 187-199.

Buroni, F.C., Sáez, A. Unique and explicit formulas for Green's function in three-dimensional anisotropic linear elasticity

(2013) Journal of Applied Mechanics, Transactions ASME, 80 (5), art. no. 051024.

Rodríguez-Tembleque, L., Buroni, F.C., Abascal, R., Sáez, A. Analysis of FRP composites under frictional contact conditions

(2013) International Journal of Solids and Structures, 50 (24), pp. 3947-3959.

Hattori, G., Sáez, A. Damage identification in multifield materials using neural networks

(2013) Inverse Problems in Science and Engineering, 21 (6), pp. 929-944.

Wünsche, M., Zhang, C.H., Sladek, J., Sladek, V., Sáez, A., García-Sánchez, F. The influences of non-linear electrical, magnetic and mechanical boundary conditions on the dynamic intensity factors of magnetoelectroelastic solids

(2012) Engineering Fracture Mechanics, 97 (1), pp. 297-313.

Hattori, G., Rojas-Díaz, R., Sáez, A., Sukumar, N., García-Sánchez, F. New anisotropic crack-tip enrichment functions for the extended finite element method

(2012) Computational Mechanics, 50 (5), pp. 591-601.

Wünsche, M., García-Sánchez, F., Sáez, A. Analysis of anisotropic Kirchhoff plates using a novel hypersingular BEM

(2012) Computational Mechanics, 49 (5), pp. 629-641.

Wünsche, M., Sáez, A., García-Sánchez, F., Zhang, C. Transient dynamic crack analysis in linear magnetoelectroelastic solids by a hypersingular time-domain BEM

(2012) European Journal of Mechanics, A/Solids, 32, pp. 118-130.

Rojas-Díaz, R., Denda, M., García-Sánchez, F., Sáez, A. Dual BEM analysis of different crack face boundary conditions in 2D magnetoelectroelastic solids

(2012) European Journal of Mechanics, A/Solids, 31 (1), pp. 152-162.

Rojas-Díaz, R., Sukumar, N., Sáez, A., García-Sánchez, F. Fracture in magnetoelectroelastic materials using the extended finite element method

(2011) International Journal for Numerical Methods in Engineering, 88 (12), pp. 1238-1259.

Rojas-Díaz, R., García-Sánchez, F., Sáez, A., Rodríguez-Mayorga, E., Zhang, C. Fracture analysis of plane piezoelectric/piezomagnetic multiphase composites under transient loading

(2011) Computer Methods in Applied Mechanics and Engineering, 200 (45-46), pp. 2931-2942.

Wünsche, M., Zhang, C., García-Sánchez, F., Sáez, A., Sladek, J., Sladek, V. Dynamic crack analysis in piezoelectric solids with non-linear electrical and mechanical boundary conditions by a time-domain BEM

(2011) Computer Methods in Applied Mechanics and Engineering, 200 (41-44), pp. 2848-2858.

Buroni, F.C., Ortiz, J.E., Sáez, A. Multiple pole residue approach for 3D BEM analysis of mathematical degenerate and non-degenerate materials

(2011) International Journal for Numerical Methods in Engineering, 86 (9), pp. 1125-1143.