**Integrated Numerical-Experimental Assessment of the E** ff**ect of the AZ31B Anisotropic Behaviour in Extended-Surface Treatments by Laser Shock Processing**

### **Ignacio Angulo \*, Francisco Cordovilla, Ánge<sup>l</sup> García-Beltrán, Juan A. Porro, Marcos Díaz and José Luis Ocaña**

UPM Laser Centre. ETS Ingenieros Industriales. Universidad Politécnica de Madrid. C/José Gutiérrez Abascal, 2, 28006 Madrid, Spain; francisco.cordovilla.baro@upm.es (F.C.); agarcia@etsii.upm.es ( Á.G.-B.); japorro@etsii.upm.es (J.A.P.); marcos.diaz@upm.es (M.D.); jlocana@etsii.upm.es (J.L.O.)

**\*** Correspondence: ignacio.angulo@upm.es; Tel.: +34-910676700

Received: 5 December 2019; Accepted: 22 January 2020; Published: 29 January 2020

**Abstract:** In recent years, an increasing interest in designing magnesium biomedical implants has been presented due to its biocompatibility, and grea<sup>t</sup> e ffort has been employed in characterizing it experimentally. However, its complex anisotropic behaviour, which is observed in rolled alloys, leads to a lack of reliable numerical simulation results concerning residual stress predictions. In this paper, a new model is proposed to focus on anisotropic material hardening behaviour in Mg base (in particular AZ31B as a representative alloy) materials, in which the particular stress cycle involved in Laser Shock Processing (LSP) treatments is considered. Numerical predictions in high extended coverage areas obtained by means of the implemented model are presented, showing that the realistic material's complex anisotropic behaviour can be appropriately computed and—much more importantly—it shows a particular non-conventional behaviour regarding extended areas processing strategies.

**Keywords:** laser shock processing; anisotropy; residual stress; FEM analysis; Mg AZ31B alloy
