J. Signorelli, R. Hassani, A. Tommasi, Lucan Mameri
In this article, we describe the mathematical formulation and the numerical implementation of an effective parametrization of the viscous anisotropy of orthorhombic materials produced by crystallographic preferred orientations (CPO or texture), which can be integrated into 3D geodynamic and materials science codes. Here, the approach is applied to characterize the texture-induced viscous anisotropy of olivine polycrystals, the main constituent of the Earth's upper mantle. The parameterization is based on the Hill (1948) orthotropic yield criterion. The coefficients of the Hill yield surface are calibrated based on numerical tests performed using the second order Viscoplastic Self-consistent (SO-VPSC) model. The parametrization was implemented in a 3D thermo-mechanical finite-element code developed to model large-scale geodynamical flows, in the form of a Maxwell rheology combining isotropic elastic and anisotropic non-linear viscous behaviors. The implementation was validated by comparison with results of the analytical solution and of the SO-VPSC model for simple shear and axial compression of a homogeneous anisotropic material. An application designed to examine the effect of texture-induced viscous anisotropy on the reactivation of mantle shear zones in continental plates highlights unexpected couplings between localized deformation controlled by variations in the orientation and intensity of the olivine texture in the mantle and the mechanical behavior of the elasto-viscoplastic overlying crust. Importantly, the computational time only increases by a factor 2-3 with respect to the classic isotropic Maxwell viscoelastic rheology. Comment: 32 pag.; 5 figures; 4 tables
{"title":"An effective parameterization of texture-induced viscous anisotropy in\u0000 orthotropic materials with application for modeling geodynamical flows","authors":"J. Signorelli, R. Hassani, A. Tommasi, Lucan Mameri","doi":"10.46298/jtcam.6737","DOIUrl":"https://doi.org/10.46298/jtcam.6737","url":null,"abstract":"In this article, we describe the mathematical formulation and the numerical\u0000implementation of an effective parametrization of the viscous anisotropy of\u0000orthorhombic materials produced by crystallographic preferred orientations (CPO\u0000or texture), which can be integrated into 3D geodynamic and materials science\u0000codes. Here, the approach is applied to characterize the texture-induced\u0000viscous anisotropy of olivine polycrystals, the main constituent of the Earth's\u0000upper mantle. The parameterization is based on the Hill (1948) orthotropic\u0000yield criterion. The coefficients of the Hill yield surface are calibrated\u0000based on numerical tests performed using the second order Viscoplastic\u0000Self-consistent (SO-VPSC) model. The parametrization was implemented in a 3D\u0000thermo-mechanical finite-element code developed to model large-scale\u0000geodynamical flows, in the form of a Maxwell rheology combining isotropic\u0000elastic and anisotropic non-linear viscous behaviors. The implementation was\u0000validated by comparison with results of the analytical solution and of the\u0000SO-VPSC model for simple shear and axial compression of a homogeneous\u0000anisotropic material. An application designed to examine the effect of\u0000texture-induced viscous anisotropy on the reactivation of mantle shear zones in\u0000continental plates highlights unexpected couplings between localized\u0000deformation controlled by variations in the orientation and intensity of the\u0000olivine texture in the mantle and the mechanical behavior of the\u0000elasto-viscoplastic overlying crust. Importantly, the computational time only\u0000increases by a factor 2-3 with respect to the classic isotropic Maxwell\u0000viscoelastic rheology.\u0000\u0000 Comment: 32 pag.; 5 figures; 4 tables","PeriodicalId":115014,"journal":{"name":"Journal of Theoretical, Computational and Applied Mechanics","volume":"73 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128963841","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Elastic guided wave focusing is of great interest for applications such as vibroacoustic control, energy harvesting, or Structural Health Monitoring. Different strategies allow generation of this effect, GRadient-INdex devices in particular exploit medium with varying properties such as thickness to reproduce an adequate refractive index profile as in optics. The resulting continuous profiles have a curved geometry that can be hard to manufacture, and be difficult to integrate in a given design. The purpose of this paper is to propose a discrete design for a GRIN lens. It is composed of segments selected in number and thickness to give similar focusing effects as a continuous lens profile. The identified configuration is manufactured and bounded on an aluminium plate to evaluate the effective focusing performances. Numerical and experimental vibrometry results confirm that the proposed lens exhibits a fixed focal point over a broad frequency range. The discrete design overcomes fabrication issues encountered in continuous design, allowing for an easier integration in devices for elastic wave control.
{"title":"Passive discrete lens for broadband elastic guided wave focusing","authors":"E. Sadoulet-Reboul, G. Matten, K. Yi, M. Ouisse","doi":"10.46298/jtcam.6652","DOIUrl":"https://doi.org/10.46298/jtcam.6652","url":null,"abstract":"Elastic guided wave focusing is of great interest for applications such as vibroacoustic control, energy harvesting, or Structural Health Monitoring. Different strategies allow generation of this effect, GRadient-INdex devices in particular exploit medium with varying properties such as thickness to reproduce an adequate refractive index profile as in optics. The resulting continuous profiles have a curved geometry that can be hard to manufacture, and be difficult to integrate in a given design. The purpose of this paper is to propose a discrete design for a GRIN lens. It is composed of segments selected in number and thickness to give similar focusing effects as a continuous lens profile. The identified configuration is manufactured and bounded on an aluminium plate to evaluate the effective focusing performances. Numerical and experimental vibrometry results confirm that the proposed lens exhibits a fixed focal point over a broad frequency range. The discrete design overcomes fabrication issues encountered in continuous design, allowing for an easier integration in devices for elastic wave control.","PeriodicalId":115014,"journal":{"name":"Journal of Theoretical, Computational and Applied Mechanics","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123800005","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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