We propose a methodological framework to perform forward asteroseismic modeling of stars with a convective core, based on gravity-mode oscillations. These probe the near-core region in the deep stellar interior. The modeling relies on a set of observed high-precision oscillation frequencies of low-degree coherent gravity modes with long lifetimes and their observational uncertainties. Identification of the mode degree and azimuthal order is assumed to be achieved from rotational splitting and/or from period spacing patterns. This paper has two major outcomes. The first is a comprehensive list and discussion of the major uncertainties of theoretically predicted gravity-mode oscillation frequencies based on linear pulsation theory, caused by fixing choices of the input physics for evolutionary models. Guided by a hierarchy among these uncertainties of theoretical frequencies, we subsequently provide a global methodological scheme to achieve forward asteroseismic modeling. We properly take into account correlations among the free parameters included in stellar models. Aside from the stellar mass, metallicity, and age, the major parameters to be estimated are the near-core rotation rate, the amount of convective core overshooting, and the level of chemical mixing in the radiative zones. This modeling scheme allows for maximum likelihood estimation of the stellar parameters for fixed input physics of the equilibrium models, followed by stellar model selection considering various choices of the input physics. Our approach uses the Mahalanobis distance instead of the often-used χ ² statistic and includes heteroscedasticity. It provides estimation of the unknown variance of the theoretically predicted oscillation frequencies.

Upon exciting a material using elastic waves, the locally induced deformation at the interfaces of internally closed defects may cause nonlinear wave mechanics and dynamics in the form of clapping and friction. As a result, both phenomena instigate spectral broadening of the excitation spectrum as well as the production of heat, directly originating from the defect. To better understand and account for the physics behind the dissipation of energy by internally closed defects as a result of the wave–interface interaction, dedicated models can be developed. In this work, we propose a 3D finite element multiphysics model that is capable of simultaneously describing the generation of nonlinearities and heating at a defect’s interface experiencing clapping and friction induced by elastic wave propagation. The model consists of three different modules. The first module describes the elastic wave propagation in a virgin/bulk material, whereas the second module captures the contact physics at the defect level. The third module is implemented to calculate the diffusion of thermal energy in the specimen. The contact physics module accounts for anharmonic and hysteretic effects, describing the nonlinear behavior of the defect’s interfaces, which is echoed in both the ultrasound spectrum and in the vibration-induced heating. A qualitative analysis of the computational model, integrating the three modules, is performed to validate the approach. Examples show that nonlinear spectral components are indeed observed as a result of the friction and the clapping experienced by the faces of the defect. At the same time, a localized temperature increase due to the induced friction is noted, and its response at the outer surface of the sample is examined. The qualitative validation approves that the model is ready to be tested further quantitively, and to compare its predictions to experiments.

We present a numerical modeling tool for engineering applications related to materials and systems having internal frictional contacts in their structure. The technique is based on a semi-analytical method for simulating contact mechanical problems, called the Method of Memory Diagrams (MMD) [1,3], which is able to calculate hysteretic frictional contact responses. The MMD is applicable when an axisymmetric contact system is excited by an arbitrarily changing shift in 3D [2] and can be extended to the contact of globally plane surfaces with isotropic roughness. The method uses some assumptions and does not provide the full functionality of purely numerical contact modeling, but is much more efficient computationally. This quantitative gain in performance makes the MMD applicable to the case of acoustic or random excitation signals containing a large number of oscillations.The integration of the MMD contact model in a finite element environment [4] (COMSOL) allows to simulate acoustic wave propagation and vibration in structures or materials containing hidden frictional interfaces (cracks, delaminations, loose joints, etc). We discuss proof-of-concept results in a simple 3D geometry containing to a surface-breaking crack insonified by an oblique compression wave simultaneously exciting normal and tangential interactions.