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Personne# Antonio Joaquin Garcia Suarez

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Publications associées (13)

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The technique referred as ray approximation treats wave propagation in a heterogeneous medium at the infinitely small wavelength limit. This classic simplification allows useful approximate analytical results to be obtained in cases where complete description of the waveform behaviour is virtually unattainable, hence its wide use in physics. In seismology, this approximation has been widely applied. This paper presents an application in one-dimensional site response (1DSR) analysis: it is used herein, first to explain and elucidate the generality of some previous observations as to the use of the harmonic mean of a shear-wave velocity profile to represent the global behaviour of a site; and second to partially settle an open question in 1DSR, namely ‘What are the equivalent homogeneous properties that yield the same response, in terms of natural frequencies and resonance amplitude, for a given inhomogeneous site?’, providing a few assumptions are met – chiefly, that excitations of sufficiently high frequency are considered.

2022Antonio Joaquin Garcia Suarez, Jean-François Molinari, Yannick André Neypatraiky, Sacha Zenon Wattel

Model-free data-driven computational mechanics (DDCM) [Kirchdoerfer & Ortiz, 2016] is a new paradigm for simulations in solid mechanics. As in the classical method, the boundary value problem is formulated with physics-based PDEs such as the balance of momentum and compatibility equations, which together define the admissibility conditions. However, DDCM does not use phenomenological constitutive laws to close the problem. Instead it uses directly data on material response, originating from either exper- iments or micro-physical simulations, in order to reduce constitutive modeling bias. The problem is solved in phase space where the admissibility conditions define a manifold and the material behavior is represented by a set of material points. DDCM aims to find the admissible state that best matches the material points. The DDCM framework has been formulated and used to solve problems in statics and dynamics, for multi- scale modeling, and has been coupled to classical solvers such as the finite element method to run simulations more efficiently. In this work, DDCM is applied to a frictional interface. Data-driven finite-thickness cohesive elements are sandwiched between two linear elastic bodies solved with FEM. The material response database is populated from micro-physical discrete simulations of two contacting rough surfaces sliding against each other. Through interactions between the interface, the bulk and the boundary conditions, complex behaviors such as dynamically propagating slip fronts arise.

2023Transfer functions are constantly used in both Seismology and Geotechnical Earthquake Engineering to relate seismic ground motion at different depths within strata. In the context of diffusive theory, they also appear in the expression of the imaginary part of 1D Green's functions. In spite of their remarkable importance, their mathematical structure is not fully understood yet, except in the simplest cases of two or three layers at most. This incomplete understanding, in particular as to the effect of increasing number of layers, hinders progress in some areas, as researchers have to resort to expensive and less conclusive numerical parametric studies. This text presents the general form of transfer functions for any number of layers, overcoming the above issues. The mathematical structure of these transfer functions comes defined as a superposition of independent harmonics, whose number, amplitudes and periods we fully characterize in terms of the properties of the layers in closed-form. Owing to the formal connection between seismic wave propagation and other phenomena that, in essence, represent different instances of wave propagation in a linear-elastic medium, we have extended the results derived elsewhere, in the context of longitudinal wave propagation in modular rods, to seismic response of stratified sites. The ability to express the reciprocal of transfer functions as a superposition of independent harmonics enables new analytical approaches to assess the effect of each layer over the overall response. The knowledge of the general closed-form expression of the transfer functions allows to analytically characterize the long-wavelength asymptotics of the horizontal-to-vertical spectral ratio for any number of layers.

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