Interior energy focusing within an elasto-plastic material

Tadi, M.; Rabitz, Herschel; Sik, Kim Young; Aşkar, Attila; Prévost, Jean‐Hérve; McManus, J. Barry

doi:10.1016/0020-7683(95)00137-9

Cited by 3 publications

(2 citation statements)

References 12 publications

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“…(16) and, in turn, substituting forv x | i,m+ 1 2 and u x | i,m+ 1 2 in Eqs. (14)- (15), the displacements at (i, m + 1) can be related to the variables defined in the domain according tô…”

Section: Free Surface Boundarymentioning

confidence: 99%

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Finite Difference Methods for Elastic Wave Propagation in Layered Media

Tadi

2004

J. Comp. Acous.

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This paper is concerned with the numerical modeling of elastic wave propagation in layered media. It considers two isotropic homogeneous elastic solids in perfect contact. The interface is parallel to the free surface. Two finite difference methods are developed. The usefulness of the methods are investigated for long time simulations and the accuracy of the results are compared with the response from an approximate model.

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Section: Free Surface Boundarymentioning

confidence: 99%

“…The inverse of such a matrix is not in general sparse. As a result, for long time simulations, one often uses approximations that leads to a diagonal mass matrix 15,16 which is at the expense to the accuracy.…”

Section: Introductionmentioning

confidence: 99%

Finite Difference Methods for Elastic Wave Propagation in Layered Media

Tadi

2004

J. Comp. Acous.

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Adjoint Equation-Based Inverse-Source Modeling to Reconstruct Moving Acoustic Sources in a One-Dimensional Heterogeneous Solid

Lloyd

Jeong

2018

J. Eng. Mech.

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Full-Waveform Inversion of Incoherent Dynamic Traction in a Bounded 2D Domain of Scalar Wave Motions

Guidio

Jeong

2021

J. Eng. Mech.

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This paper presents a full-waveform inversion method for reconstructing the temporal and spatial distribution of unknown, incoherent dynamic traction in a heterogeneous, bounded solid domain from sparse, surficial responses. This work considers SH wave motions in a two-dimensional ( D) domain. The partial-differential-equation (PDE)-constrained optimization framework is employed to search a set of control parameters, by which a misfit between measured responses at sensors on the top surface induced by targeted traction and their computed counterparts induced by estimated traction is minimized. To mitigate the solution multiplicity of the presented inverse problem, we employ the Tikhonov (TN) regularization on the estimated traction function. We present the mathematical modeling and numerical implementation of both optimize-then-discretize (OTD) and discretize-then-optimize (DTO) approaches. The finite element method (FEM) is employed to obtain the numerical solutions of state and adjoint problems. Newton's method is utilized for estimating an optimal step length in combination with the conjugate-gradient scheme, calculating a desired search direction, throughout a minimization process.Numerical results present that the complexity of a material profile in a domain increases the error between reconstructed traction and its target. Second, the OTD and DTO approaches lead to the same inversion result. Third, when the sampling rate of the measurement is equal to the timestep for discretizing estimated traction, the ratio of the size of measurement data to the number of the control parameters can be as small as : in the presented work. Fourth, it is acceptable to tackle the presented inverse modeling of dynamic traction without the TN regularization. Fifth, the inversion performance is more compromised when the noise of a larger level is added to the measurement data, and using the TN regularization does not improve the inversion performance when noise is added to the measurement. Sixth, our minimizer suffers from solution multiplicity less when it identifies dynamic traction of lower frequency content than that of higher frequency content. The wave responses in a computational domain, induced by targeted traction and its reconstructed one, are in excellent agreement with each other. Thus, if the presented dynamic-input inversion algorithm is extended in realistic D settings, it could reconstruct seismic input motions in a truncated domain and, then, replay the wave responses in a computational domain.

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Interior energy focusing within an elasto-plastic material

Cited by 3 publications

References 12 publications

Finite Difference Methods for Elastic Wave Propagation in Layered Media

Finite Difference Methods for Elastic Wave Propagation in Layered Media

Adjoint Equation-Based Inverse-Source Modeling to Reconstruct Moving Acoustic Sources in a One-Dimensional Heterogeneous Solid

Full-Waveform Inversion of Incoherent Dynamic Traction in a Bounded 2D Domain of Scalar Wave Motions

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