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We consider a class of models for nonlinearly elastic surfaces in this work. We have in mind thin, highly deformable structures modeled directly as two-dimensional nonlinearly elastic continua, accounting for finite membrane and bending…
Computational multiscale methods for analyzing and deriving constitutive responses have been used as a tool in engineering problems because of their ability to combine information at different length scales. However, their application in a…
The present paper is the second part of a twofold work, whose first part is reported in [3], concerning a newly developed Virtual Element Method (VEM) for 2D continuum problems. The first part of the work proposed a study for linear elastic…
We establish existence of positive non-decreasing radial solutions for a nonlocal nonlinear Neumann problem both in the ball and in the annulus. The nonlinearity that we consider is rather general, allowing for supercritical growth (in the…
This work introduces an end-to-end framework for inverse design of elastic networks directly in the space of constitutive behaviors. A constitutive prior is constructed from noisy stress-strain data using a latent representation that…
The calibration of solid constitutive models with full-field experimental data is a long-standing challenge, especially in materials which undergo large deformation. In this paper, we propose a physics-informed deep-learning framework for…
A well-posed stress-driven mixture is proposed for Timoshenko nano-beams. The model is a convex combination of local and nonlocal phases and circumvents some problems of ill-posedness emerged in strain-driven Eringen-like formulations for…
In this study, we develop a fractional-calculus based constitutive model for capturing nonlocal interactions over the multiphysics response in solids. More specifically, we develop constitutive relations for nonlocal piezoelectricity…
This work presents the design of nonlinear stabilization techniques for the finite element discretization of Euler equations in both steady and transient form. Implicit time integration is used in the case of the transient form. A…
Recent equations of motion for the large deflections of a cantilevered elastic beam are analyzed. In the traditional theory of beam (and plate) large deflections, nonlinear restoring forces are due to the effect of stretching on bending;…
This paper is concerned with the analysis of the Cauchy problem of a general class of two-dimensional nonlinear nonlocal wave equations governing anti-plane shear motions in nonlocal elasticity. The nonlocal nature of the problem is…
Within the framework of the thermal wave model, an investigation is made of the longitudinal dynamics of high energy charged particle beams. The model includes the self-consistent interaction between the beam and its surroundings in terms…
The present paper proposes a novel Bayesian, computational strategy in the context of model-based inverse problems in elastostatics. On one hand we attempt to provide probabilistic estimates of the material properties and their spatial…
Inspired by the penalization of the domain approach of Lions & Sznitman, we give a sense to Neumann and oblique derivatives boundary value problems for nonlocal, possibly degenerate elliptic equations. Two different cases are considered:…
A challenge in the theory of integrable systems is to show for every nonultralocal quantum integrable model, a possible connection to an ultralocal model. Some of such gauge connections were discovered earlier. We complete the task by…
The classical local Neumann problem is well studied and solutions of this problem lie, in general, in a Sobolev space. In this work, we focus on nonlocal Neumann problems with measurable, nonnegative kernels, whose solutions require less…
This research explores refined boundary conditions for a traction-free surface in a non-local micropolar half-space, combining non-local and micropolar elasticity effects to study Rayleigh wave propagation in an isotropic, homogeneous…
We consider the inverse boundary value problem of determining the Lam\'e moduli of an isotropic, static elasticity equations of system at the boundary from the localized Dirichlet-to-Neumann map. Assuming appropriate local regularity…
Biological soft tissues exhibit substantial inter-subject variability, making the automation of constitutive material modeling essential for patient-specific analysis and design. Such materials are not only highly nonlinear but also display…
Periodically forced turbulence is used as a test case to evaluate the predictions of two-equation and multiple-scale turbulence models in unsteady flows. The limitations of the two-equation model are shown to originate in the basic…