[图书][B] Mathematical elasticity: Three-dimensional elasticity
PG Ciarlet - 2021 - SIAM
Introduction Since the completion of this volume in 1986, there has been an enormous
amount of fundamental advances in the theory of three-dimensional elasticity (Chapters 6 …
amount of fundamental advances in the theory of three-dimensional elasticity (Chapters 6 …
A handbook of Г-convergence
A Braides - Handbook of Differential Equations: stationary partial …, 2006 - Elsevier
Publisher Summary This chapter discusses the main properties of Γ-convergence, in
particular those that are useful in the actual computation of Γ-limits. For some classes of …
particular those that are useful in the actual computation of Γ-limits. For some classes of …
[图书][B] Nonlocal Modeling, Analysis, and Computation: Nonlocal Modeling, Analysis, and Computation
Q Du - 2019 - SIAM
Nonlocal Modeling, Analysis, and Computation : Back Matter Page 1 Bibliography [1] L.
ABDELOUHAB, J. BONA, M. FELLAND, AND J.-C. SAUT, Nonlocal models for nonlinear …
ABDELOUHAB, J. BONA, M. FELLAND, AND J.-C. SAUT, Nonlocal models for nonlinear …
On the variational limit of a class of nonlocal functionals related to peridynamics
T Mengesha, Q Du - Nonlinearity, 2015 - iopscience.iop.org
In this paper we study variational problems on a bounded domain for a nonlocal elastic
energy of peridynamic-type which result in nonlinear systems of nonlocal equations. The …
energy of peridynamic-type which result in nonlinear systems of nonlocal equations. The …
Γ-convergence of graph Ginzburg-Landau functionals
Y Van Gennip, AL Bertozzi - Adv. Differential Equations, 2012 - projecteuclid.org
We study Γ-convergence of graph-based Ginzburg–Landau functionals, both the limit for
zero diffusive interface parameter ε→ 0 and the limit for infinite nodes in the graph m→∞ …
zero diffusive interface parameter ε→ 0 and the limit for infinite nodes in the graph m→∞ …
Fracture and size effect in mechanical metamaterials
We resort to variational methods to evaluate the asymptotic behavior of fine metamaterials
as a function of cell size. To zeroth order, the metamaterial behaves as a micropolar …
as a function of cell size. To zeroth order, the metamaterial behaves as a micropolar …
Variational convergence of the Scharfetter–Gummel scheme to the aggregation-diffusion equation and vanishing diffusion limit
A Hraivoronska, A Schlichting, O Tse - Numerische Mathematik, 2024 - Springer
In this paper, we explore the convergence of the semi-discrete Scharfetter–Gummel scheme
for the aggregation-diffusion equation using a variational approach. Our investigation …
for the aggregation-diffusion equation using a variational approach. Our investigation …
Characterization of function spaces of vector fields and an application in nonlinear peridynamics
T Mengesha, Q Du - Nonlinear Analysis, 2016 - Elsevier
The paper introduces a class of nonlocal derivative operators defined over vector fields that
turn out to satisfy a nonlocal integration by parts formula. We demonstrate that in several …
turn out to satisfy a nonlocal integration by parts formula. We demonstrate that in several …
Reduction of the resonance error—Part 1: Approximation of homogenized coefficients
A Gloria - Mathematical models and methods in applied sciences, 2011 - World Scientific
This paper is concerned with the approximation of effective coefficients in homogenization of
linear elliptic equations. One common drawback among numerical homogenization methods …
linear elliptic equations. One common drawback among numerical homogenization methods …
Linearization and localization of nonconvex functionals motivated by nonlinear peridynamic models
T Mengesha, JM Scott - Continuum Mechanics and Thermodynamics, 2024 - Springer
We consider a class of nonconvex energy functionals that lies in the framework of the
peridynamics model of continuum mechanics. The energy densities are functions of a …
peridynamics model of continuum mechanics. The energy densities are functions of a …