Approximating dynamic phase-field fracture in viscoelastic materials with a first-order formulation for velocity and stress [PDF]
, 2023 We investigate a model for dynamic fracture in viscoelastic materials at small strains. While the sharp crack interface is approximated with a phase-field method, we consider a viscous evolution with a quadratic dissipation potential for the phase-field ...
Thomas, Marita +2 more
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Asymptotic corrections to the low-frequency theory for a cylindrical elastic shell [PDF]
, 2023 The general scaling underlying the asymptotic derivation of 2D theory for thin shells from the original equations of motion in 3D elasticity fails for cylindrical shells due to the cancellation of the leading-order terms in the geometric relations for ...
Kaplunov
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Analysis of Vibrations in Large Flexible Hybrid Systems
, 2005 The mathematical model of a real flexible elastic system with distributed and discrete parameters is considered. It is a partial differential equation with non-classical boundary conditions.
Delfim F.M. Torres +5 more
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Internal dynamics around static-deformation FEM states [PDF]
, 2005 Constant velocity or constant force FEM solutions are static-deformation states, where the elastic deformation is stationary. These are the typical operation conditions.
Ligterink, N.E.
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KdV-like solitary waves in two-dimensional FPU-lattices
, 2018 We prove the existence of solitary waves in the KdV limit of two-dimensional FPU-type lattices using asymptotic analysis of nonlinear and singularly perturbed integral equations. In particular, we generalize the existing results by Friesecke and Matthies
Chen, Fanzhi, Herrmann, Michael
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Self-consistent field theory for a polymer brush. Part II: The effective chemical potential [PDF]
, 2019 The most successful mean-field model to describe the collective behaviour of the large class of macromolecular polymers is the self-consistent field theory (SCFT). Still, even for the simple system of a grafted dry polymer brush, the mean-field equations
Münch, Andreas, Wagner, Barbara
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Analytical estimations of limit cycle amplitude for delay-differential equations [PDF]
, 2016 The amplitude of limit cycles arising from Hopf bifurcation is estimated for nonlinear delay-differential equations by means of analytical formulas. An improved analytical estimation is introduced, which allows more accurate quantitative prediction of ...
Insperger, Tamás +2 more
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The Vibration Spectrum of Two Euler–Bernoulli Beams Coupled Via a Dissipative Joint [PDF]
, 2017 The asymptotic estimation of the vibration spectrum for a system of two identical Euler–Bernoulli beams coupled via each of the four standard types of linear dissipative joint has been solved for the case when one beam is clamped and the other beam is ...
Abriola, Chris +3 more
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Double scale analysis of periodic solutions of some non linear vibrating systems [PDF]
, 2013 We consider {\it small solutions} of a vibrating system with smooth non-linearities for which we provide an approximate solution by using a double scale analysis; a rigorous proof of convergence of a double scale expansion is included; for the forced ...
Brahim, Nadia Ben, Rousselet, Bernard
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Self-consistent field theory for a polymer brush. Part I: Asymptotic analysis in the strong-stretching limit [PDF]
, 2019 In this study we consider the self-consistent field theory for a dry, in- compressible polymer brush, densely grafted on a substrate, describing the average segment density of a polymer in terms of an effective chemical potential for the interaction ...
Münch, Andreas, Wagner, Barbara
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