Related papers: An HHT-$\alpha$-based finite element framework for…
We consider a model problem of the scattering of linear acoustic waves in free homogeneous space by an elastic solid. The stress tensor in the solid combines the effect of a linear dependence of strains with the influence of an existing…
Heating generated by high-intensity focused ultrasound waves is central to many emerging medical applications, including non-invasive cancer therapy and targeted drug delivery. In this study, we aim to gain a fundamental understanding of…
This paper is devoted to a numerical analysis of a fractional viscoelastic wave propagation model that generalizes the fractional Maxwell model and the fractional Zener model. First, we convert the model problem into a velocity type…
Acoustic wave propagation through a homogeneous material embedded in an unbounded medium can be formulated as a boundary integral equation and accurately solved with the boundary element method. The computational efficiency deteriorates at…
The paper studies the interaction of a longitudinal wave with transverse waves in general isotropic and unconstrained hyperelastic materials, including the possibility of dissipation. The dissipative term chosen is similar to the classical…
In a recent article the authors showed that the radiative Transfer equations with multiple frequencies and scattering can be formulated as a nonlinear integral system. In the present article, the formulation is extended to handle reflective…
The paper begins with a novel variational formulation of Duffing equation using the extended framework of Hamilton's principle (EHP). This formulation properly accounts for initial conditions, and it recovers all the governing differential…
The numerical analysis of elastic wave propagation in unbounded media may be difficult to handle due to spurious waves reflected at the model artificial boundaries. Several sophisticated techniques such as nonreflecting boundary conditions,…
Topological mechanical metamaterials have enabled new ways to control stress and deformation propagation. Exemplified by Maxwell lattices, they have been studied extensively using a linearized formalism. Herein, we study a two-dimensional…
This paper reports a theoretical and numerical framework to model nonlinear waves in elastic-plastic solids. Formulated in the Eulerian frame, the governing equations employed include the continuity equation, the momentum equation, and an…
The numerical analysis of elastic wave propagation in unbounded media may be difficult due to spurious waves reflected at the model artificial boundaries. This point is critical for the analysis of wave propagation in heterogeneous or…
Generalized impedance boundary conditions are effective, approximate boundary conditions that describe scattering of waves in situations where the wave interaction with the material involves multiple scales. In particular, this includes…
We demonstrate that wave amplification enables even weak nonlinearities to reshape linear wave-packet transport in nonreciprocal systems. We study the dynamics of bulk Gaussian wave packets in the Hatano--Nelson model with onsite cubic…
This paper presents a general non-linear computational formulation for rotation-free thin shells based on isogeometric finite elements. It is a displacement-based formulation that admits general material models. The formulation allows for a…
We propose a new numerical method to solve the Cahn-Hilliard equation coupled with non-linear wetting boundary conditions. We show that the method is mass-conservative and that the discrete solution satisfies a discrete energy law similar…
We present a phenomenological approach to dispersion in nonlinear elasticity. A simple, thermomechanically sound, constitutive model is proposed to describe the (non-dissipative) properties of a hyperelastic dispersive solid, without…
The analysis of wave propagation problems in linear damped media must take into account both propagation features and attenuation process. To perform accurate numerical investigations by the finite differences or finite element method, one…
In this paper, we analyse the dynamics of a pattern-forming system close to simultaneous Turing and Turing--Hopf instabilities, which have a 1:1 spatial resonance, that is, they have the same critical wave number. For this, we consider a…
We develop a linear fully discrete structure-preserving finite element method for a diffuse-interface model of tumour growth. The system couples a Cahn--Hilliard type equation with a nonlinear reaction-diffusion equation for nutrient…
We present a stability and convergence analysis of the space-time continuous finite element method for the Hamiltonian formulation of the wave equation. More precisely, we prove a continuous dependence of the discrete solution on the data…