Thermodynamic Effects in Wave Propagation

Numerical study of temperature effects on the poro-viscoelastic behavior of articular cartilage.

Numerical study of the hydrofoil cavitation flow with thermodynamic effects

The effect of wave propagation in nonhomogeneous elastic solid whose elastic parameters depend on one space coordinate only is considered. The stress and displacement components are assumed to depend on this same space coordinate and time alone. Taking Young’s modulus E=E0 cos αx and density ρ=ρ0 cos αx, we obtain the general solution for the problem of wave propagation in nonhomogeneous elastic rod. Particular cases in which a modified sawtooth, square, and half sine wave rectifier output as input wave, fed through one end of the rod, are studied, and the displacement u(x,t) is obtained. Graphs are drawn to study the behaviour of the input waves at time t=2 s, α=0.01, and =3.5.

A finite element framework is presented for analyzing crack-tip phenomena in transversely isotropic, strain-limiting elastic materials. Mechanical response is characterized by an algebraically nonlinear constitutive model, relating stress to linearized strain. Non-physical strain singularities at the crack apex are mitigated, ensuring bounded strain magnitudes. This methodology significantly advances boundary value problem (BVP) formulation, especially for first-order approximate theories. For a transversely isotropic elastic solid with a crack, the governing equilibrium equation, derived from linear momentum balance and the nonlinear constitutive model, is reduced to a second-order, vector-valued, quasi-linear elliptic BVP. This BVP is solved using a robust numerical scheme combining Picard-type linearization with a continuous Galerkin finite element method for spatial discretization. Numerical results are presented for various loading conditions, including uniform tension, non-uniform slope, and parabolic loading, with two distinct material fiber orientations. It is demonstrated that crack-tip strain growth is substantially lower than stress growth. Nevertheless, strain energy density is found to be concentrated at the crack tip, consistent with linear elastic fracture mechanics principles. The proposed framework provides a robust basis for formulating physically meaningful, rigorous BVPs, critical for investigating fundamental processes like crack propagation, damage, and nucleation in anisotropic, strain-limiting elastic solids under diverse loading conditions.

A systematic development of a continuum model is presented, which is capable of describing the magneto-mechanical behavior of magnetic polymer gels commonly referred to as “ferrogels”. In the present research, ferrogels are treated as multicomponent, multiphase materials. They consist of a polymer network (P), fixed magnetic particles (f), mobile magnetic particles (m), and liquid (L). By considering ferrogels as multicomponent materials, interaction among constituents of ferrogels can be captured. This helps in understanding the process occurring inside ferrogels under the influence of external stimuli, such as magnetic fields. In our modeling approach, the field equations of ferrogels are derived within the framework of the theory of mixtures. The basic equations include Maxwell’s equations, balance of mass, linear momentum, angular momentum, energy, and entropy. In the framework of the theory of mixtures, balance relations are first presented at the constituent level also referred to as partial balance relations. By summing partial balance relations over all constituents and imposing the restrictions of theory of mixtures, balance relations of mixture (for the ferrogel) are obtained. In the current work the specific magnetization (magnetization per density) is considered as an evolving variable. It is demonstrated that balance of angular momentum is satisfied using the evolution equation of specific magnetization and constitutive laws. In the process of modeling, a suitable free energy function is introduced and thermodynamically consistent constitutive laws are formulated. Introducing certain assumptions, a reduced model of the ferrogel, a coupled magneto-mechanical formulation, is subsequently presented. The reduced model consists only of a polymer network (P) and fixed magnetic particles (f). It is concluded that the reduced model compares well to the existing ones in the literature. The magneto-mechanical problem based on the reduced model is solved in 2D using the finite element method. The only unknowns for the finite element method implementation are mechanical displacement and magnetic potential. Deformation of a ferrogel in a magnetic field is subsequently investigated. Elongation and contraction of a ferrogel are observed when a magnetic field is applied in the x- and y-directions, respectively. The numerical results were compared with existing experimental work in the literature. A good qualitative agreement was found between numerical and experimental results.

We show that the reasoning in favor of a symmetric couple stress tensor in Yang et al.'s introduction of the modified couple stress theory contains a gap, but we present a reasonable physical hypothesis, implying that the couple stress tensor is traceless and may be symmetric anyway. To this aim, the origin of couple stress is discussed on the basis of certain properties of the total stress itself. In contrast to classical continuum mechanics, the balance of linear momentum and the balance of angular momentum are formulated at an infinitesimal cube considering the total stress as linear and quadratic approximation of a spatial Taylor series expansion.

Surface wave propagation effects on buried segmented pipelines

On wave propagation in elastic solids with a doubly periodic array of cracks

Wave propagation through elastic solids with a periodic array of arbitrarily shaped defects

Non-hydrostatic modeling of drag, inertia and porous effects in wave propagation over dense vegetation fields

A simple procedure, based on Love’s approximate theory [The Mathematical Theory of Elasticity (Cambridge U. P., Cambridge, England, 1927), 4th ed.] for wave propagation in a bar, is proposed in order to consider dispersive effects in wave propagation in a thin-walled, fluid-filled, elastomer tube. It is assumed that the perturbation from steady flow in the tube is small enough that a linearized theory is valid, and that the elastic modulus of the tube is small compared with the bulk modulus of the fluid so that compressibility of the fluid can be neglected. The flexural rigidity of the tube wall, the inertia of the tube wall, and the radial inertia of the fluid are taken into account, and an approximate expression for the dispersion relation for the fundamental mode is obtained. In order to investigate the dispersive effects, resulting from inclusion of the inertia and flexural rigidity of the tube wall and the radial inertia of the fluid in the model, an initial value problem is considered in detail. The fast Fourier transform is used to obtain numerical solutions for small and intermediate times. Numerical results are presented in graphical form.

This paper is concerned with the existence of classical solutions to the following nonlinear system of evolution equations $$ \left\{ \begin{gathered} \frac{\partial }{{\partial t}}A(v) + \lambda B(v) + v \cdot \nabla A(v) + N(v) + \nabla p = f \hfill \\ \nabla \cdot v = 0 \hfill \\ \end{gathered} \right. $$ (1.1) in a space-time region Ω × (0, T), where Ω denotes a bounded two- or three-dimensional domain. By A and B above, we denote linear differential operators with constant coefficients, N is a nonlinear differential operator and λ ∈ R. For the problem to be well set, we need, of course, to supplement the equations (1.1) with appropriate initial and boundary conditions. Equations of this type arise naturally, e.g. from the balance of linear momentum and from the equation of continuity governing the motion of non-Newtonian fluids, with p denoting the pressure, v the velocity field and f the given body force.

This study analyzes the lethal clinical condition of aortic dissections from a numerical point of view. On the basis of previous contributions by Gültekin et al. (Comput Methods Appl Mech Eng 312:542–566, 2016 and 331:23–52, 2018), we apply a holistic geometrical approach to fracture, namely the crack phase-field, which inherits the intrinsic features of gradient damage and variational fracture mechanics. The continuum framework captures anisotropy, is thermodynamically consistent and is based on finite strains. The balance of linear momentum and the crack evolution equation govern the coupled mechanical and phase-field problem. The solution scheme features the robust one-pass operator-splitting algorithm upon temporal and spatial discretizations. Based on experimental data of diseased human thoracic aortic samples, the elastic material parameters are identified followed by a sensitivity analysis of the anisotropic phase-field model. Finally, we simulate an incipient propagation of an aortic dissection within a multi-layered segment of a thoracic aorta that involves a prescribed initial tear. The finite element results demonstrate a severe damage zone around the initial tear and exhibit a rather helical crack pattern, which aligns with the fiber orientation. It is hoped that the current contribution can provide some directions for further investigations of this disease.

Interface elasticity effects in polymer-filled nanoporous metals

To analyse the behaviour of thin structures of dielectric elastomer (DE) material a solid shell finite element is presented. The main characteristics of DEs are a non‐linear hyper elastic behaviour, the quasi‐incompressibility, and the ability to transform electric energy into mechanical work. Applying a voltage to thin DE structures may produce large elongation strains of 120‐380%. These large strains, the efficient electro‐mechanical coupling, and the light weight make DEs very attractive for the usage in actuators. Thus, there is a need for detailed research. With respect to the electro‐mechanical coupling a constitutive model is presented. An electric stress tensor and a total stress tensor are introduced by considering the electrical body force and couple in the balance of linear momentum and angular momentum, respectively. The governing equations are derived and embedded in the solid shell formulation. The element formulation is based on a Hu‐Washizu mixed variational principle using six independent fields: displacements, electric potential, strains, electric field, mechanical stresses, and dielectric displacements. It allows large deformations and accounts for physical nonlinearities to capture two of the main characteristics of DEs. The shell element could be applied for the modelling of arbitrary curved thin structures. The ability of the present element formulation is demonstrated in several examples. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)