Linear elasticity

About: Linear elasticity is a research topic. Over the lifetime, 9080 publications have been published within this topic receiving 258684 citations.

Thermomechanics of monolayer graphene: Rippling, thermal expansion and elasticity

Abstract: Thermomechanical properties of monolayer graphene with thermal fluctuation are studied by both statistical mechanics analysis and molecular dynamics (MD) simulations. While the statistical mechanics analysis in the present study is limited by a harmonic approximation, significant anharmonic effects are revealed by MD simulations. The amplitude of out-ofplane thermal fluctuation is calculated for graphene membranes under both zero stress and zero strain conditions. It is found that the fluctuation amplitude follows a power-law scaling with respect to the linear dimension of the membrane, but the roughness exponents are different for the two conditions due to anharmonic interactions between bending and stretching modes. Such thermal fluctuation or rippling is found to be responsible for the effectively negative in-plane thermal expansion of graphene at relatively low temperatures, while a transition to positive thermal expansion is predicted as the anharmonic interactions suppress the rippling effect at high temperatures. Subject to equi-biaxial tension, the amplitude of thermal rippling decreases nonlinearly, and the in-plane stress-strain relation of graphene becomes nonlinear even at infinitesimal strain, in contrast with classical theory of linear elasticity. It is found that the tangent biaxial modulus of graphene depends on strain non-monotonically, decreases with increasing temperature, and depends on membrane size. Both statistical mechanics and MD simulations suggest considerable entropic contribution to the thermomechanical properties of graphene, and as a result thermal rippling is intricately coupled with thermal expansion and thermoelasticity for monolayer graphene membranes.

2-D solution for free vibrations of parabolic shells using generalized differential quadrature method

Abstract: The Generalized Differential Quadrature (GDQ) procedure is developed for the free vibration analysis of complete parabolic shells of revolution and parabolic shell panels The First-order Shear Deformation Theory (FSDT) is used to analyze the above moderately thick structural elements The treatment is conducted within the theory of linear elasticity, when the material behaviour is assumed to be homogeneous and isotropic The governing equations of motion, written in terms of internal resultants, are expressed as functions of five kinematic parameters, by using the constitutive and kinematic relationships The solution is given in terms of generalized displacement components of the points lying on the middle surface of the shell The discretization of the system by means of the Differential Quadrature (DQ) technique leads to a standard linear eigenvalue problem, where two independent variables are involved The results are obtained taking the meridional and circumferential co-ordinates into account, without using the Fourier modal expansion methodology Several examples of parabolic shell elements are presented to illustrate the validity and the accuracy of GDQ method Numerical solutions are compared with the ones obtained using commercial programs such as Abaqus, Ansys, Femap/Nastran, Straus, Pro/Mechanica Very good agreement is observed Furthermore, the convergence rate of natural frequencies is shown to be very fast and the stability of the numerical methodology is very good The accuracy of the method is sensitive to the number of sampling points used, to their distribution and to the boundary conditions Different typologies of non-uniform grid point distributions are considered The effect of the distribution choice of sampling points on the accuracy of GDQ solution is investigated New numerical results are presented

Phase-field modeling of a fluid-driven fracture in a poroelastic medium

Abstract: In this paper, we present a phase field model for a fluid-driven fracture in a poroelastic medium. In our previous work, the pressure was assumed given. Here, we consider a fully coupled system where the pressure field is determined simultaneously with the displacement and the phase field. To the best of our knowledge, such a model is new in the literature. The mathematical model consists of a linear elasticity system with fading elastic moduli as the crack grows, which is coupled with an elliptic variational inequality for the phase field variable and with the pressure equation containing the phase field variable in its coefficients. The convex constraint of the variational inequality assures the irreversibility and entropy compatibility of the crack formation. The phase field variational inequality contains quadratic pressure and strain terms, with coefficients depending on the phase field unknown. We establish existence of a solution to the incremental problem through convergence of a finite dimensional approximation. Furthermore, we construct the corresponding Lyapunov functional that is linked to the free energy. Computational results are provided that demonstrate the effectiveness of this approach in treating fluid-driven fracture propagation.

On the linear elastic properties of regular and random open-cell foam models

Abstract: Foams can be created from coagulation of gas bubbles in liquid. After removal of cell faces, an open-cell foam remains consisting of a strut framework. In the past, mechanical properties were estimated by a small unit cell consisting of only a few struts. However, the random geometry of the foam can be of importance for the linear elastic properties. Here, large foam unit cells are created using Voronoi techniques. A smooth transition from regular to random geometries is made, showing the strong sensitivity of the mechanical properties from the geometry of the microstructure. Uniaxial global loads are transmitted through chains of highly loaded struts. The deformation of the struts in the foam is a mixture of bending and normal deformation, the ratio of which shown here to be dependent on the magnitude of the density.