Linear elasticity

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

Anisotropic stiffness measurements in a stress-path triaxial cell

Abstract: Anisotropy plays a significant role in many geotechnical problems. This paper describes how the anisotropic stiffness properties of soils may be assessed through stress path triaxial tests. Local strain instrumentation has been optimised to identify the linear elastic region of sand without sacrificing the ability to study behavior at strains up to 15%; the system described performs equally well with sands, silts and clays. A novel technique has been developed in which multi-directional shear wave velocity measurements are combined with static tests to provide a complete description of the soil's cross-anisotropic elastic properties through a simple manipulation of classical elastic theory. Results obtained in tests on a dense sand are presented to demonstrate the system capabilities, show how the theoretical approach may be applied in practice, and draw attention to some interesting features of the soil's elastic anisotropy.

Aortic valve leaflet mechanical properties facilitate diastolic valve function

Abstract: This work was concerned with the numerical simulation of the behaviour of aortic valves whose material can be modelled as non-linear elastic anisotropic Linear elastic models for the valve leaflets with parameters used in previous studies were compared with hyperelastic models, incorporating leaflet anisotropy with pronounced stiffness in the circumferential direction through a transverse isotropic model The parameters for the hyperelastic models were obtained from fits to results of orthogonal uniaxial tensile tests on porcine aortic valve leaflets The computational results indicated the significant impact of transverse isotropy and hyperelastic effects on leaflet mechanics; in particular, increased coaptation with peak values of stress and strain in the elastic limit The alignment of maximum principal stresses in all models follows approximately the coarse collagen fibre distribution found in aortic valve leaflets The non-linear elastic leaflets also demonstrated more evenly distributed stress and strain which appears relevant to long-term scaffold stability and mechanotransduction

Plane strain bifurcations of elastic layered structures subject to finite bending: theory versus experiments

Abstract: Finite plane strain bending is solved for a multilayered elastic–incompressible thick plate. This multilayered solution, previously considered only in the case of homogeneity, is in itself interesting and reveals complex stress states such as the existence of more than one neutral axis for certain geometries. The bending solution is employed to investigate possible incremental bifurcations. The analysis reveals that a multilayered structure can behave in a completely different way from the corresponding homogeneous plate. For a thick plate of neo-Hookean material, for instance, the presence of a stiff coating strongly affects the bifurcation critical angle. Experiments designed and performed to substantiate our theoretical findings demonstrate that the theory can be effectively used as a design tool for predicting the capability of an elastic multilayered structure to be subject to a finite bending without suffering localized crazing.

Thin-coating contact mechanics with adhesion

Abstract: An elementary theory for a rigid spherical indenter contacting a thin, linear elastic coating that is bonded to a rigid substrate was developed. This theory predicts that contact area varies as the square root of the compressive load in contrast to Hertz theory where contact area varies as the two-thirds power of the compressive load. Finite element analysis confirmed an approximate square root dependence of contact area on compressive load when the coating thickness-to-indenter radius ratio is less than 0.1 and when the coating Poisson’s ratio is less than 0.45. Thin-coating contact mechanics theories that use either the Derjaguin-Muller-Toporov (DMT) approximation or the Johnson-Kendall-Roberts (JKR) approximation were also developed. In addition, a finite element simulation capability that includes adhesion was developed and verified. Illustrative finite element simulations that include adhesion were then performed for a thin elastic coating (rigid indenter/substrate). Results were compared with the thin-coating contact theories and the transition from DMT-like to JKR-like response was examined.

Analysis of a heterogeneous multiscale fem for problems in elasticity

Abstract: This paper is concerned with a finite element method (FEM) for multiscale problems in linear elasticity. We propose a method which discretizes the physical problem directly by a macroscopic FEM, coupled with a microscopic FEM resolving the micro scale on small cells or patches. The assembly process of the unknown macroscopic model is done without iterative cycles. The method allows to recover the macroscopic properties of the material in an efficient and cheap way. The microscale behavior can be reconstructed from the known micro and macro solutions. We give a fully discrete convergence analysis for the proposed method which takes into account the discretization errors at both micro and macro levels. In the case of a periodic elastic tensor, we give a priori error estimates for the displacement and for the macro and micro strains and stresses as well as an error estimate for the numerical homogenized tensor.