Papers by Keyword: Nonlinear Elasticity

Abstract: The results of the numerical solution of the problem about interaction between spherical stamp and weakly compressible elastic specimen are investigated. The nonlinear generalization of linear elastic Hencky model is used as a constitutive relation. The results of the indentation problem solution are in good agreement with experimental data. The tests were performed on the kinematical loading fixture. The influence of geometrical parameters of specimen during indentation test on stress strain state and macro response are investigated.

Abstract: Approaches to mathematical modeling of nonlinear strain dynamics in heteromodular and porous materials are discussed; the mechanical properties of media are described in terms of the simple piecewise linear elastic models. Several nonstationary 1D boundary value problems show that the singularity of model relationships gives rise to shock waves and centered Riemann waves in generalized solutions. Nonstationary load modes leading to the listed nonlinear effects are indicated separately for heteromodular and porous media.

Abstract: This study is conducted to investigate the effects of losing fluid during extension of rabbit ACL (Anterior Cruciate Ligament) on its nonlinear behavior. The incompressible Neo-Hookean model is employed for modeling the mechanical response of ACL under the uniaxial loading. The material properties of the ligament are characterized by measuring the deformation of a continuum element regarding to two assumptions, the exact and near incompressible cases. In the near incompressible assumption, it is assumed that some fluids exit during ligament extension which influence the nonlinear structural response of the ACL. Finally, considering the nonlinearity of the ligament due to the material behavior and geometrical effect, the ligament behavior is modeled using the nonlinear FEM solution. This study provides a new insight based on the model incompressibility for the ACL of the rabbit knee. These findings help researchers to predict the patterns of injuries that occur in the ligament for different amount of losing fluid by developing the computational model to assess the nonlinear response

Abstract: The results of mathematical modeling of the dynamic interaction of a plane longitudinal shock wave with a plane interface between two isotropic nonlinear elastic materials are presented. The mechanical properties of deformable solid are given by the elastic Murnaghan model. The dynamic processes of deformations distribution are studied in the framework of the theory of singular surfaces. The numerical solutions of the corresponding self-similar problem with strong and weak deformations discontinuities in the reflected and refracted wave packages have been obtained on the basis of the developed scheme of computational experiment.

Abstract: In this work, the nonlinear elasticity of hexagonal Ti₂C monolayer is studied by first-principles calculations. The second-and third-order elastic constants were calculated using nonlinear elasticity theory. The nonlinear stress-strain relationship depending on higher order elastic constants was also revealed. The intrinsic breaking strength and corresponding breaking strain were deduced as 11.9 N/m at the maximum strain 16.6% for Ti₂C monolayer.

Abstract: The paper is devoted to development and numerical implementation for a numerical method for investigation of stress-strain state of the solids with large elastic-plastic deformations. Calculation algorithm is based on the linearized equation of virtual work, defined to actual state. The arc-length method is used. A spatial discretization is based on the finite element method. The developed algorithm of investigation of large elastic-plastic deformations is tested on the solution of the necking of circular bar problem and a conical shell subjecting to a constant ring load.

Abstract: One-dimensional process of formation and the subsequent motion of a plane transverse shock wave is studied on the basis of solutions of the corresponding nonlinear evolutionary equation. This equation defines behaviour of the solution in front area of wave process and follows from inner series of a matched asymptotic expansions method. A comparative analysis of the volume deformation and forming processes will be carried out and their basic differences are specified. In the capacity of model examples solutions of some concrete boundary value problems of a dynamic shear deformation are observed.

Abstract: Based on hyperbolic nonlinear elastic constitutive model of unloading rock mass, the anchoring rock mass of excavation spillway of a hydropower station has been taken for the study. And considering the impact of excavation unloading process, three reinforcement programs are compared and analyzed. Overall, the constraint by system anchors on deformation of the spillway slope is limited. If the limit on the slope deformation is higher, pre-stressed cables are necessary.

Abstract: MAX phases, include Ti3SiC2, Ti2AlC etc, are machinable ternary carbides or nitrides with excellent properties. These materials, however, have obvious nonlinear elastic deformation due to nano- layered crystal structure. The stress-strain curves of cyclically load-unload test have obvious hysteretic loops. Because of this mechanical hysteresis, the strain of MAX phases at one time is not determined only by the stress applied to the sample at this time. Here the influence of grain size, chemical composition and porosity on the nonlinear elastic strain was introduced. Because of two properties of this hysteresis: wiping out and congruency, the classic hysteretic mathematic model (Preisach-Mayergoyz model, P-M model) can be applied to calculate the strain of MAX phases after any complex deformation history.

Abstract: The presence of damage or cracks modifies the elastic properties of a sample, introducing nonlinear components in the elastic response to an ultrasonic excitation. Among other effects, we discuss here conditioning and memory, i.e. the transition of the sample to a new (non equilibrium) elastic state when perturbed by a strain, even at a relatively low amplitude. A quantification of these phenomena can be the basis for a novel Nondestructive Method to evaluate the integrity of a structural or mechanical component.