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In this paper, the influence of plastic deformation on the rebound behaviour of spheres during oblique impacts with a substrate at various impact angles is analysed using Finite Element Methods (FEM). Both oblique impacts of the elastic spheres with an elastic-plastic substrate and those of an elastic-plastic sphere with an elastic substrate are considered. For each impact case, impact angles ranging from 0° to 85° are specified by either keeping the impact speed constant, i.e, changing impact angle will vary both the normal impact velocities and tangential velocities, or keeping the normal impact velocity constant, i.e., only the tangential velocities are changed for different impact angles. It has been found that, during oblique impacts, the plastic deformation not only dissipates the initial impact kinetic energy but also leads to permanent deformation of the impacting bodies that significantly affect the rebound behaviour of the spheres, especially at relatively high impact angles. Consequently, the rebound behaviour of spheres during oblique impacts depends upon which of contacting bodies (the sphere or the substrate) deforms plastically and different rebound behaviours were observed between the impacts of an elastic sphere with an elastic-plastic substrate and those of an elastic-plastic spheres with an elastic substrate.

A semi-analytical procedure is presented to solve the elastoplastic buckling problem of cylindrical shells made of functionally groded materials (FGMs) under combined axial and torsional loads. The elastoplastic properties are assumed to vary smoothly according to the power law distribution rule, introduced in the J2 deformation theory for formulation of the constitutive relation of FGMs in the framework of the Tamura–Tomota–Ozawa (TTO) model, which is a volume fraction-based material model. The critical condition is deduced by the Ritz method. Assuming the uniform prebuckling strain, a biaxial stress state analysis is conducted to determine the analytical position of the elastoplastic interface, which is used in the integration of the elastoplastic internal force and all the material-related structural parameters. Finally, an iterative procedure is adopted to find the exact elastoplastic critical load. Numerical results indicate the effects of the inhomogeneous parameter and the elastoplastic material properties of their constituents on the stability region and plastic flow region of the materials.

Dynamic elastoplastic analysis is a subject of great engineering importance and can practically be handled only by numerical methods due to its complexity. The aim of this paper is to develop the meshless local natural neighbor interpolation (MLNNI) method to perform the dynamic analysis of elastoplastic structures under plane stress or plane strain conditions. The MLNNI, as an effective truly meshless method for solving partial differential equations, employs local weak forms over a local subdomain and shape functions from the natural neighbor interpolation (NNI). The shape functions so formulated possess delta function property and, therefore, the essential boundary conditions can be implemented as ease as in the finite element method (FEM). The predictor-corrector form of the Newmark algorithm is used for the time-marching process and iterations are performed at every time step. The applied loads can have any transient time variation. Comparative results are presented at the end to illustrate the effectiveness of the proposed method and demonstrate its accuracy.

Numerical implementation of an anisotropic constitutive model for clays (SANICLAY) is presented. Moreover, a case study in which a soil embankment is placed on a K₀-consolidated over-consolidated clay is analyzed by conducting an elastoplastic fully-coupled finite element analysis. It is shown that anisotropy has significant impact on the ground settlement caused by the placement of soil embankment and on the pore pressure generation and dissipation within the foundation soil. The simulations using SANICLAY favorably compare with the field measurements of ground settlement and pore pressure. The drawbacks of the use of an isotropic elastoplastic model (Cam Clay) are also demonstrated.

In this paper, a hierarchic high-order three-dimensional finite element formulation is studied for hyperelastic and anisotropic elastoplastic problems at finite strains. The element formulation allows for anisotropic ansatz spaces supporting efficient discretizations of beam-, plate-, and shell-like structures. Several benchmark examples are investigated and the results of the high-order formulation are compared to analytic solutions and different mixed finite element formulations. Special emphasis will be placed on locking effects, robustness with respect to high aspect ratios and element distortion as well as anisotropies related to the material model. Furthermore, the interplay between the chosen ansatz space for the displacement field and mapping function in the context of geometrically nonlinear problems are studied.

It is a troublesome and focused problem of solid mechanics to solve shell structures with Smoothed particle hydrodynamics (SPH), which is a fully meshfree method. In this paper, an integral model of SPH shell is proposed to more accurately capture the nonlinear strain along the thickness direction. Though the idea is similar to the "Gaussian integral point" in Finite element method (FEM), it is absent and just the first presentation in SPH. Furthermore, focusing on the metal materials, a high-efficiency iteration algorithm for plasticity is derived and the plastic damage theory of Lemaitre–Chaboche is also introduced based on the studies of Caleyron et al. (2011). As for the dynamic fracture of SPH shell, the multiple line segments algorithm is proposed to treat crack adaptively, which overcomes the mesh dependency occurring in mesh method. These algorithms and theories are successfully applied in the integral model of SPH shell of elasticity, plastic damage and dynamic fracture. Finally, the linear and nonlinear analyses of geometry and material are carried out with FEM, the global model and the integral model of SPH shell to prove the feasibility and the accuracy of the integral model.

An improved interpolating element-free Galerkin (IIEFG) method for elastoplasticity is proposed in this paper. In the IIEFG method, the shape functions are constructed by the improved interpolating moving least-squares (IIMLS) method, and the final system equations are obtained by using the Galerkin weak form of elastoplasticity. Compared with the interpolating moving least-squares (IMLS) method, the weight functions are not singular in the IIMLS method, in which the shape functions have the interpolating property. The IIMLS method has fewer unknown coefficients to be solved in the trial functions than the moving least-squares (MLS) approximation. Hence, the IIEFG method is able to directly enforce the displacement boundary condition and obtain numerical solutions with high computational accuracy and efficiency. To show advantages of the IIEFG method, some selected elastoplastic examples are given.

Torsional loading of elastoplastic materials leads to size effects which are not captured by classical continuum mechanics and require the use of enriched models. In this work, an analytical solution for the torsion of isotropic perfectly plastic Cosserat cylindrical bars with circular cross-section is derived in the case of generalized von Mises plasticity accounting solely for the symmetric part of the deviatoric stress tensor. The influence of the characteristic length on the microrotation, stress and strain profiles as well as torsional size effects are then investigated. In particular, a size effect proportional to the inverse of the radius of the cylinder is found for the normalized torque. A similar analysis for an extended plasticity criterion accounting for both the couple-stress tensor and the skew-symmetric part of the stress tensor is performed by means of systematic finite element simulations. These numerical experiments predict size effects which are similar to those predicted by the analytical solution. Saturation effects and limit loads are found when the couple-stress tensor enters the yield function.