International Journal of Solids and Structures最新文献

A finite strain micromechanical analysis is presented for the prediction of the loss of microscopic stability of a class of metal matrix composites that are subjected to axial compressive loading and undergoing large deformations. The metallic constituent behavior is modeled by the single crystal anisotropic plasticity theory in which, due to the resolved shear stresses, plastic deformations occur along certain pre-defined slip planes. Thus, this incremental plasticity theory is capable of providing the effect of the applied axial loading on the induced shear stresses which dominate the microbuckling. The composites are assumed to possess slight imperfections at the interfaces, and in order to satisfy the interfacial conditions, a perturbation expansion is employed which yields zero and first order micromechanical analysis problems. The zero order problem corresponds to the micromechanical modeling of the composite with no imperfections, whereas the solution of the first order problem is utilized to obtain the critical stresses and deformations at which bifurcation buckling occurs. Both problems are solved by employing the finite strain high-fidelity generalized method of cells (HFGMC) micromechanics. Applications are given for various types of single crystal matrix composites including layered, particulate, continuous and short fiber composites. Finally, a comparison between the compressive strengths of a standard metal matrix boron/aluminum and SiC/single crystal composites is presented and discussed.

In this paper, a new algorithm to solve the elastic quarter-space, the eighth-space and the finite-length-space contact problems is proposed. This corresponds to an extension of the Hertz theory. The theoretical foundations of such a problem are limited, due to the presence of displacements at the free edges- or stresses at the virtual edges — resulting to complex boundary conditions. The new approach presented here is 3D and based on Guilbault’s ingenious fast correction method. In this approach, the edge effects are taken into account by introducing two corrective factors ${\psi }_1$, ${\psi }_2$ respectively on the $\left(Ox\right)$ and $\left(Oz\right)$ axes to replace the mirror pressure iterative process of Hetenyi. The exact numerical values of these two correction factors are derived analytically. The results show that the free edge can substantially increase locally the contact pressure and therefore the stresses and displacement fields if close to the contact area. So the pressure field and the contact zone present an asymmetry which is more pronounced as the free edge is getting closer. This study is carried out on spaces with one, two and four free edges which will be respectively called: quarter-space, eighth-space and finite-length-space. A validation is performed using a Finite Element Method (FEM) analysis. A parametric study is also performed to exhibit the differences with the Hertz solution, including in the situation where one expects the truncation of the contact area when the free edge is virtually located within the Hertz contact area.

Capturing the buckling instability mechanics of multi-layered film/substrate structures is essential for providing theoretical guidelines for designing flexible electronics (e.g., stretchable interconnects and strain-limiting structures) and understanding the morphogenesis in biology and geology. Previous buckling models of tri-layer substrate/film/substrate structures usually assumed infinite substrate thickness and incomplete forms of interfacial shear stress, failing to distinguish between local wrinkling and global buckling. In this work, we extend our previous model (Yuan et al., 2023) by accounting for both finite substrate thickness and a complete form of interfacial shear stress, without assuming uniform membrane strain in the film, to study the buckling instability of tri-layer structures. The local wrinkling versus global buckling is distinguished through energy analysis, yielding phase diagrams for a wide range of geometric parameters and material properties. The effects of finite substrate thickness and moduli on the critical compressive strain and wavelength for the onset of local wrinkling are thoroughly investigated. The high accuracy of current model is demonstrated by the excellent agreement between analytical predictions and finite element analysis. This study provides new insights into the stability analysis of substrate/film/substrate systems, and will aid in the design of flexible electronics.

In this paper, the dynamic shear response and failure of Ti-6Al-4V using four different test specimen geometries, viz. Hat-Shaped Specimen (HSS), Flat Hat-Shaped Specimen (FHSS), Chip Hat-Shaped Specimen (CHSS) and Double Shear Specimen (DSS), are critically examined and compared. Through a combination of experiments (using the standard Split-Hopkinson Pressure Bar system), finite-element simulations and metallographic examinations of their fracture morphology, the dynamic shear characteristics (strain hardening, strain rate strengthening effect and failure strain) of Ti-6Al-4V obtained using the different specimen geometries are critically examined, compared and analyzed. It will be shown that differences in the stress/strain uniformity, the plastic deformation zone, and the stress state induced by the different specimen geometries lead to discrepancies in the measured shear response and failure that were observed. The shear stress–strain curve obtained using the DSS will be shown to be more precise than the other specimen geometries.

This work focuses on dynamic continualization of multifield multilayered metamaterials in order to obtain energetically-consistent models able to provide an accurate description of the dispersive behavior of the corresponding discrete system. Continuum models, characterized by constitutive and inertial non-localities, have been identified through a recently proposed enhanced continualization scheme. They are identified by governing equations both of the integro-differential and higher-order gradient-type, whose regularization kernel or pseudo-differential functions accounting for shift operators are formally expanded in Taylor series. The adopted regularization kernel exhibits polar singularities at the edge of the first Brillouin zone, thus assuring the convergence of the frequency spectrum to the one of the Lagrangian system in the entire wave vector domain. The validity of the proposed approach is assessed through the investigation of multilayered discrete lattices with an antitetrachiral topology, where local resonators act as rigid links among the layers. The convergence of dispersion curves of the continuum model to the ones of the Lagrangian model is proved in the whole first Brillouin zone as the adopted continualization order increases, both considering the propagation and the spatial attenuation of Bloch waves inside the metamaterial. A low frequency continualization is also provided, leading to the identification of a first-order medium.

The modeling of the visco-electro-elastic behavior of functionally graded beam benders with PZT constituents is accomplished via a hierarchical framework that is based on the homogenization technique for composite layers and the laminate theory for a composite laminate. The representation of a bulk PZT constituent is based on linear visco-electro-elastic constitutive equations. The resulting bending displacements of PZT-graded bimorph and multimorph are obtained under the assumption of the Euler–Bernoulli beam. The experimental data of the bending displacements versus applied voltage are compared with the predictions for a bimorph and a multimorph, resulting in a good agreement. The responses of a bender to a complete cycle of applied voltage are shown in order to reveal the critical hysteretic actuation due to the presence of a visco-electro-elastic PZT material in a functionally graded piezoelectric beam bender which is made by functionally graded piezoelectric materials.

Architectured materials are engineered materials with specific geometries and arrangements to exhibit desired mechanical properties. One class of architectured material is the Topologically interlocked material (TIM) system. In TIM systems, a plurality of convex particles is assembled under specific geometric constraints such that a load-carrying structure is obtained without the need for an adhesive bond between building blocks. Past investigations have considered TIM systems with building blocks and assemblies with a high degree of symmetry. Here the geometric constraints commonly imposed on the geometry of the system are relaxed. Two new types of skewed building blocks are introduced: one with only a rotational symmetry and no mirror symmetry, and one without rotational or mirror symmetry. These blocks are used to build even and odd-numbered assemblies and to create TIM systems with both mirror and rotational symmetry, rotational symmetry only, and no symmetry. A vector field representing the material architecture is introduced and demonstrated to connect architecture and mechanical behavior. It is demonstrated that load transfer patterns in the TIM system closely match the geometric symmetry. This allows for the demonstration of achiral and chiral mechanical behavior as represented by the presence of reaction moments for the centrally loaded square TIM assembly. The chirality of the building blocks manifests itself in the mechanical behavior of the TIM system only once the deflection of the system opens the contacts between building blocks such that building blocks accommodate deformation. Chiral building blocks diffuse the load from the central load path dominant in the TIM systems built from achiral blocks. This construction concept allows for simultaneous improvements in mechanical properties (strength and stiffness) solely from geometry.

The Mullins effect is a highly anisotropic damage phenomenon exhibited by filled rubbers among other soft materials. When filled rubbers are subjected to uniaxial tension, their apparent stiffness drops in the direction of stretching but is essentially unaltered in the transverse directions. However, micromechanical full-network models where Mullins softening is described at the level of individual chains often predict that uniaxial deformations induce transverse softening in addition to softening in the stretching direction. Moreover, these approaches typically require the storage of damage state variables for each chain, which is computationally expensive. Taking an alternative approach, we present a full-network model for the Mullins effect where the damage state is described by a single macroscopic damage tensor from which the damage state in each direction can be calculated. The evolution of damage is specified through damage surfaces and damage flow rules, which depend on the directions of principal stretches. The model is shown to reproduce experimental data for filled rubbers sequentially subjected to uniaxial tension in different directions. The model is also implemented in the finite element software ABAQUS as a user subroutine UMAT to illustrate the suitability of the model to simulate non-homogeneous deformation states.

We report on circular buckles experimentally observed by optical and atomic force microscopy on gold ductile thin films deposited by physical vapor deposition on silicon wafers. It is shown that, whatever the radius blister dimensions, their maximum deflections are higher than those expected by the elastic theory. It suggests that plastic events may take place in the film, impacting on the blister morphology as a result. Based on nanoindentation experiments carried out on our gold films, a proper plastic hardening law has been determined by calculations using the finite elements method. The influence of this elasto-plastic behavior on the buckled circular profiles has been then numerically studied, compared to the experimental observations and discussed.