Well-posedness of a model of strain gradient plasticity for plastically irrotational materials

The initial boundary value problem corresponding to a model of strain gradient plasticity due to [Gurtin, M., Anand, L., 2005. A theory of strain gradient plasticity for isotropic, plastically irrotational materials. Part I: Small deformations. J. Mech. Phys. Solids 53, 1624–1649] is formulated as a variational inequality, and analysed. The formulation is a primal one, in that the unknown variables are the displacement, plastic strain, and the hardening parameter. The focus of the analysis is on those properties of the problem that would ensure existence of a unique solution. It is shown that this is the case when hardening takes place. A similar property does not hold for the case of softening. The model is therefore extended by adding to it terms involving the divergence of plastic strain. For this extended model the desired property of coercivity holds, albeit only on the boundary of the set of admissible functions.     

Size effects on void growth in single crystals with distributed voids

The effect of void size on void growth in single crystals with uniformly distributed cylindrical voids is studied numerically using a finite deformation strain gradient crystal plasticity theory with an intrinsic length parameter. A plane strain cell model is analyzed for a single crystal with three in-plane slip systems. It is observed that small voids allow much larger overall stress levels than larger voids for all the stress triaxialities considered. The amount of void growth is found to be suppressed for smaller voids at low stress triaxialities. Significant differences are observed in the distribution of slips and on the shape of the deformed voids for different void sizes. Furthermore, the orientation of the crystalline lattice is found to have a pronounced effect on the results, especially for the smaller void sizes.     

混凝土的弹塑性损伤双面本构模型

针对混凝土材料拉压应变空间下损伤机制的不同,结合连续损伤力学和塑性理论建立了一个全新的本构模型。该模型中损伤和塑性变形的演变由应变空间的同一个非弹性曲面来控制,但对拉压应变空间中非弹性曲面的演变分别采用了随动强化法则和各向同性演化规律。计算结果表明,该模型能较好地描述混凝土材料在单轴及多轴单调加载和低周反复荷载下的典型非线性特征。     

Enhancing the Bolzon–Schrefler–Zienkiewicz Constitutive Model for Partially Saturated Soil

This paper presents an enhanced version of the elasto-plastic model for partially saturated soil first proposed by Bolzon, Schrefler and Zienkiewicz in 1996, “BSZ” model, which uses the effective stress tensor and suction as independent stress variables. It is recalled that the effective stress tensor proposed by Lewis and Schrefler in 1982 is thermodynamically consistent and, compared with other choices of stress tensors, results particularly suitable for partially saturated soil mechanics. A hydraulic constitutive relationship and a hydraulic hysteresis are introduced in the model, to take into account the irreversible deformation during cyclic drying and wetting until structural collapse. For this reason the plastic rate of strain is split into the sum of two components: one depending on the effective stress tensor and the other one on suction. This is the new feature of the BSZ model. This enhanced model is then cast into a thermodynamical framework at macroscopic level and it is shown that it is possible to derive the constitutive law from the Helmholtz free energy and a dissipation function, both for associative and non- associative plasticity. Finally the model predictions have been compared with experimental data for Sion slime, with particular emphasis on the deviatoric part, and model predictions of hysteretic behaviour have been investigated in case of a wetting and drying cycle on compacted betonite–kaolin.     

The impulsive response of sandwich beams: Analytical and numerical investigation of regimes of behaviour

An analytical model is developed to classify the impulsive response of sandwich beams based on the relative time-scales of core compression and the bending/stretching response of the sandwich beam. It is shown that an overlap in time scales leads to a coupled response and to the possibility of an enhanced shock resistance. Four regimes of behaviour are defined: decoupled responses with the sandwich core densifying partially or completely, and coupled responses with partial or full core densification. These regimes are marked on maps with axes chosen from the sandwich beam transverse core strength, the sandwich beam aspect ratio and the level of blast impulse. In addition to predicting the time-scales involved in the response of the sandwich beam, the analytical model is used to estimate the back face deflection, the degree of core compression and the magnitude of the support reactions. The predictions of the analytical model are compared with finite element (FE) simulations of impulsively loaded sandwich beams comprising an anisotropic foam core and elastic, ideally plastic face-sheets. The analytical and numerical predictions are in good agreement up to the end of core compression. However, the analytical model under-predicts the peak back face deflection and over-predicts the support reactions, especially for sandwich beams with high strength cores. The FE calculations are employed to construct design charts to select the optimum transverse core strength that either minimises the back face deflections or support reactions for a given sandwich beam aspect ratio or blast impulse. Typically, the value of the transverse core strength that minimises the back face deflection also minimises the support reactions. However, the optimal core strength depends on the level of blast impulse, with higher strength cores required for greater blasts.     

The indenter tip radius effect in micro- and nanoindentation hardness experiments.

Nix and Gao established an important relation between the microindentation hardness and indentation depth. Such a relation has been verified by many microindentation experiments (indentation depths in the micrometer range), but it does not always hold in nanoindentation experiments (indentation depths approaching the nanometer range). Indenter tip radius effect has been proposed by Qu et al. and others as possibly the main factor that causes the deviation from Nix and Gao's relationship. We have developed an indentation model for micro- and nanoindentation, which accounts for two indenter shapes, a sharp, conical indenter and a conical indenter with a spherical tip. The analysis is based on the conventional theory of mechanism-based strain gradient plasticity established from the Taylor dislocation model to account for the effect of geometrically necessary dislocations. The comparison between numerical result and Feng and Nix's experimental data shows that the indenter tip radius effect indeed causes the deviation from Nix-Gao relation, but it seems not be the main factor. The project supported by the National Natural Science Foundation of China (10121202) and the Ministry of Education of China (20020003023)     

Some issues associated with the intermediate space in single-crystal plasticity

In this study we show that some discussions of finite-deformation single-crystal plasticity are conceptually flawed in their focus on a set referred to as the intermediate configuration. Specifically, we prove that what is usually referred to as the intermediate configuration is not a configuration but instead a vector space that we term the intermediate space. We argue that when applied to single crystals this intermediate space represents the lattice.     

Mechanical annealing under low-amplitude cyclic loading in micropillars

Mechanical annealing has been demonstrated to be an effective method for decreasing the overall dislocation density in submicron single crystal. However, simultaneously significant shape change always unexpectedly happens under extremely high monotonic loading to drive the pre-existing dislocations out of the free surfaces. In the present work, through in situ TEM experiments it is found that cyclic loading with low stress amplitude can drive most dislocations out of the submicron sample with virtually little change of the shape. The underlying dislocation mechanism is revealed by carrying out discrete dislocation dynamic (DDD) simulations. The simulation results indicate that the dislocation density decreases within cycles, while the accumulated plastic strain is small. By comparing the evolution of dislocation junction under monotonic, cyclic and relaxation deformation, the cumulative irreversible slip is found to be the key factor of promoting junction destruction and dislocation annihilation at free surface under low-amplitude cyclic loading condition. By introducing this mechanics into dislocation density evolution equations, the critical conditions for mechanical annealing under cyclic and monotonic loadings are discussed. Low-amplitude cyclic loading which strengthens the single crystal without seriously disturbing the structure has the potential applications in the manufacture of defect-free nano-devices.