The field of application of Functionally Graded Materialsis steadily expanding, which stimulates research in the relevant areas. In relation to penetration mechanics, these are primarily experimental studies of multilayer barriers consisting of plates “in contact” with various mechanical properties. Despite intensive research, explicit formulas for integral penetration characteristics (penetration depth and ballistic limit) cannot be obtained, except for the case when sequential penetration of layers (barriers with large gaps between layers). In this article, explicit formulas for the depth of penetration into an semi-infinite shield and for the ballistic limit velocity applying penetration into a shield of a finite thickness are derived assuming that the hardness of the barrier material varies continuously depending on barrier depth. The theoretical analysis is based on a model that represents the normal stress at points on the surface of the penetrating body that are in contact with the barrier as a quadratic function of the normal component of local impactor velocity with a zero linear term (the Vitman - Stepanov model). Difference of the dynamic hardness in different points of impactor-barrier contact is taken into account. It is also assumed that the nose of the striker has the form of a straight circular cone and the initial stage of penetration when the striker is not completely immersed in the barrier is ignored.

In this review, the traditional tasks of high-speed penetration are defined as tasks aimed at describing the movement of penetrators in monolithic barriers and determining integral characteristics of penetration, such as the depth of penetration into a semi-infinite shield or the ballistic limit when penetrating the barrier of finite thickness. Most of the papers on penetration mechanics dedicated to such problems are based on experimental and numerical methods; many of them are based on the use of analytical methods. Tasks that do not fall into this category will be referred to as non-traditional; this review is dedicated to them, with the main emphasis on tasks for the study of which the use of analytical methods or the potential and feasibility of using them has been characteristic. These are the tasks of penetration into non-monotonic barriers (multilayer layers with adjacent layers or with air gaps between them); the task of optimizing the shape of the strikers; the task of modeling and optimizing the active penetration when controlling the movement of the penetrator (the use of impactor with jet thruster to increase the penetration depth with retaining the integrity of the penetrator when getting soil samples from the surface of the planets or when delivering explosives to the object of destruction; the use of artillery for driving piles); the effectiveness analysis of segmented impactors (impactors with spaced elements); and others. An important feature of the review is the desire to highlight the characteristic methodological features of the implemented approaches, which are often hidden behind the list of research results. The material presented in the review covers promising areas of research and designed to facilitate orientation in the relevant topics, in particular, to select a revevant topic of the thesis, which is of both theoretical and practical interest.

Calculations related to pile driving play an important role in construction. Therefore, corresponding processes are controlled by regulatory documents, including the necessary formulas, which are accompanied by numerous tables and graphs, allowing the use of techniques in specific conditions of construction. The basis of such applied methods are the results of research in mechanics; the results of such studies are widely presented in the literature. This article is made within the framework of such studies. The article presents an approximate approach based on the evaluation of the real values of the parameters that determine the process of driving the pile. The proposed approach allowed to obtain an approximate formula to calculate the motion of the pile in soil by successive blows of the hammer falling freely. The following ways to analyze and improve models within this approach are outlined: (1) analysis of the accuracy of the proposed model by its presentation with the results of experiments and calculations using other models as well as with recommendations of normative instruments; (2) generalization of the model for the case when the mechanical properties of the soil vary depending on the depth of immersion into the soil.

This survey includes, mainly, investigations that Were published during recent years and a few earlier studies that were not included in the review by the same authors published in 2012. The survey covers analytical, numerical and experimental studies in which the effect of layering, spacing and change of the order of the plates on the protective performance of metallic shields against high-speed impact is investigated, and also studies that suggested analytical methods for optimization of multilayered shields. (C) 2016 Elsevier Ltd. All rights reserved.

On the basis of generalization of the Florence model to several ceramic layers, it is proved that arranging the ceramic plates in order of increasing material density implies the maximum the ballistic limit velocity of the armor in comparison with other arrangements.

We describe virtually all known analytical models for predicting protective properties of concrete shields against normal high-speed impact by rigid projectiles. Presented formulas can be directly used in practical calculations. Particular emphasis is given to widely used one-stage and two-stage models which are systemized in a hierarchical classification system using a unified approach. One-stage models employ the same formula along the whole trajectory of a projectile for calculating a force exerted on a penetrating projectile by a shield. In the case of two-stage models, a resistance force at the first stage of penetration is a linear function of the instantaneous depth of penetration while at the second stage of penetration normal stresses at every location on projectile-shield contact surface are polynomial function of normal velocity component. Conditions of continuity of the resistance force and velocity of a projectile are invoked in the transition point between these two sub-models. A wide variety of models can be devised by using different sub-models at each stage of penetration.

The survey is dedicated to approximate empirical and analytical models which were suggested for describing high-speed penetration into geological shields. This review differs from the previously published reviews on this topic in the following respects: (i) includes a large number of models; (ii) describes models suggested during recent years; (iii) much attention is given to models which have been originally published in Russian and are not well known in the West. References list includes 81 items.