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We investigate finite plane deformations of an elliptic rigid inclusion embedded in a soft matrix that is made of a particular class of harmonic-type hyperelastic materials. The inclusion is assumed to be perfectly bonded to the matrix, which is subjected to a constant remote in-plane loading. Utilizing the Cauchy integral techniques associated with conformal mappings, we derive closed-form solutions for the full-field deformation, Piola stress, and Cauchy stress in the entire matrix. Numerical examples are presented to illustrate the current solutions in comparison with those established from linear elasticity theory. We find that in terms of the Cauchy stress around the inclusion, the maximum normal stress component always appears at the endpoints of the major axis of the inclusion, irrespective of the magnitude of the remote loading, while the maximum hoop stress component occurs not exactly at the above-mentioned endpoints when the remote loading exceeds a certain value. In particular, we identify an exact explicit formula for determining the relative rotation of the inclusion during deformation induced by a remote uniaxial loading of arbitrarily given magnitude and direction. [ABSTRACT FROM AUTHOR]

A variational inequality describing an elastic body with a finite set of rigid inclusions is considered. The Signorini condition is imposed on a part of the boundary of the body. On the other part a homogeneous Dirichlet boundary condition is specified. The inclusions are arranged such that distance between any two inclusions is not less than a given positive number. All inclusions are located at a nonzero distance from the outer boundary. An inverse problem is investigated, which consists in identification of positions of the rigid inclusions from the measurement of displacements on an observation boundary. Continuous dependency of the solution of the forward problem on parameters of inclusions' location and rotation is established. This provides existence of a solution for the inverse identification problem. [ABSTRACT FROM AUTHOR]

Two models are considered, which describe the equilibrium state of an inhomogeneous two-dimensional body with two connected rigid inclusions. The first model corresponds to an elastic body with two-dimensional rigid inclusions located in regions with a constant width (curvilinear rectangle and trapezoid). The second model involves thin inclusions described by curves. In both models, it is assumed that there is a crack described by the same curve on the interface between the elastic matrix and rigid inclusions. The crack boundaries are subjected to a one-sided condition of non-penetration. The dependence of the solutions of equilibrium problems on the width of two-dimensional inclusions is studied. It is shown that the solutions of equilibrium problems in the presence of two-dimensional inclusions in a strong topology are reduced to the solutions of problems for thin inclusions with the width parameter tending to zero. [ABSTRACT FROM AUTHOR]

We consider a multiphysics problem of equilibrium for a two-dimensional elastic body containing a thin rigid and thin elastic inclusions. The inclusions delaminate from the elastic matrix, forming a crack; therefore, the problem is posed in a nonsmooth domain with a cut. The mathematical model of the delaminated thin rigid inclusion was developed on the assumption that the function of rigid inclusion displacement has a prescribed structure. The elastic inclusion is modeled in the framework of theory of Timoshenko beam. The problem statement is presented both in a form of a variational inequality and in the form of a boundary value problem including the junction conditions in a common point of inclusions. The boundary condition on the crack faces has a form of inequality and as a result, the problem is non-linear. As a consequence, the construction of an algorithm for the numerical solution of the problem requires the use of additional analytical methods. The methods of domain decomposition, the method of Lagrange multipliers, and the finite element method are used. An algorithm for the numerical solution of the problem is constructed, and a computational example is provided. [ABSTRACT FROM AUTHOR]

Nonlinear mathematical models describing an equilibrium state of composite bodies which may come into contact with a fixed non-deformable obstacle are investigated. We suppose that the composite bodies consist of an elastic matrix and one or two built-in volume (bulk) rigid inclusions. These inclusions have a rectangular shape and one of them can vary its location along a straight line. Considering a location parameter as a control parameter, we formulate an optimal control problem with a cost functional specified by an arbitrary continuous functional on the solution space. Assuming that the location parameter varies in a given closed interval, the solvability of the optimal control problem is established. Furthermore, it is shown that the equilibrium problem for the composite body with joined two inclusions can be considered as a limiting problem for the family of equilibrium problems for bodies with two separate inclusions.

In this paper the magnetoelastic problem of an infinite homogeneous isotropic soft ferromagnetic material with a rigid inclusion and exerting a uniform magnetic flux is studied. • The analytical solutions are completely exact, and operable for complex shapes. • The relative rigid-body displacement of the rigid inclusion is introduced. • The solutions have a finite form for rigid inclusion shaped by laurent polynomial. • The concentrations are closely related to the contour and orientation of inclusion. The analytical investigations on a rigid inclusion embedded in a soft ferromagnetic material in two-dimensional space subjected to uniform magnetic load at infinity have been carried out, with the magnetic insulation boundary of the rigid inclusion. In our study, explicit solutions of the magnetic and stress fields are obtained based on linear magnetoelastic theory and complex variable theory. The relative rigid-body displacement of the rigid inclusion is considered to ensure the boundary condition and constraint satisfied accurately. It is found that the analytic solutions of Kolosov-Muskhelishvili (K-M) potentials have a compact form when the shape of rigid inclusion is characterized by Laurent polynomial with finite terms. As examples, the rigid-body displacement, magnetic flux and stress on the boundary of elliptic and polygonal rigid inclusions are analyzed, respectively. Our results show that the rigid-body displacement caused by a non-strong magnetic load is small, while the orientation and contour curvature of the rigid inclusions have significant effects on the distribution of the stress and magnetic flux fields. In addition, the maximum magnetic flux and maximum stress do not always occur at the maximum curvature point. For polygonal rigid inclusions, the orientations in which the extreme concentration is obtained are closely related to the number of tips of the inclusions. [ABSTRACT FROM AUTHOR]

This paper deals with the plane deformation concerning a rigid inclusion embedded in an infinite elastic matrix under a uniform remote stress. The rigid inclusion is assumed to be perfectly bonded to the matrix and its geometry is described by a polynomial mapping function with an arbitrary number of terms. The potential functions representing the stress field in the matrix are obtained in an explicit form using the Cauchy integral techniques other than the pure series expansion techniques which are not that wieldy in expanding the derivation. In addition to the explicit solution, specific examination of the stress distribution around some polygonal rigid inclusions is conducted by increasing the number of terms in the mapping function (a strictly polygonal shape of the inclusion corresponds to an infinite number of terms, and since inclusions in engineering are often chamfered, it is reasonable and of reference significance to take finite terms in the mapping function). We find that for a quasi-polygonal inclusion defined by a finite-term mapping function, increasing number of terms in the mapping function leads to only a slight change in the stress distribution at a large majority of the interface, and particularly not all the stress components in the vicinity of the corners of the inclusion increase as the corners of the inclusion become sharper with increasing number of terms in the mapping function. Specially, for the stress components that are intensified unboundedly at the corners of the inclusion with increasing number of terms in the mapping function, we establish and numerically justify a simple exponential relation between them and the curvature of the interface at the corners. [ABSTRACT FROM AUTHOR]

In this paper, we study the stress concentration around a circular rigid inclusion in an incompressible anisotropic homogeneous nonlinearly elastic thin sheet subjected to in-plane finite deformation uniaxial extension. Two classes of material symmetry are considered: transverse isotropy and orthotropy. For the case of transverse isotropy, a three-parameter constitutive relation that under infinitesimal deformations reduces appropriately to the classical incompressible linearized elastic transversely isotropic constitutive relation is studied. Similarly, a six-parameter constitutive relation is considered for the case of orthotropic material symmetry. These constitutive relations may be suitable to describe the response of transversely isotropic and orthotropic bodies subjected to moderate deformations. [ABSTRACT FROM AUTHOR]

The article concerns a junction problem for two-dimensional elastic body with a thin elastic inclusion and a volume rigid inclusion. It is assumed that the inclusions have a common point. A delamination of the thin inclusion from the surrounding elastic body is assumed thus forming an interfacial crack. Constraint-type boundary conditions are imposed at the crack faces to prevent interpenetration between the faces. Moreover, a connection between the crack faces is characterized by a positive damage parameter. Limit transitions are justified as the damage parameter tends to infinity and to zero. In addition to this, a transition to limit is analysed as a rigidity parameter of the thin inclusion tends to infinity. Limit models are investigated. In particular, junction conditions at the common point are found for all cases considered. This article is part of the theme issue 'Non-smooth variational problems and applications'. [ABSTRACT FROM AUTHOR]

A new mathematical model describing an equilibrium of a thermoelastic heterogeneous Kirchhoff–Love plate is considered. A corresponding nonlinear variational problem is formulated with respect to a two-dimensional domain with a cut. This cut corresponds to an interfacial crack located on a given part of the boundary of a flat rigid inclusion. The flat inclusion is described by a cylindrical surface. Due to the presence of the flat rigid inclusion in the plate, restrictions of the functions describing displacements to the corresponding curves satisfy special constraints having a linear form. Displacement boundary conditions of an inequality type are set on the crack faces that ensure a mutual non-penetration of opposite crack faces. Solvability of the problem is proved. Under the assumption that the solution of the variational problem is smooth enough, an equivalent differential formulation is found. This article is part of the theme issue 'Non-smooth variational problems and applications'. [ABSTRACT FROM AUTHOR]

A scheme for solving the problem of determining the probability of failure and probabilistic (statistical) characteristics of the failure loading magnitude of a composite material plate is considered. The plate structure is a flat homogeneous matrix with stochastically distributed rigid rod inclusions. The geometric parameters of inclusions are considered independent random variables with given probability distribution laws. The expressions for the failure loading distribution function, the probability of failure, the mean value, and the dispersion of the failure loading were received and presented. Their dependence on the type of stress state, the inclusion number, and matrix Poisson’s ratio were studied graphically.

Abstract We consider a family of variational problems on the equilibrium of a composite Kirchhoff–Love plate containing two flat rectilinear rigid inclusions, which are connected in a hinged manner. It is assumed that both inclusions are delaminated from an elastic matrix, thus forming an interfacial crack between the inclusions and the surrounding elastic media. Displacement boundary conditions of an inequality type are set on the crack faces that ensure a mutual nonpenetration of opposite crack faces. The problems of the family depend on a parameter specifying the coordinate of a connection point of the inclusions. For the considered family of problems, we formulate a new inverse problem of finding unknown coordinates of a hinge joint point. The continuity of solutions of the problems on this parameter is proved. The solvability of this inverse problem has been established. Using a passage to the limit, a qualitative connection between the problems for plates with flat and bulk hinged inclusions is shown.

In the absence of high-quality soils, the rigid inclusion reinforcement technique has been extensively used in geotechnical engineering practice to meet the serviceability requirements of construction projects. This article aims to investigate the behavior of a single footing placed on soft soil reinforced by four rigid inclusions using three-dimensional (3D) finite difference modeling (FDM). A set of full-scale experimental tests are used as references for the development of the numerical approach. The concurrence of the numerical and experimental data allows us to assess the load transfer platform thickness influence on the system under centered and eccentric loading conditions. Some preliminary insights can thus be obtained based on this analysis for the soft soil improvement using rigid inclusions at the design stage. [ABSTRACT FROM AUTHOR]

An elastoplastic rotating cylinder with a rigid inclusion and fixed ends is investigated. The analysis is based on infinitesimal strain theory, Schmidt-Ishlinskii yield criterion, and its associated flow rule and perfectly plastic material behavior. Both loading and unloading stages are studied. The closed-formed solutions for all stages of deformation including secondary plastic flow are obtained. The results are illustrated by the distributions of the stresses and plastic strains in a cylinder rotating at different speeds.

Within the framework of Kirchhoff–Love plate theory, we analyze a variational model for elastic plates with rigid inclusions and interfacial cracks. The main feature of the model is a fully coupled nonpenetration condition that involves both the normal component of the longitudinal displacements and the normal derivative of the transverse deflection of the crack faces. Without making any artificial assumptions on the crack geometry and shape variation, we prove that the first-order shape derivative of the potential deformation energy is well defined and provide an explicit representation for it. The result is applied to derive the Griffith formula for the energy release rate associated with crack extension. [ABSTRACT FROM AUTHOR]

We consider a family of variational problems on the equilibrium of a composite Kirchhoff–Love plate containing two flat rectilinear rigid inclusions, which are connected in a hinged manner. It is assumed that both inclusions are delaminated from an elastic matrix, thus forming an interfacial crack between the inclusions and the surrounding elastic media. Displacement boundary conditions of an inequality type are set on the crack faces that ensure a mutual nonpenetration of opposite crack faces. The problems of the family depend on a parameter specifying the coordinate of a connection point of the inclusions. For the considered family of problems, we formulate a new inverse problem of finding unknown coordinates of a hinge joint point. The continuity of solutions of the problems on this parameter is proved. The solvability of this inverse problem has been established. Using a passage to the limit, a qualitative connection between the problems for plates with flat and bulk hinged inclusions is shown. [ABSTRACT FROM AUTHOR]

Abstract We consider equilibrium problems for a cracked composite plate with a thin cylindrical rigid inclusion. Deformation of an elastic matrix is described by the Timoshenko model. The plate is assumed to have a through crack that does not touch the rigid inclusion. In order to describe mutual nonpenetration of the crack faces we impose a boundary condition in the form of inequality on the crack curve. For a family of appropriate variational problems, we analyze the dependence of their solutions on the location of the rigid inclusion. We formulate an optimal control problem with a cost functional defined by an arbitrary continuous functional on the solution space, while the location parameter of inclusion is chosen as the control parameter. The existence of a solution to the optimal control problem and a continuous dependence of the solutions in a suitable Sobolev space with respect to the location parameter are proved.

The model of a plate brittle material reinforced with randomly sized and placed rigid rectilinear inclusions that do not interact with each other is considered. The geometric parameters of inclusions (length and orientation) are statistically independent random variables, with certain given laws of probability distribution. Diagrams of statistical strength criterion for such plates are constructed under conditions of comprehensive tension-compression. The diagrams are constructed for plates using a material of a different structural inhomogeneity and Poisson's ratio of an elastic homogeneous matrix. The statistical nature of the scale effect is studied, the intensity of which depends on the type of stress state. [ABSTRACT FROM AUTHOR]

A new nonlinear mathematical model is proposed that describes an equilibrium of a two-dimensional elastic body with two interacting thin rigid inclusions. Thin rigid inclusions are defined by straight line segments. In the initial state of the body, both inclusions are in contact at one breaking point. Both inclusions can move, subject to the conditions in the form of systems of inequalities describing a possible contact of the inclusions. These three systems of inequalities for infinitesimal rigid displacements correspond to three possible cases of mutual configurations of inclusions in equilibrium state. Inclusions exfoliate near the breaking point from the elastic matrix, in other words, there are cracks of a given length on both sides of thin inclusions. Nonpenetration conditions of the Signorini type are imposed on the curves defining the cracks. On a part of the outer boundary, clamping conditions are prescribed. The problem is formulated as a minimization of an energy functional over a non-convex set of possible displacements defined in an appropriate Sobolev space. The existence of a solution to the problem is proved. Optimality conditions of the solution have been obtained under the condition of sufficient smoothness of the solution. [ABSTRACT FROM AUTHOR]

Abstract We consider equilibrium problems for an inhomogeneous two-dimensional body with a crack and a rigid inclusion. The matrix of the body is assumed to be elastic. The boundary condition on the crack curve is an inequality describing mutual nonpenetration of the crack faces. We study two different equilibrium models. For the first model, we assume that a volume rigid inclusion is described by a domain. The second one describes a body containing a set of connected thin rigid inclusions, each corresponding to a curve. The crack is given by the same curve in both models. We prove that the solutions of equilibrium problems corresponding to the second model strongly converge to the problem solution for the first model as the number of inclusions tends to infinity.

The stress concentration factor (SCF) along the boundary of a hole and a rigid inclusion in an infinite isotropic solid under the anti-plane shear is revisited by using degenerate kernels in the boundary integral equation (BIE) although this result was obtained by invoking the extended circle theorem of Milne-Thomson as well as the complex variable approach. The degenerate kernel of series form for the closed-form fundamental solution is used for the circle and the ellipse in terms of polar and elliptic coordinates, respectively. The slender ratio of the ellipse and the orientation are two parameters for our study. The strain energy density along the boundary is increased or decreased due to the different types of loading and various aspect ratios of the ellipse. An analytical solution for the SCF is then derived for any orientation of the ellipse relative to the applied load. The reciprocal relation for the SCF between a hole and a rigid inclusion with respect to different loading is also addressed. Besides, this analytical derivation can clearly show the appearing mechanism why the BEM/BIEM suffers the degenerate scale in the rigid inclusion. [ABSTRACT FROM AUTHOR]

This paper is based on small-scale laboratory tests (1:10) of a rigid inclusion-improved soil under normal gravity. A low area improvement ratio (2.4%) under monotonic and cyclic loading was used. 3D numerical calculations are performed to model these tests. The proposed numerical modeling is performed by the finite element method (FEM) using the ABAQUS software. A representative elementary volume model is suggested for reducing the calculation time. A hypoplastic constitutive model (HYP model) is applied for the load transfer platform (LTP). A total of three geometrical configuration cases of the experimental tests are numerically considered including a rigid slab over a mattress of 100 mm on the reinforced soil, a mattress of 100 mm on the reinforced soil, and a rigid slab over a mattress of 50 mm on the reinforced soil. The proposed numerical results are compared to the experimental data and the previous numerical results of Houda. The cyclic response of the systems is shown in terms of soil arching and settlements. The decrease in pile efficacy and the cumulative settlements are exhibited. The HYP model allows to better simulate the soil arching mechanisms inside the LTP than the CYsoil model used in the Houda's research work. A good concordance between the proposed numerical results and the experimental data was obtained. [ABSTRACT FROM AUTHOR]

A new type of non-classical 2D contact problem formulated over non-convex admissible sets is proposed. Specifically, we suppose that a composite body in its undeformed state touches a wedge-shaped rigid obstacle at a single contact point. Composite bodies under investigation consist of an elastic matrix and a rigid inclusion. In this case, the displacements on the set, corresponding to a rigid inclusion, have a predetermined structure that describes possible parallel shifts and rotations of the inclusion. The rigid inclusion is located on the external boundary and has the form of a wedge. The presence of the rigid inclusion imposes a new type of non-penetration condition for certain geometrical configurations of the obstacle and the body near the contact point. The sharp-shaped edges of the obstacle effect such sets of admissible displacements that may be non-convex. For the case of a thin rigid inclusion, which is described by a curve and a volume (bulk) rigid inclusion specified in a subdomain, the energy minimization problems are formulated. The solvability of the corresponding boundary value problems is proved, based on analysis of auxiliary minimization problems formulated over convex sets. Qualitative properties of the auxiliary variational problems are revealed; in particular, we have found their equivalent differential formulations. As the most important result of this study, we provide justification for a new type of mathematical model for 2D contact problems for reinforced composite bodies.

Determination of the bearing capacity from pile load tests on rigid inclusions In addition to conventional pile foundations, rigid inclusion is often used in problematical ground conditions to satisfy the requirements of serviceability and stability for the foundation of structures. In order to gain knowledge about the load‐bearing behaviour of the columns, test loads were carried out. Static and dynamic test loads were applied. The rigid inclusion were equipped with fibre‐optic measurement technology to enable separate determination of the shaft and base resistances. The information gained from the measurements on the load transfer behaviour shows that the rigid inclusion have higher total resistances and in particular shaft resistances than auger piles, which were manufactured as reference with the same diameter and the same tie‐in length in identical ground conditions. It is shown that common design methods only partially reflect the measured load‐settlement behaviour. The test results are the basis for future adjustments of the design methods for rigid inclusion. [ABSTRACT FROM AUTHOR]

An elastoplastic rotating cylinder with a rigid inclusion under plane strain condition is investigated. The analysis is based on infinitesimal strain theory, Tresca's yield condition, and its associated flow rule and perfectly plastic material behavior. Both loading and unloading are considered. It is established that secondary plastic flow may occur during unloading after a previous rotation, and the exact solutions for all stages of deformation are obtained. The results are illustrated by the distributions of the displacement, stress and plastic strain in a cylinder rotating at different speeds. [ABSTRACT FROM AUTHOR]

We consider equilibrium problems for a cracked composite plate with a thin cylindrical rigid inclusion. Deformation of an elastic matrix is described by the Timoshenko model. The plate is assumed to have a through crack that does not touch the rigid inclusion. In order to describe mutual nonpenetration of the crack faces we impose a boundary condition in the form of inequality on the crack curve. For a family of appropriate variational problems, we analyze the dependence of their solutions on the location of the rigid inclusion. We formulate an optimal control problem with a cost functional defined by an arbitrary continuous functional on the solution space, while the location parameter of inclusion is chosen as the control parameter. The existence of a solution to the optimal control problem and a continuous dependence of the solutions in a suitable Sobolev space with respect to the location parameter are proved. [ABSTRACT FROM AUTHOR]

In recent decades due to the development and diversification of construction technologies, soil improvement procedures became a competitive and cost-effective alternative to increase the load-bearing capacity of the subsoil, while reducing deformations of the structure. Attributed to urbanization, lands with insufficient soil bearing capacity are becoming construction sites, for which it is essential to influence or increase the bearing capacity of the subsoil for the safety and compatibility of structures. Soil reinforcement with concrete elements is used in more and more construction project in Hungary. The structural behavior of traditional pile foundation is well known, and adequate standards are available during the planning process. On the other hand, soil improvement procedures, in our case for the design of rigid inclusion foundation no standards are available only guidelines and recommendations. Because of that in almost all cases, the design phase includes numerical modelling, which is used to prove the efficiency of the system and receive a more accurate picture of the real structural behavior. [ABSTRACT FROM AUTHOR]

A non-linear model describing the equilibrium of a cracked plate with a volume rigid inclusion is studied. We consider a variational statement for the Kirchhoff–Love plate satisfying the Signorini-type non-penetration condition on the crack faces. For a family of problems, we study the dependence of their solutions on the location of the inclusion. We formulate an optimal control problem with a cost functional defined by an arbitrary continuous functional on a suitable Sobolev space. For this problem, the location parameter of the inclusion serves as a control parameter. We prove continuous dependence of the solutions with respect to the location parameter and the existence of a solution of the optimal control problem. [ABSTRACT FROM AUTHOR]

• The composite method of numerical and intelligence approaches is used to evaluate the performance of a single footing over RI-reinforced soft soil. • A novel hybrid LCMWSO-based RF model is an effective intelligence model for predicting LTE. • Model-1 containing seven variables (L, LT, LE, E, CF, FA, CR) is the best prediction model. • The load transfer platform thickness is the most important variable for the LTE prediction. The rigid inclusion (RI) reinforcement technique has been increasingly used to reduce settlements for engineering constructions over soft soils. However, the load transfer mechanisms within the granular mattress are not well understood, especially for the RI-reinforced systems with the presence of structural elements such as footings. To evaluate the performance of a single footing over RI-reinforced soft soils, a novel intelligence approach combining the white shark optimizer (WSO) and the Logistic chaotic mapping (LCM) was proposed to optimize the random forest (RF) model for predicting the load transfer efficiency (LTE). Seven variables were considered to systematically investigate the LTE, including the loading magnitude (L), the load eccentricity (LE), the geometrical and strength parameters of the load transfer platform thickness (LT), Young's modulus (E), cohesion (C) and friction angle (F)) and the compression ratio (CR). Based on the feature selection method, nine different combination models were developed to estimate the LTE. Their performances were compared using the determination coefficient (R2), the root mean squared error (RMSE), the variance accounted for (VAF) and the Willmott's index (WI). The evaluation results indicated that the LWSO-RF model containing seven variables (L, LT, LE, E, CF, FA, CR) is the best one as it gives the highest prediction accuracy in both the training and testing phases. The sensitivity results demonstrated that LT is the most important variable for the LTE prediction. This work utilizes an intelligence approach to extend the traditional numerical simulation analysis for predicting the LTE, which provides additional guidance to further assess the performance of foundations over RI-reinforced soft soil. [ABSTRACT FROM AUTHOR]

This paper is based on small-scale laboratory tests (1:10) of a rigid inclusion-improved soil under normal gravity. A low area improvement ratio (2.4%) under monotonic and cyclic loading was used. 3D numerical calculations are performed to model these tests. The proposed numerical modeling is performed by the finite element method (FEM) using the ABAQUS software. A representative elementary volume model is suggested for reducing the calculation time. A hypoplastic constitutive model (HYP model) is applied for the load transfer platform (LTP). A total of three geometrical configuration cases of the experimental tests are numerically considered including a rigid slab over a mattress of 100 mm on the reinforced soil, a mattress of 100 mm on the reinforced soil, and a rigid slab over a mattress of 50 mm on the reinforced soil. The proposed numerical results are compared to the experimental data and the previous numerical results of Houda. The cyclic response of the systems is shown in terms of soil arching and settlements. The decrease in pile efficacy and the cumulative settlements are exhibited. The HYP model allows to better simulate the soil arching mechanisms inside the LTP than the CYsoil model used in the Houda’s research work. A good concordance between the proposed numerical results and the experimental data was obtained.

Interaction of migrating {101¯2} twin boundary with obstacles was analyzed by atomistic and finite elements computer simulations of magnesium. Two types of obstacles were considered: one is a non-shearable obstacle and another one is the void inside bulk material. It is shown that both types of obstacles inhibit twin growth and increased stress is necessary to engulf the obstacle in both cases. However, the increase of critical resolved shear stress is higher for the passage of the twin boundary through raw of voids than for interaction with non-shearable obstacles.

In this paper we consider the inverse problem of determining a rigid inclusion inside a thin plate by applying a couple field at the boundary and by measuring the induced transversal displacement and its normal derivative at the boundary of the plate. The plate is made by non-homogeneous, linearly elastic, and isotropic material. Under suitable a priori regularity assumptions on the boundary of the inclusion, we prove a constructive stability estimate of log type. A key mathematical tool is a recently proved optimal three-spheres inequality at the boundary for solutions to the Kirchhoff-Love plate's equation. [ABSTRACT FROM AUTHOR]

An equilibrium problem for an elastic body containing a rigid inclusion is solved. There is a delamination crack on a portion of the interface between the inclusion and the elastic body. Mutual nonpenetration conditions are set on the crack faces. According to the solution method, the problem with a rigid inclusion can be treated as a limit one for a family of problems with a crack. A numerical method relying on a modified duality scheme and the Uzawa algorithm is proposed for solving the problem. FEM-based numerical results are presented. [ABSTRACT FROM AUTHOR]

Under study is some two-dimensional model describing equilibriumof a composite solid with a thin rigid inclusion and a crack. A boundary condition of Signorini's type is prescribed on the crack curve. For a family of corresponding variational problems, the dependence is analyzed of their solutions on the parameter characterizing the location of the rigid inclusion. The existence of solution of the optimal control problem is proved. For this problem, the quality functional is defined with the help of an arbitrary continuous functional on the solution space, while the location of the inclusion is chosen as the control parameter. [ABSTRACT FROM AUTHOR]

The use of rigid inclusions for soil bearing capacity and/or settlement control offers an efficient and economical alternative to the traditional pile foundations. The general approach towards analyzing a slab or a raft foundation on a rigid inclusion system is through the use of unit cell models constructed in programs which incorporate either the finite element or finite difference method. This type of model offers information regarding the interaction of the rigid inclusion with the surrounding soil and with the transfer layer. However, the effect of the inclusions on the global behavior of the slab or raft foundation cannot be anticipated in this manner. As such, three dimensional finite element models are necessary in order to study aspects such as the influence of foundation rigidity and the type and distribution of foundation loading on the bending moments and shear forces that develop in the raft or slab. In this article the results of an analysis of a raft foundation on a rigid inclusion reinforced soil, modelled in the finite element software, Plaxis 3D, are presented and discussed. [ABSTRACT FROM AUTHOR]

Development of effective methods of determining the stress-strain state thin-walled structures with inclusions, reinforcements and other stress concentrators is an important task, both from a theoretical and practical point of view, by reason of their great practical application. Aim: The aim of the research is to analyze the elastic-deformed state of a spherical shallow shell. Materials and Methods: In this work, based on the generalized scheme of integral transformations, a constructive method of direct numerical-analytical solutions of boundary value problem of calculating the stress-strain state of a spherical shallow shell with the inclusion in bending is proposed. Results: The results of numerical calculations are presented. Calculations allow predicting the value of deformation of the cylindrical shells structure with reinforcements and determining the optimum parameters for the design or manufacture. The obtained results can be used in determining the strength characteristics of structural elements that consist of composite materials. The article contains comparative analysis of the results and demonstrates the effectiveness of the method for solving this class of problems.

Abstract We study the contact problems for elastic plates with a rigid inclusion. We consider the case of frictionless contact between the rigid part of the plate and a rigid obstacle. The contact is modeled with the Signorini-type nonpenetration condition. The deformation of the transversely isotropic elastic part of the plate is described by the Timoshenko model. We analyze the dependence of solutions to the contact problems on the size of rigid inclusion. The existence of a solution to the optimal control problem is proved. For that problem, the cost functional characterizes the deviation of the displacement vector from a given function, whereas the size parameter of rigid inclusion is chosen as the control function.