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We use Muskhelishvili's complex variable formulation to study the interaction problem associated with a circular incompressible liquid inclusion embedded in an infinite isotropic elastic matrix subjected to the action of an edge dislocation at an arbitrary position. A closed-form solution to the problem is derived largely with the aid of analytic continuation. We obtain, in explicit form, expressions for the internal uniform hydrostatic stresses, nonuniform strains and nonuniform rigid body rotation within the liquid inclusion; the hoop stress along the liquid-solid interface on the matrix side and the image force acting on the edge dislocation. We observe that (1) the internal strains and rigid body rotation within the liquid inclusion are independent of the elastic property of the matrix; (2) the internal hydrostatic stress field within the liquid inclusion is unaffected by Poisson's ratio of the matrix and is proportional to the shear modulus of the matrix; and (3) an unstable equilibrium position always exists for a climbing dislocation. [ABSTRACT FROM AUTHOR]

A solution for a dilatation line which occupies an arbitrary position in an elastic wedge with free surfaces and an arbitrary apex angle is found for the first time. The analytical expressions are given in the Mellin space for the stress fields of the dilatation line. It is shown that the free surfaces of the wedge strongly affect upon the stress fields. The axial and hydrostatic stress components are not equal to zero outside the dilatation line. They are strongly inhomogeneous and can change their signs, while their magnitude is comparable with that of the other non-vanishing stress components. They also demonstrate strong non-monotonic and alternating dependence on the wedge apex angle. For the wedge apex angles of 180° and 360°, the non-vanishing stress components of the dilatation line are represented in an explicit form. The results obtained can be used for solving similar problems for long elastic dilatation inclusions of arbitrary cross section embedded to wedge-shaped elastic bodies. The paper is devoted to the memory of our friend and colleague Igor Sevostianov who gave a great contribution to micromechanics of composite and porous materials. [ABSTRACT FROM AUTHOR]

This work aims to give a comprehensive and accurate view of those micromechanical models that have been developed over the past two decades by our research team. We hereby refer to the distinct capabilities and theoretical difficulties of such models published in various journals by discussing them in a more integrated manner. We also believe that our community can find a significant benefit from this work through below mentioned discussions, which answer many of the questions asked by researchers and those interested in this field. Returning to this work topic, the low-cycle fatigue (LCF) life is highly affected by microstructural instabilities, inhomogeneity and shear bands formation. The first type of damage is related to the nuclei of fatigue microcracks, for several FCC and BCC metals generally governed by continuous irreversible slips within the intensive slip bands. The second type of damage concerns ductile damage caused by cavitation induced by plastic strain and hydrostatic stress. Thereby, fatigue-failure is a relevant topic that requires further explanations to better understand the plausible damaging mechanisms of microcracks and/or microvoids at lower levels of observation. To model the microcracks initiation, some attempts were conducted via micromechanical models assuming, for example, that the microcracks initiate at the crystallographic slip system level describing the LCF response of metals under simple and complex loading paths. In this overview, the latest development of mixed approach with double character called Micromechanical Determinist-Probabilistic Model (MDPM) coupled with damage will be presented with its generalized structure. [ABSTRACT FROM AUTHOR]

Based on the Mohr–Coulomb yield criterion, an analytical method is presented to determine the plastic zone in an infinite plate weakened by a circular hole and subjected to non-hydrostatic stresses at infinity. It is worth noting that this paper considers the more complicated case that the plastic zone cannot completely surround the hole, namely the elastoplastic interface is non-enclosed. Initially, the non-circular elastic zone in the physical plane is mapped onto the outer region of a unit circle in the image plane by the conformal transformation in the complex variable method. Thereby, determining the elastoplastic interface is equivalent to solving the mapping function coefficients. The nonlinear equations for solving the coefficients are established by considering both the stress continuity conditions along the elastoplastic interface and the stress boundary conditions along the elastic part of the hole. Naturally, the problem can be further transformed into an optimization problem, which is ultimately achieved by the differential-evolution algorithm; what is more, an analytical solution with high accuracy is obtained. Based on the programmed computing, the influences of various parameters on the shape and size of the plastic zone are given. [ABSTRACT FROM AUTHOR]

We apply conformal mapping techniques with analytic continuation to study the existence of a uniform hydrostatic stress field inside a non-elliptical inclusion bonded to an infinite matrix via a finite thickness interphase layer when the matrix is simultaneously subjected to a concentrated couple as well as uniform remote in-plane stresses. We show that the desired internal uniform hydrostatic stress field is possible for given material and geometric parameters provided a certain constraint is placed on the remote loading. Subsequently, when the single loading parameter, five material parameters and three geometric parameters are prescribed, all of the unknown complex coefficients appearing in the series representing the corresponding conformal mapping function can be uniquely determined from a set of nonlinear recurrence relations. We find that the internal uniform hydrostatic stress field, the constant mean stress in the interphase layer and the hoop stress along the inner interface on the interphase layer side are all unaffected by the existence of the concentrated couple whereas the non-elliptical shape of the (three-phase) inclusion is attributed solely to the influence of the nearby concentrated couple. [ABSTRACT FROM AUTHOR]

Material models for ductile damage, crack initiation, and crack growth are of high interest, e.g. for metal forming simulations. Empirical engineering approaches are often applied, but the numerical results are sensitive to the discretization if no method is utilized to prevent ill-posedness of the underlying boundary value problem due to strain softening. In order to face this issue, an empirical damage model is equipped with a gradient-enhancement which introduces an additional length scale parameter. Until the initiation of damage, the material is modeled with standard von Mises plasticity. Damage initiation is taken into account by an uncoupled failure indicator. After damage initiation, material degradation is assumed to be driven by a non-local quantity, which depends on plastic deformation and stress triaxiality. During damage evolution, the macroscopic material behavior becomes dependent on hydrostatic stress, which is motivated by well known void growth and coalescence mechanisms. A calibration strategy is developed to determine the parameters of strain hardening, damage initiation, and damage evolution as well as the internal length step-by-step. The proposed model is calibrated to experimental data of a pressure vessel steel. Reasonable predictions of smooth and notched tensile tests as well as a small punch test show the validity of the model for loadings from moderate to high stress triaxialities. [ABSTRACT FROM AUTHOR]

We study the internal stress resultants inside an elastic inhomogeneity of arbitrary shape embedded in an infinite Kirchhoff plate (matrix) via an intermediate coating. Each material phase is considered an isotropic laminated plate and the surrounding matrix is subjected to uniform remote membrane stress resultants and bending moments. We find that internal uniform hydrostatic stress resultants within the inhomogeneity can be achieved when (i) the mapping function characterizing the shape of the inhomogeneity is identified and specialized accordingly; (ii) the relative coating thickness should satisfy a higher-order algebraic equation; (iii) several restrictions on the remote loading should be satisfied for given material and geometric parameters of the composite plate. When all these conditions are met, the hoop membrane stress resultant and hoop bending moment on the coating side are uniform along the entire inhomogeneity–coating interface. [ABSTRACT FROM AUTHOR]

A cylindrical structure undergoing volume expansion and contraction is common in engineering practice. For example, the charging (discharging) process of axisymmetrical batteries will give rise to volume expansion (shrinkage). The nitriding process of axles for better fatigue performance also introduces volume expansion. Here, by taking the equivalence of volume expansion (or shrinkage) as continuous insertion (or distraction) of infinitesimal dislocations, we supply a framework to solve the stress field of a cylinder with arbitrary insertion (distraction) profile of materials along the radial direction. Under the assumptions that the volume expansion profile along the axis of a cylinder is uniform and the deformation is small so that the current configuration is regarded as the original, we supply analytical solutions of stress fields to several typical volume expansion or shrinkage profiles. Our analysis shows that different volume variation gives rise to either high tensile stress in the surface or hydrostatic tension in the core, and supplies distinct failure mechanisms in cylindrical batteries. [ABSTRACT FROM AUTHOR]

A series of multistage triaxial compression, creep, and stress relaxation tests were conducted on frozen loess at the temperature of −6℃ in order to study the damage evolution and recrystallization enhancement of mechanical properties during deformation process. The effect of strain rate, confining pressure, and hydrostatic stress history in the degradation laws of mechanical properties is investigated further. The strain rate has a significant influence on the stress–strain curve which dominates the evolution trend of mechanical properties. The mechanical behaviors (strength, stiffness, and viscosity) of frozen loess all exhibit evident response for the consolidation and pressure melting phenomenon caused by the confining pressure. The multistage loading tests under different hydrostatic stresses are capable of differentiating the development characteristics of mechanical properties during axial loading and hydrostatic compression process, respectively. The testing results indicated that the recrystallization of the ice particle in the frozen soils is an important microscopic factor for enhancement behaviors of mechanical parameters during the deformation process. This strengthening degree of mechanical properties is determined by temperature, duration time, deformation degree, and stress state during the recrystallization process. The phase transformation led by pressure melting and ice recrystallization is a nonnegligible changing pattern of frozen soils microstructure, which has apparent role in the damage evolution of mechanical properties. [ABSTRACT FROM AUTHOR]

The present paper investigates the effect of initial stress, irregularity depth, irregularity factor and magneto-elastic coupling parameter on the dynamic response due to a normal moving load with constant velocity on the free surface of an irregular magneto-elastic transversely isotropic half-space under the state of hydrostatic initial stress. The expressions for normal stress and shear stress are obtained in closed form analytically. The considerable effect of initial stress, irregularity depth, irregularity factor and magneto-elastic coupling parameter on normal stress and shear stress are computed numerically and depicted by means of graphs. Moreover, comparative study highlighting the effect of various types of irregularity viz. rectangular irregularity, parabolic irregularity and no irregularity on the normal stress and shear stress is a key feature of the study. [ABSTRACT FROM AUTHOR]

In this paper, we built a mathematical model to study the influence of the initial stress on propagation of longitudinal waves in a hollow infinite circular cylinder in the presence of an axial initial magnetic field. The elastic cylinder is assumed to be made of a tetragonal system material. The problem is described by the equations of elasticity, taking into account the effect of the initial stress and the electro-magnetic equations of Maxwell. This requires the solution of the equations of motion in cylindrical coordinates with the z-axis directed along the axis of the cylinder. The displacement components will be obtained by founding the analytical solutions of the motion’s equations. The frequency equations have been obtained in the form of a determinant involving Bessel functions. The roots of the frequency equation give the values of the characteristic circular frequency parameters of the first three modes for various geometries when the initial hydrostatic stress is compression or tension. These roots, which correspond to various modes, are numerically calculated and presented graphically. This study shows that waves in a solid body propagating under the influence of an initial stress can differ significantly from those propagating in the absence of the initial stress. The results of this research are used in analyzing the relationship between magnetic field, the initial stress and the frequency equation and could lead to discussions for using the magnetic field and the initial stress in ultrasound imaging. [ABSTRACT FROM AUTHOR]

This paper represents the author’s contribution to the second world-wide failure exercise using his failure mode concept modelling capability. The second world-wide failure exercise deals with the behaviour of isotropic material and unidirectional as well as multidirectional unidirectional laminae-composed laminates subjected to three-dimensional (triaxial) states of stress. Twelve challenging test cases were provided by the organisers and those covered stress–strain curves and failure envelopes under three-dimensional stress states. The application of the new failure mode concept model has extended the three-dimensional modelling by taking into account the effects of hydrostatic pressure and second glass temperature shift factor on the stress–strain curves and failure envelopes. The failure mode concept model was capable of successfully solving the majority of all the problems and a comparison between the predictions and test data is planned to be published in Part B of the second world-wide failure exercise. [ABSTRACT FROM AUTHOR]

A new strain energy based failure model is developed for fibrous composite laminates under multi-axial loadings, taking into account the effect of hydrostatic stress. A failure mode dependent exponential stiffness reduction model is used to predict material response beyond the initial failure. Predicted mechanical responses and failure envelopes are presented for the 12 benchmark test cases of Part A of the Second World Wide Failure Exercise. The cases cover a wide variety of isotropic, unidirectional and multidirectional laminates under combined in-plane, out-of-plane and triaxial loadings. Both stress–strain curves and the complete failure envelopes were successfully predicted. In some instances, the failure envelopes were open. The predictions together with suitable adjustment of certain parameters are compared with test data in Part B of the Second World Wide Failure Exercise, to be published in Journal of Composite Materials. [ABSTRACT FROM AUTHOR]

Triaxial failure analysis using multicontinuum decomposition has been employed at the constituent level to predict nonlinear damage behavior and failure envelopes, all involving through-thickness stresses. In addition, a structural analysis algorithm is presented and is found to be numerically highly efficient in that the relationships between composite properties and damaged or failed constituent properties are completely determined prior to structural analysis. As a part of the Second World-Wide Failure Exercise, three-dimensional failure envelopes and stress–strain curves involving isotropic materials as well various unidirectional and multi-directional materials are presented for 12 test cases requested by the organizers. The present paper provides new developments in the multicontinuum methodology including: (a) modification of the constituent failure criteria, (b) incorporation of pressure effects, (c) new damage analyses, and (d) implementation into a commercial finite element package. Correlation with experimental results is provided in a second article addressing Part B of the Second World-Wide Failure Exercise. [ABSTRACT FROM AUTHOR]