The size dependence of micro-toughness in ductile fracture

Micro-toughness in ductile fracture is defined as the plastic work dissipated per unit fracture surface area in the material separation processes of void growth and coalescence. A micromechanics model for the estimation of the size dependence of micro-toughness in ductile fracture is presented. Size effects are incorporated in the model using the conventional mechanism-based strain gradient plasticity (CMSG) theory. A finite element model of an axisymmetric representative unit cell with an initial spherical void is used to validate model predictions. Two characteristic length scales emerge from the model. The initial void radius sets the scale for the initial spherical void growth. For the subsequent void coalescence, the scale is set by the width of the intervoid ligament. Energy dissipation in ductile fracture is found to be dominated by the mechanisms of coalescence, and the micro-toughness in ductile fracture is found to be size dependent for dimple sizes approximately one order of magnitude larger than the material length scale.     

The stress concentration near a rigid line inclusion in a prestressed, elastic material. Part I.: Full-field solution and asymptotics

A lamellar (zero-thickness) rigid inclusion, so-called ‘stiffener’, is considered embedded in a uniformly prestressed (or prestrained), incompressible and orthotropic elastic sheet, subject to a homogeneous far-field deformation increment. This problem is solved under the assumption of plane strain deformation, with prestress principal directions and orthotropy axes aligned with the stiffener. A full-field solution is obtained solving the Riemann-Hilbert problem for symmetric incremental loading at infinity (while for shear deformation the stiffener leaves the ambient field unperturbed). In addition to the full-field solution, the asymptotic Mode I near-tip representation involving the corresponding incremental stress intensity factor are derived and these results are complemented with the Mode II asymptotic solution. For null prestress, the full-field stress state is shown to match correctly with photoelastic experiments performed by us (on two-part epoxy resin samples containing an aluminum lamina). Our experiments also confirm the fracture patterns for a brittle material containing a stiffener, which do not obey a hoop-stress criterion and result completely different from those found for cracks. Issues related to shear band formation and evaluation of energy release rate for a stiffener growth (or reduction) are deferred to Part II of this article.     

Stability of convex shells of revolution made of particulate composites with physically nonlinear matrix and damageable inclusions

The problem of bifurcation instability of shells of revolution made of particulate composites with physically nonlinear matrix and damageable inclusions is formulated and solved __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 6, pp. 70–80, June 2008.     

Banach空间中混合型微分─积分包含解的存在性

研究可分Ｂａｎａｃｈ空间中一类混合型的微分－积分包含，证明了解的存在性，其单值情形改进和推广了文［１～３］中关于混合型微分－积分方程的若干存在性结果．     

Existence Results on the Second-Order Nonconvex Sweeping Processes with Perturbations

We prove several existence theorems for second-order differential inclusions of the form , when K and F are two convex or nonconvex set-valued mappings taking their values in a Hilbert space.     

Determination of Fluid Inclusion Electrolytes by Atomic Absorption Spectroscopy as of the Water Leachates of Crushed or Decrepitated Quartz Samples from Madan,Bulgaria

Two methods of opening fluid inclusions in hydrothermal quartz from Madan (Bulgaria) – mechanical (crushing) and thermal (decrepitation), followed by water leaching of the released components – were applied and compared. Problems concerning the sample preparation procedure, such as choice of an optimal sample mass and grain fraction, contamination of the grain surfaces, as well as the influence of La³⁺ and Cs⁺ additions on the water leaches etc., are discussed. The mol ratios X/Na (X=K, Ca, Mg, Mn) were determined by flame or electrothermal vaporization AAS of the dilute solutions obtained. The total salinity of inclusion fluid estimated by classical microcryometry is used to calculate the total concentrations of the main ions (Na⁺, K⁺, Ca²⁺, Mg²⁺ and Mn²⁺) in the water phase of the inclusions. Furthermore, the maximum concentrations of Pb²⁺ and Cu²⁺ were evaluated.     

On the Dynamics of a Differential Inclusion Built upon a Nonconvex Constrained Minimization Problem

In this paper, we study the dynamics of a differential inclusion built upon a nonsmooth, not necessarily convex, constrained minimization problem in finite-dimensional spaces. In particular, we are interested in the investigation of the asymptotic behavior of the trajectories of the dynamical system represented by the differential inclusion. Under suitable assumptions on the constraint set and the two involved functions (one defining the constraint set, the other representing the functional to be minimized), it is proved that all the trajectories converge to the set of the constrained critical points. We present also a large class of constraint sets satisfying our assumptions. As a simple consequence, in the case of a smooth convex minimization problem, we have that any trajectory converges to the set of minimizers.Research partially supported by the research project CNR-GNAMPA Mathematical Methods for Control Theory and supported in part by the European Communitys Human Potential Program under Contract HPRN-CT-2002-00281, Evolution Equations.     

An Averaging Method for Singularly Perturbed Systems of Semilinear Differential Inclusions with C0-Semigroups

We consider a system of two semilinear differential inclusions with infinitesimal generators of C ₀-semigroups. The nonlinear terms are of high frequency with respect to time and periodic with a specified period. Moreover, they are condensing in the state variables (x,y) with respect to a suitable measure of noncompactness. The goal of the paper is to give sufficient conditions to guarantee, for >0 sufficiently small, the existence of periodic solutions and to study their behaviour as 0. The main tool to achieve this is the topological degree theory for uppersemicontinuous, condensing vector fields.     

Directionally Continuous Selections and Nonconvex Evolution Inclusions

In Bressan and Staicu, Set-Valued Anal. 2 (1994), 415–437, qualitative properties for solutions of the evolution inclusion Ax+F(t,x), with A generator of a contractive semigroup and F a lower semicontinuous closed valued multifunction defined on compact subset of R×cl(D(A)), were deduced as corollaries of similar properties for solutions of the evolution inclusion Ax+G(t,x), where G is upper semicontinuous compact convex valued, obtained from a suitable directionally continuous selection from F.In this paper we prove that the compactness assumption on the domain of F can be avoided.     

Implicit resolvent dynamical systems for quasi variational inclusions

In this paper, we suggest and analyze a class of implicit resolvent dynamical systems for quasi variational inclusions by using the resolvent operator technique. We show that the trajectory of the solution of the implicit dynamical system converges globally exponentially to the unique solution of the quasi variational inclusions. Our results can be considered as a significant extension of the previously known results.