Abstract: Abstract
In a phase-field approach to fracture crack propagation is modeled
by means of an additional continuous field. In this paper, two
problems of linear elastic fracture mechanics are studied
experimentally and numerically in order to evaluate the
practicability of the phase-field approach and to validate the
measured parameters. At first, a three-point bending experiment of
silicon dies is simulated assuming static plate bending. Then, wave
propagation and spallation in a Hopkinson bar test are analyzed in a
dynamic regime. The simulations show that phase-field fracture
reproduces the experimental results with high accuracy. The results
are comparable to other fracture simulations, e.g., the cohesive
element technique. In total, the phase-field approach to fracture is
capable of tracking crack evolution in a very convenient and
quantitatively correct way. PubDate: 2015-05-27

Abstract: Abstract
We discuss the solution of Saint-Venant’s problem for solids with helical anisotropy. Here the governing relations of the theory of elasticity in terms of displacements were presented using the helical coordinate system. We proposed an approach to construct elementary Saint-Venant solutions using integration of ordinary differential equations with variable coefficients in the case of a circular cylinder with helical anisotropy. Elementary solutions correspond to problems of extension, of torsion, of pure bending and of bending of shear force. The solution of the problem is obtained using small parameter method for small values of twist angle and numerically for arbitrary values. Numeric results correspond to problems of extension–torsion. Dependencies of the stiffness matrix (in dimensionless form) on angle between the tangent to the helical coil and the axis of the cylinder corresponding to stiffness on stretching and torsion are illustrated graphically for different values of material and geometrical parameters. PubDate: 2015-05-26

Abstract: Abstract
The procedure for reuse of finite element method (FEM) programs for heat transfer and structure analysis to solve advanced thermo-mechanical problems is presented as powerful algorithm applicable for coupling of other physical fields (magnetic, fluid flow, etc.). In this case, nonlinear Block-Gauss–Seidel partitioned algorithm strongly couples the heat transfer and structural FEM programs by a component-based software engineering. Component template library provides possibility to exchange the data between the components which solve the corresponding subproblems. The structural component evaluates the dissipative energy induced by inelastic strain. The heat transfer component computes the temperature change due to the dissipation. The convergence is guaranteed by posing the global convergence criterion on the previously locally converged coupled variables. This enables reuse of software and allows the numerical simulation of thermo-sensitive problems. PubDate: 2015-05-23

Abstract: In the following analysis, we present a rigorous solution for the problem of a circular elastic inclusion surrounded by an infinite elastic matrix in finite plane elastostatics. The inclusion and matrix are separated by a circumferentially inhomogeneous imperfect interface characterized by the linear spring-type imperfect interface model where the interface is such that the same degree of imperfection is realized in both the normal and tangential directions. Through the use of analytic continuation, a set of first-order coupled ordinary differential equations with variable coefficients are developed for two analytic potential functions. The unknown coefficients of the potential functions are determined from their analyticity requirements and some additional problem-specific constraints. An example is then presented for a specific class of interface where the inclusion mean stress is contrasted between the homogeneous interface and inhomogeneous interface models. It is shown that, for circumstances where a homogeneously imperfect interface may not be warranted, the inhomogeneous model has a pronounced effect on the mean stress within the inclusion. PubDate: 2015-05-20

Abstract: A novel method for damage detection of multi-cracked beam-like structures by analyzing the static deflection is presented. The damage incurred produces a change in the stiffness of the beam. This causes a localized singularity which can be identified by a wavelet analysis of the displacement response. The existence and location of the cracks can be revealed by positions of the peaks in the continuous wavelet transform (CWT). To achieve this, the static profile of beams is analyzed with Gauss2 wavelet to identify the cracks. Beams under some ideal boundary and prescribed load conditions are considered. The deflected shape of the beam with open and fatigue cracks has been simulated under static loading using lumped crack models adopted from fracture mechanics and involving various degrees of complexity. The deflection of cracked beam in closed form for several cases of loads, crack sizes, and crack locations is calculated, and an explicit expression for the damage index (DI), based on CWT, is developed; it is demonstrated that the proposed damage index does not depend on mechanical properties of a homogeneous beam, and that the DI of one crack does not depend on the size and location of other cracks in a multiple cracked beam. Hence, the obtained expression for the DI can be used to find the size of each crack independently. Numerical results show that the method can detect cracks of small depth and is also applicable under the presence of measurement noise. PubDate: 2015-05-19

Abstract: Phase-field approaches to fracture allow for convenient and efficient simulation of complex fracture pattern. In this paper, two variational formulations of phase-field fracture, a common second-order model and a new fourth-order model, are combined with a finite deformation ansatz for general nonlinear materials. The material model is based on a multiplicative decomposition of the principal stretches in a tensile and a compressive part. The excellent performance of the new approach is illustrated in classical numerical examples. PubDate: 2015-05-19

Abstract: Boundaries and junctions (both internal and external) can contribute significantly to the plastic deformation of metallic solids, especially when the average size of the grains (phases) is less than hundred nanometres or when the size of the solid itself is of the order of microns. The overall permanent deformation of the solid is a result of a coupling between bulk plasticity with moving interfaces/junctions/edges and intrinsic plasticity of internal and external surfaces. We use a novel continuum thermodynamic theory of plastic evolution, with incoherent interfaces and non-splitting junctions, to derive flow rules for bulk and surface plasticity in addition to kinetic relations for interface, edge, and junction motion, all coupled to each other. We assume rate-independent associative isotropic plastic response with bulk flow stress dependent on accumulated plastic strain and an appropriate measure of inhomogeneity. The resulting theory has two internal length scales: one given by the average grain size and another associated with the material inhomogeneity. PubDate: 2015-05-19

Abstract: The coupled system of nonlinear partial differential equations for momentum, diffusion and energy is examined in terms of Hadamard instability, which in a unified way provides the conditions of both “negative creep” and “spinodal decomposition” (loss of convexity of thermodynamic functions) (Markenscoff in Quart Appl Math 59:147–151, 2001; Quart Appl Math 59:471–477, 2001) by balancing terms of different orders in the eigenvalue equation. It is shown here that instabilities of “negative creep” occur in both infinite and finite domains. PubDate: 2015-05-17

Abstract: Mathematical questions pertaining to linear problems of equilibrium dynamics and vibrations of elastic bodies with surface stresses are studied. We extend our earlier results on existence of weak solutions within the Gurtin–Murdoch model to the Steigmann–Ogden model of surface elasticity using techniques from the theory of Sobolev’s spaces and methods of functional analysis. The Steigmann–Ogden model accounts for the bending stiffness of the surface film; it is a generalization of the Gurtin–Murdoch model. Weak setups of the problems, based on variational principles formulated, are employed. Some uniqueness-existence theorems for weak solutions of static and dynamic problems are proved in energy spaces via functional analytic methods. On the boundary surface, solutions to the problems under consideration are smoother than those for the corresponding problems of classical linear elasticity and those described by the Gurtin–Murdoch model. The weak setups of eigenvalue problems for elastic bodies with surface stresses are based on the Rayleigh and Courant variational principles. For the problems based on the Steigmann–Ogden model, certain spectral properties are established. In particular, bounds are placed on the eigenfrequencies of an elastic body with surface stresses; these demonstrate the increase in the body rigidity and the eigenfrequencies compared with the situation where the surface stresses are neglected. PubDate: 2015-05-17

Abstract: Using the classical model of rigid perfectly plastic solids, the strain rate intensity factor has been previously introduced as the coefficient of the leading singular term in a series expansion of the equivalent strain rate in the vicinity of maximum friction surfaces. Since then, many strain rate intensity factors have been determined by means of analytical and semi-analytical solutions. However, no attempt has been made to develop a numerical method for calculating the strain rate intensity factor. This paper presents such a method for planar flow. The method is based on the theory of characteristics. First, the strain rate intensity factor is derived in characteristic coordinates. Then, a standard numerical slip-line technique is supplemented with a procedure to calculate the strain rate intensity factor. The distribution of the strain rate intensity factor along the friction surface in compression of a layer between two parallel plates is determined. A high accuracy of this numerical solution for the strain rate intensity factor is confirmed by comparison with an analytic solution. It is shown that the distribution of the strain rate intensity factor is in general discontinuous. PubDate: 2015-05-16

Abstract: Diffuse and sharp interface models represent two alternatives to describe phase transitions with an interface between two coexisting phases. The two model classes can be independently formulated. Thus there arises the problem whether the sharp limit of the diffuse model fits into the setting of a corresponding sharp interface model. We call a diffuse model admissible if its sharp limit produces interfacial jump conditions that are consistent with the balance equations and the second law of thermodynamics for sharp interfaces. We use special cases of the viscous Cahn–Hilliard equation to show that there are admissible as well as non-admissible diffuse interface models. PubDate: 2015-05-16

Abstract: The Peach–Koehler expressions for the glide and climb components of the force exerted on a straight dislocation in an infinite isotropic medium by another straight dislocation are derived by evaluating the plane and antiplane strain versions of J integrals around the center of the dislocation. After expressing the elastic fields as the sums of elastic fields of each dislocation, the energy momentum tensor is decomposed into three parts. It is shown that only one part, involving mixed products from the two dislocation fields, makes a nonvanishing contribution to J integrals and the corresponding dislocation forces. Three examples are considered, with dislocations on parallel or intersecting slip planes. For two edge dislocations on orthogonal slip planes, there are two equilibrium configurations in which the glide and climb components of the dislocation force simultaneously vanish. The interactions between two different types of screw dislocations and a nearby circular void, as well as between parallel line forces in an infinite or semi-infinite medium, are then evaluated. PubDate: 2015-05-13

Abstract: This paper is devoted to the compactness framework and the convergence theorem for the Lax–Friedrichs and Godunov schemes applied to a
\({2 \times 2}\)
system of non-strictly hyperbolic nonlinear conservation laws that arises from mathematical models for oil recovery. The presence of a degeneracy in the hyperbolicity of the system requires a careful analysis of the entropy functions, whose regularity is necessary to obtain the result. For this purpose, it is necessary to combine the classical techniques referring to a singular Euler–Poisson–Darboux equation with the compensated compactness method. PubDate: 2015-05-08

Abstract: Shape memory alloys (SMA) comport an interesting behavior. They can undertake large strains and then recover their undeformed shape by heating. In this context, one of the aspects that challenged many researchers was the development of a mathematical model to predict the behavior of a known SMA under real-life conditions, or finite strain. This paper is aimed at working out a finite strain mathematical model for a Ni–Ti SMA, under the superelastic experiment conditions and under uniaxial mechanical loading, based on the Zaki–Moumni 3D mathematical model developed under the small perturbations assumption. Within the current article, a comparison between experimental findings and calculated results is also investigated. The proposed finite strain mathematical model shows good agreement with experimental data. PubDate: 2015-05-05

Abstract: In the present work, thermodynamical properties of a GaAs quantum wire with equilateral triangle cross section are studied. First, the energy levels of the system are obtained by solving the Schrödinger equation. Second, the Tsallis formalism is applied to obtain entropy, internal energy, and specific heat of the system. We have found that the specific heat and entropy have certain physically meaningful values, which mean thermodynamic properties cannot take any continuous value, unlike classical thermodynamics in which they are considered as continuous quantities. Maximum of entropy increases with increasing the wire size. The specific heat is zero at special temperatures. Specific heat decreases with increasing temperature. There are several peaks in specific heat, and these are dependent on quantum wire size. PubDate: 2015-05-05

Abstract: The previous paper by the authors (Siriwat and Meleshko in Contin Mech Thermodyn 24:115–148, 2012) was devoted to group analysis of one-dimensional nonisentropic equations of fluids with internal inertia. A direct approach was employed for finding the admitted Lie group. This approach allowed to perform a partial group classification of the considered equations with respect to a potential function. The present paper completes this group classification by an efficient algebraic method. PubDate: 2015-05-01

Abstract: Exact solutions of elastic Kirchhoff plates are available only for special geometries, loadings and kinematic boundary constraints. An effective solution procedure, based on an analogy between functionally graded orthotropic Saint-Venant beams under torsion and inhomogeneous isotropic Kirchhoff plates, with no kinematic boundary constraints, is proposed. The result extends the one contributed in Barretta (Acta Mech 224(12):2955–2964, 2013) for the special case of homogeneous Saint-Venant beams under torsion. Closed-form solutions for displacement, bending–twisting moment and curvature fields of an elliptic plate, corresponding to a functionally graded orthotropic beam, are evaluated. A new benchmark for computational mechanics is thus provided. PubDate: 2015-05-01

Abstract: Though targeting at different scales, the theory of objective structures and the theory of materially uniform bodies have some issues in common. We highlight those aspects of the two theories that share similar ideas, as well as delineate areas where they are inherently different. Prompt by the fact that materially uniform but inhomogeneous bodies ultimately describe dislocations into solids, we propose a way for defining continuous distribution of dislocations for objective structures. In the course of doing, so we draw upon combined theories of algebraic topology and discrete exterior calculus to model crystal elasticity. We also need a generalization of the theory of materially uniform bodies suitable for a class of micromorphic bodies. PubDate: 2015-05-01

Abstract: A semi-analytic solution for the elastic/plastic distribution of stress and strain in a spherical shell subject to pressure over its inner and outer radii and subsequent unloading is presented. The Bauschinger effect is taken into account. The flow theory of plasticity is adopted in conjunction with quite an arbitrary yield criterion and its associated flow rule. The yield stress is an arbitrary function of the equivalent strain. It is shown that the boundary value problem is significantly simplified if the equivalent strain is used as an independent variable instead of the radial coordinate. In particular, numerical methods are only necessary to evaluate ordinary integrals and solve simple transcendental equations. An illustrative example is provided to demonstrate the distribution of residual stresses and strains. PubDate: 2015-05-01