SUMMARYA vector potential for the electric induction is applied to static three-dimensional fully coupled electromechanical problems. A Coulomb gauge condition imposed on the electric vector potential improves the convergence behaviour of nonlinear problems, and in combination with a discrete set of Dirichlet boundary conditions, it can enforce unique vector potential solutions. Based on a spectral analysis of the sti ness matrix, the Coulomb gauge is compared with other gauge conditions. A penalized version of the weak vector potential formulation with Coulomb gauge is proposed and tested on some numerical examples in electrostatics, piezoelectricity and ferroelectricity.

SUMMARYReturn mapping algorithms for a rather general class of phenomenological rate-independent models for ferroelectroelastic materials are presented. The fully coupled thermodynamically consistent threedimensional constitutive model with two internal variables (remanent polarization vector and remanent strain tensor) proposed by C. M. Landis in 2002 is used for the simulation of electromechanical hysteresis effects in polycrystalline ferroelectric ceramics. Based on the operator splitting methodology, the return mapping algorithm employs the closest point projection scheme to obtain an efficient and robust integration of the constitutive model. The consistent tangent operator is obtained in closed form by linearizing the return mapping algorithm, and is found to be non-symmetric in the general case due to the dependence of the switching criterion on internal variables. Conditions that provide the symmetry of the consistent tangent matrix are analyzed. The compactness and generality of the received relations are achieved by means of using the thermodynamically based compact notations combining mechanical and electrical values. Both the cases scalar potential finite element (FE) formulation (primary variables: strain and electric field) and vector potential FE formulation (primary variables: strain and electric displacement) are considered. The accuracy and robustness of the algorithms are assessed through numerical examples.

The weight function method is described to analyze the crack growth behavior in functionally graded materials and in particular materials with a rising crack growth resistance curve. Further, failure of graded thermal barrier coatings (TBCs) under cyclic surface heating by laser irradiation is modeled on the basis of fracture mechanics. The damage of both graded and non-graded TBCs is found to develop in several distinct stages: vertical cracking → delamination → blistering → spalling. This sequence can be understood as an effect of progressive shrinkage due to sintering and high-temperature creep during thermal cycling, which increases the energy-release rate for vertical cracks which subsequently turn into delamination cracks. The results of finite element modeling, taking into account the TBC damage mechanisms, are compatible with experimental data. An increase of interface fracture toughness due to grading and a decrease due to ageing have been measured in a four-point bending test modified by a stiffening layer. Correlation with the damage observed in cyclic heating is discussed. It is explained in which way grading is able to reduce the damage.

The mechanisms of densification in spark plasma sintering (SPS) were investigated both analytically and numerically for a model system of two spherical metallic powder particles. From the microscopic temperature distribution, the possibility of a micro-local overheating of the particleparticle contacts was analysed for different particle sizes, contact geometries, materials, and electrical loads. It is shown that, for particles below the size of one millimetre, local overheating is below one Kelvin. Subsequently, the material transport by thermomigration, electromigration, and diffusion driven by surface curvature and external pressure was derived from microscopic field distributions obtained from analytical calculations and finite-element simulations. The results show that, while the mechanical pressure accelerates material transport by orders of magnitude, the electrical current and the temperature gradients do not. It is also shown that pulsing the current has no significant influence on the densification rate.

The problem of pulling the reinforcing bar from the concrete block is urgent for the practice, as it represents the most widespread method of experimental evaluation of characteristics of reinforced-concrete bond behavior, which are necessary for an estimation of the strength and durability of reinforced concrete structures. Fracture process of bonds at pulling the rebar from the concrete is a complex multistep process, accompanied by the presence of inhomogeneous and inelastic deformation, a rupture of adhesive bonds, the initiation and propagation of cracks of different shape and orientation, the presence of contact and tribological phenomena. The nonlinear finite-element solutions of the problem of pulling the reinforcing bar from the concrete block have been obtained with using various models of bond behavior and concrete cracking. The comparison of obtained numerical results with experimental data has been presented and discussed. The first part of the article is devoted to the models taking into account the discontinuity of the connection, while the second part is concerned with the models without explicitly taking into account of discontinuities