Dietmar Gross

On electromechanical stability analysis of dielectric elastomer actuators

Based on the total stress concept, explicit results of the equilibrium state and the critical electric field are obtained for dielectric elastomer actuators. Criticality is discussed in the frame of structure stability and electric breakdown. Specific results are given for four commonly used material models.

The equilibrium shape of an elastically inhomogeneous inclusion

Abstract A method is proposed for determining the equilibrium shape of an elastically inhomogeneous coherent precipitate in an anisotropic medium. Arbitrary eigenstrains and an isotropic interfacial energy density are taken into account. Use is made of Eshelbys notion of a “force on an interface” and boundary integral techniques are employed. Results for the plane strain case of one single inclusion and a regular array of inclusions with dilatational eigenstrains in an orthotropic matrix are presented. We find that the three factors: difference of elastic moduli in matrix and inclusion, interfacial energy and particle-particle interaction can affect the equilibrium shape in much the same way. The elastic inhomogeneity can cause strongly non-convex particle shapes and considerably affects the stability of fourfold symmetric equilibrium shapes.

3D simulation of equilibrium morphologies of precipitates

A method to calculate the 3D equilibrium shape of a misfitting, coherent second phase particle in a matrix material is proposed. Taking the interfacial energy into account the equilibrium morphology is described in terms of a generalised thermodynamic force acting on the interface. An efficient 3D boundary element method applicable to anisotropic materials is used to solve the field equations. Taking Ni-based superalloys as an example the influence of anisotropy, inhomogeneity and precipitate size on the equilibrium morphology is discussed.

Configurational forces and their application in solid mechanics

The theory of configurational forces is presented within the non-linear dynamic framework. The configurational force balance is recast in a form which resembles the equation of motion. Specializations to statics and the small strain case are given. The general use of configurational forces is discussed by help of numerous examples. Additionally the occurrence of configurational forces in the Finite Element Method is illustrated. The numerically induced configurational forces can be used to improve the numerical resolution.

Dynamic analysis of dielectric elastomer actuators

An analytical model is proposed for the dynamic analysis of a homogeneously deformed dielectric elastomer actuator (DEA) with a standard sandwich structure. The equation of motion for the DEA is obtained by the Euler-Lagrange equation. Numerical results of the model are presented to show the vibration and oscillation behaviour of the system. Resonance phenomenon and damping effects are investigated. Results are discussed in comparison with those of the related topics in the literature.

Crack growth in brittle solids under compression

The two-dimensional sliding crack model, which is motivated by the micromechanics, is applied to examine the response of brittle materials to compressive loads. The problem is treated numerically by means of a boundary element method (BEM) solving a singular integral equation for the dislocation density along the crack contour. The results are compared with experimental data and with more simplified models, illustrating the quality of the present approach. As an example, the model is applied to simulate the response of compact rock subjected to a load cycle.

On the interaction and branching of fast running cracks - a numerical investigation

Abstract Phenomena of dynamic fracture in brittle materials resulting from the interaction of fast running cracks are investigated numerically. These studies concern the influence of mutual shielding on crack paths, the stress intensity factor and crack tip speed variations, the stability of a simultaneous propagation of several cracks, and the interaction of cracks of different size. Furthermore, dynamic crack branching is investigated from a macroscopic point of view. The respective initial boundary value problem of linear elastodynamics is formulated as a system of time-domain boundary integral equations in conjunction with experimentally motivated criteria for crack growth and branching. The numerical evaluation is based on a boundary element method and an appropriate discretization of the fracture and branching criteria. Results obtained from numerical simulations are discussed with regard to the experimental findings.

A hyper-singular traction boundary integral equation method for stress intensity factor computation in a finite cracked body

Abstract This paper attempts to answer the commonly raised question: what are the parameters controlling the solution accuracy and stability when the hyper-singular traction boundary-integral equations (BIEs) are used for the dynamic (time-harmonic) linear elastic fracture analysis of a finite cracked structure. The usage of the traction BIEs together with the parabolic discretization mesh leads to hyper-singularity, when the crack lies on the boundary, even after application of a regularization procedure. In this paper two new ways, average method and shifted point method to overcome this difficulty, are proposed and compared. It is shown by numerical experiments on the examples of a cracked rectangular plate and of a cracked infinite plane that the accuracy and the convergence of the method solution depends mainly on the smoothness requirements of the solution at all collocation points.

Einige Erhaltungsstze der Kontinuumsmechanik vom J-Integral-Typ

ÜbersichtAus der Translations- und Rotationsinvarianz der allgemeinen Bilanzgleichung der Kontinuums-mechanik werden Erhaltungssätze in Form von Oberflächenintegralen hergeleitet. Für die Energiebilanz folgen daraus Erhaltungsgrößen vom J-Integral-Typ, die sich in den Fällen der Statik, der stationären ebenen Welle und der Hyperelastizität besonders vereinfachen. Sind bewegliche Energiequellen, wie Defekte vorhanden, so wird durch die Erhaltungsintegrale die Kraft auf die Quelle beschrieben.SummaryConservation laws in terms of surface integrals are derived from the translation respectively rotation invariance of general balance equations of continuum mechanics. From them conservation quantities of J-Integral type follow for the energy balance. They reduce to simpler forms in the cases of statics, of stationary plane waves and of hyperelasticity. When there are mobile energy sources like defects, then the force acting on the source is described by the conservation integrals.

A description of macroscopic damage through microstructural relaxation

In this paper a exible model for the description of damage in heterogeneous structural materials is presented. The approach involves solving the equations of equilibrium, with unilateral constraints on the maximum attainable values of selected internal variables. Due to the unilateral constraints, the problem is non-linear. Accordingly, a simple iterative algorithm is developed to solve this problem by (1) computing the internal elds with the initial undamaged microstructure and (2) reducing the material stiness at locations where the constraints are violated. This process is repeated until a solution, with a corresponding microstructure, that satises the equations of equilibrium and the constraints, is found. The corresponding microstructure is the nal ‘damaged’ material. As an application, the method is used in an incremental fashion to generate response curves describing the progressive macroscopic damage for a sample of commonly used bre-reinforced Aluminum=Boron composite. The results are compared to laboratory experiments published by Kyono et al. 1 and computational results using standard numerical methods, published by Brockenbrough et al. 2 ? 1998