Michael Wünsche

Semi-permeable crack analysis in magnetoelectroelastic solids

This paper discusses various electromagnetic boundary conditions on the crack-faces in two-dimensional magnetoelectroelastic materials. For this purpose, a meshless method based on the local Petrov?Galerkin approach is developed to solve the initial-boundary value problems of two-dimensional cracked magnetoelectroelastic solids with nonlinear electrical and magnetic boundary conditions on the crack-faces. A Heaviside step function as the test function is applied in the weak form to derive local integral equations. Nodal points are spread on the analyzed domain and each node is surrounded by a small circle for simplicity. The spatial variations of the displacements, electric and magnetic potentials are approximated by the moving least-squares (MLS) scheme. After performing the spatial integrations, one obtains a system of ordinary differential equations for certain nodal unknowns. That system is solved numerically by the Houbolt finite-difference scheme as a time-stepping method. An iterative solution algorithm is developed to consider nonlinear electromagnetic crack-face boundary conditions.

Numerical and Experimental Investigations of Curved Fatigue Crack Growth under Biaxial Proportional Cyclic Loading

The paper presents numerical and experimental results of continued studies of curved fatigue crack growth in arbitrarily pre-cracked isotropic sheets under biaxial proportional plane loading. The predictor-corrector method (PCM) was extended in order to analyse the growth of multiple crack systems. As a result, the program PCCS-2D was written to run within ANSYS without any user interaction. In order to check the accuracy and efficiency of the method biaxial crack growth simulations were carried out for a fracture mechanics cruciform specimen. The results are compared with experimental findings obtained by specimens made of 6061 aluminium alloy in T651 condition using a 250kN biaxial servohydraulic testing machine. From the numerical and experimental results, we conclude, that the proposed predictor-corrector method can be used in curved crack growth simulation also under biaxial proportional loading conditions.

Interface Crack in Anisotropic Solids under Impact Loading

In this paper, transient dynamic crack analysis in two-dimensional, layered, anisotropic and linear elastic solids is presented. For this purpose, a time-domain boundary element method (BEM) is developed. The homogeneous and anisotropic layers are modeled by the multi-domain BEM formulation. Time-domain elastodynamic fundamental solutions for linear elastic and anisotropic solids are applied in the present BEM. The spatial discretization of the boundary integral equations is performed by a Galerkin-method while a collocation method is implemented for the temporal discretization of the arising convolution integrals. An explicit time-stepping scheme is developed to compute the discrete boundary data and the crack-opening-displacements (CODs). To show the effects of the material anisotropy and the dynamic loading on the dynamic stress intensity factors, numerical examples are presented and discussed.

Numerical Simulation of Multiple Fatigue Crack Growth with Additional Crack Initiation

In this paper, advanced numerical simulations of curved crack growth in the case of multiple crack systems in combination with the analysis of the plastic limit load by the lower bound theorem of plasticity are presented. In order to take additionally initiated cracks during the crack growth process into account, the numerical simulation algorithm has been extended by using the Smith-Watson-Topper (SWT) parameter in combination with a linear fatigue damage accumulation.

Semi-Permeable Cracks in Magnetoelectroelastic Solids under Impact Loading

In this paper, transient dynamic crack analysis in two-dimensional, linear magnetoelectroelastic solids by considering different electrical and magnetical crack-face boundary conditions is presented. For this purpose, a time-domain boundary element method (TDBEM) using dynamic fundamental solutions is developed. The spatial discretization of the boundary integral equations is performed by a Galerkin-method while a collocation method is implemented for the temporal discretization of the arising convolution integrals. An explicit time-stepping scheme is applied to compute the discrete boundary data and the generalized crack-opening-displacements. Iterative algorithms are implemented to deal with the non-linear electrical and magnetical semi-permeable crack-face boundary conditions.

Cracks in Magnetoelectroelastic Solids under Impact Loading

In this paper, transient dynamic crack analysis in two-dimensional, linear magnetoelectroelastic solids is presented. For this purpose, a time-domain boundary element method (BEM) is developed and the elastodynamic fundamental solutions for linear magnetoelectroelastic and anisotropic materials are derived. The spatial discretization of the boundary integral equations is performed by a Galerkin-method while a collocation method is implemented for the temporal discretization of the arising convolution integrals. An explicit time-stepping scheme is developed to compute the discrete boundary data and the generalized crack-opening-displacements. To show the effects of the coupled fields and the different dynamic loading conditions on the dynamic intensity factors, numerical examples will be presented and discussed.

Flexoelectric Effect for Cracks in Piezoelectric Solids

The finite element method (FEM) is developed to analyse 2-D crack problems where the electric field and displacement gradients exhibit a size effect penomenon. This phenomenon in micro/nanoelectronic structures is described by the strain-and electric field-gradients in constitutive equations. The governing equations are derived using variational principles with the corresponding boundary conditions. The FEM formulation with C1-continuous elements is subsequently developed and implemented. An example is presented and discussed to demonstrate the effects of the strain-and electric intensity-gradients on the electro-mechanical behavior of cracked solids.

Gradient piezoelectricity for cracks under an impact load

The flexoelectric effect on elastic waves is investigated in nano-sized cracked structures. The strain gradients are considered in the constitutive equations of a piezoelectric solid for electric displacements and the higher-order stress tensor. The governing equations with the corresponding boundary conditions are derived from the variational principle. The finite element method (FEM) is developed from the principle of virtual work. It is equivalent to the weak-form of derived governing equations in gradient elasticity. The computational method can be applied to analyze general 2D boundary value problems in size-dependent piezoelectric elastic solids with cracks under a dynamic load. The FEM formulation is implemented for strain-gradient piezoelectricity under a dynamic load.

Analysis of Cracks in Functionally Graded Piezoelectric Materials by a Frequency-Domain BEM

Time-harmonic crack analysis in two-dimensional piezoelectric functionally graded materials (FGMs) is presented in this paper. A frequency-domain boundary element method (BEM) is developed for this purpose. Since fundamental solutions for piezoelectric FGMs are not available, a boundary-domain integral formulation is derived. This requires only the frequency-domain fundamental solutions for homogeneous piezoelectric materials. The radial integration method is adopted to compute the resulting domain integrals. The collocation method is used for the spatial discretization of the frequency-domain boundary integral equations. Adjacent the crack-tips square-root elements are implemented to capture the local square-root-behavior of the generalized crack-opening-displacements properly. Special regularization techniques based on a suitable change of variables are used to deal with the singular boundary integrals. Numerical examples will be presented and discussed to show the influences of the material gradation and the dynamic loading on the intensity factors.

Fracture Mechanics Analysis of Size-Dependent Piezoelectric Solids under a Thermal Load

General 2D boundary value problems of piezoelectric nanosized structures with cracks under a thermal load are analyzed by the finite element method (FEM). The size-effect phenomenon observed in nanosized structures is described by the strain-gradient effect. The strain gradients are considered in the constitutive equations for electric displacement and the high-order stress tensor. For this model, the governing equations are derived with the corresponding boundary conditions using the variational principle. Uncoupled thermoelasticity is considered, thus, the heat conduction problem is analyzed independently of the mechanical fields in the first step. A numerical example is presented and discussed to demonstrate the effects of the strain-gradient.