Micromechanically based stress and strain-rate flow potentials for anisotropic polycrystals

The dissipation of rigid-viscoplastic material behaviour is related to the stress flow potential and its Legendre-Fenchel conjugated strain-rate flow potential. In this paper micromechanically based approximation of these flow potentials, expressed in terms of the deviatoric stresses and strain-rates, is derived from texture measurements. The dual potentials for single face-centered cubic crystals are approximated in terms of Fourier expansion with tensorial texture coefficients. The macroscopic flow stress and strain-rate potentials for an aggregate of polycrystals can be deduced from those of single crystal under the assumption of either homogeneous strain-rate, or homogeneous stress field from the codf measurements. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Micromechanical Generalization of the Mises-Hill Anisotropy Yield Criterion

This paper proposes a new micromechanically motivated yield criterion expressed in terms of the leading tensorial texture coefficient of the crystallite orientation distribution function. The central finding is that although only a 4th–order anisotropy tensor occurs in the expression for the yield locus, the ansatz provides significantly better results in comparison to the quadratic Hill condition. The improvement is due to cubic and quartic tensorial contributions in terms of the stress direction. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Effective Flow Potentials for Anisotropic Polycrystals

In this paper a micromechanically based flow potential for anisotropic fcc polycrystals is derived that takes into account the crystallite orientation distribution function (codf) in terms of tensorial texture coefficients. The effective flow potential is based on a representation theorem for anisotropic scalar functions depending on a 2nd-order tensor. A priori unknown functions in the representation are determined by defining and solving explicitly a minimization problem over SO(3). Important analytical properties of the coefficient matrix of the minimization problem are discussed. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Inverse Identification of Delamination Regions in Layered CFRP-Composites

In this paper we are concerned with the complete non-destructive reconstruction (shape, depth and topology) of delaminations in one damaged interface in layered composites using the Cauchy data on the outer boundary. The proposed method combines an iterative algorithm for solution of mixed ill-posed elliptical boundary value problems and a parameter estimation in sense of the ill-posed optimization problems. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The free-discontinuity problem of inverse crack identification from boundary measurements

The inverse crack identification of planar cracks from elastostatics boundary measurements is regarded as free-discontinuity problem in respect to the unknown displacement field and the discontinuity region of the cracked body. The proposed solution strategy is based on the variational approximation of the sharp interface problem by elliptic functionals developed by Ambrosio and Tortorelli. The numerical calculation is realized by the finite element method. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Re-entrant corner problems for isotropic materials and layered composites

Modern materials like composites in different types require new methods in computational fracture mechanics. Besides of classical fracture mechanics we have to solve the asymptotic solution around crack tips. This can be done on the basis of the Kondratiev s theorem with the Pietrov-Galerkin method to solve the unknown eigenvalues for those problems. Additionally, we have to de.ne instead classical modes I, II and III, mode I* up to mode IV* to interpret the computational results for the unknown eigenvalues. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)