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Numerical computation of compliance contribution tensor of a concave pore embedded in a transversely isotropic matrix

Abstract : The main objective of this work is to estimate the compliance contribution tensor of the concave pore inhomogeneitysurrounded by a transversely isotropic matrix. In this light, we make use of a recently developedadapted boundaryconditionsbased Finite Elements Method to incorporate the matrix anisotropy and the correction of the bias inducedby the bounded character of the mesh domain, which allows to accelerate the computation convergence withoutsacrificing its accuracy. The correction of the boundary conditions is given as functions of the Green tensor andits gradient as dependent on the anisotropic elasticity of the matrix material, which are rigorously calculated bymeans of the Fourier transform based integral method in particular for regularizing the singularities on the symmetricaxis of the transverse isotropy. Simultaneously by complying with the numerical homogenization technique, thecompliance contribution tensor is computed for different forms of pores (e.g. superspheroidal and supersphericalones, etc) embedded in an transversely isotropic matrix. The proposed numerical method is shown to be efficient andaccurate after several appropriate assessment and validation by comparing its predictions, in some particular cases,with analytical results and some available numerical ones. Finally, the effect of the pore concavity on the compliancecontribution tensor is quantitatively illustrated.
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K. Du, L. Cheng, Jean-François Barthélémy, I. Sevostianov, A. Giraud, et al.. Numerical computation of compliance contribution tensor of a concave pore embedded in a transversely isotropic matrix. International Journal of Engineering Science, Elsevier, 2020, 152, pp.103306. ⟨10.1016/j.ijengsci.2020.103306⟩. ⟨hal-02570418⟩

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