Description of a Analysis information for the article 'Profant, T., Hrstka, M., Sládek, J., Sládek, V., Kotoul, M., Asymptotic solution for a crack in an orthotropic material and the elasticity of a deformation gradient' Principal investigator: doc. Ing. Tomáš Profant, Ph.D.Institution: Institute of Solid Mechanics, Mechatronics and Biomechanincs, Brno University of Technology, Czech RepublicEmail: profant@fme.vutbr.czData Manager: Ing. Jan Bajer. Date: 04-02-2025Version: 1.0.0 ### Abstract ### The asymptotic solution for the displacement and stress fields at the tip of the crack in homogeneous orthotropic material governed by the strain gradient elasticity based on the simplified Mindlin’s Form II gradient theory is derived. The Lekhnitskii-Eshelby-Stroh (LES) formalism is applied and generalized to the fracture problem in the strain gradient elasticity for an orthotropic material. The expressions for the displacements and stress functions are derived. According to the LES formalism, the Cauchy type stresses and double stresses are expressed as the partial derivatives of the stress functions. The stress singularity exponent is evaluated from the condition of the stress-free crack faces at its tip and consequently it is derived the expression for the J-integral.The particular components of the asymptotic solutions for the displacements and the Cauchy type stresses are discussed as well as the strong singular auxiliary force tractions in front of the crack. The influence of the material symmetry orientation with respect to the crack plane orientation is shown. The SGET-ORT-HOM program generates graphs published in the articleProfant, T., Hrstka, M., Sládek, J., Sládek, V., Kotoul, M., Asymptotic solution for a crack in an orthotropic material and the elasticity of a deformation gradientSGET-ORT-HOM was written in the Ubuntu 20.04.6 LTS operating system using libraries and programs under the GNU license, which are part of the standard Ubuntu repositories. SGET-ORT-HOM is written in C language and consists of five filessget_ort_hom.csget_ort_hom_sub.csget_ort_hom_sub.hMakefilevstup1where >sget_ort_hom.csget_ort_hom_sub.*Makefilevstup1vstup1sget_ort_hom_sub.c<. In addition to the standard C libraries, SGET-ORT-HOM uses the libraries GSLGNU CncursesSGET-ORT-HOM was compiled using the GNU Compiler Collectiongcc -L/usr/lib/ -g -osget_ort_hom sget_ort_hom.c sget_ort_hom_sub.c -lgsl -lgslcblas -lm -lncursesSGET-ORT-HOM is run with the command./sget_ort_hom input1after compilation.