Inverse Problems Of Textile Material Design Based On Pressure Comfort: Mathematical Modeling Analysis And Numeircal Computation

Based on the small deformation theory of elastic mechanics, this paperestablishes a HumanBody-ElasticFabric static mechanical model. The Direct Problem(DP) is formulated into a boundary value problem for elliptic partial differentialequations (EPDEs) under suitable hypotheses. The ifnite difference method is used todiscretize the EPDEs, and the resulted linear algebraic equations with fabricdisplacement is solved by Regularized Conjugate Gradient Method(RCGM)，andhence the pressure distribution between human body and elastic fabric interface isavailable. The numerical simulation of2D and3D cases show that above numericalmethods is eiffcient and the model is correct.Based on the research of the DP, the inverse problem (IP) of determination ofelastic textile fabric from the pressure comfort is ifrstly proposed. And the IP canprovide experimental explanation and theoretical guidance to fabric type design. Theresearch of the IP consist of the following contents: Firstly we analyze the range ofpressure comfort between the human body and fabric interface. And then based on thesmall deformation theory of isotropic elastic fabrics, we construct the following leastsquares minimization functionfrom the pressure comfort indexes and the stress-strain boundary conditions. Finallywe take the human leg elastic fabric model pressure distribution as an example tosolve the IP with ifnite difference method and BFGS method. The numerical resultsshow that the best choice of the pair () of tensile modulus and shear modulussatisifes linear relation approximately, and verify the rationality of the propsed IP andeiffciency of numerical algorithms.