A generalized constitutive elasticity law for GLPD micromorphic materials, with application to the problem of a spherical shell subjected to axisymmetric loading conditions

In this work we propose to replace the GLPD hypo-elasticity law by a more rigorous generalized Hooke＇s law based on classical material symmetry characterization assumptions. This law introduces in addition to the two well- known Lame＇s moduli, five constitutive constants. An analytical solution is de- rived for the problem of a spherical shell subjected to axisymmetric loading con- ditions to illustrate the potential of the proposed generalized Hooke＇s law.