Non-linear elastic micro-dilatation theory: Matrix exponential function paradigm

作者：Ramezani Hamidreza^*; Jeong Jena

来源：International Journal of Solids and Structures, 2015, 67-68: 1-26.

DOI：10.1016/j.ijsolstr.2015.02.008

• Micro-dilatation theory
• Porous media
• Matrix exponential function
• Matrix logarithm function
• Centrosymmetry
• Large deformation
• Pore-scale
• 3D-FEM

In the present paper, the micro-dilatation theory or void elasticity is extended to both large displacement and large dilatation. Firstly, the deformation gradient tensor has been freshly defined by means of the matrix exponential function. The newly defined relation for the deformation gradient has painstakingly investigated for the uniqueness, decomposition issues as well as objectivity and isotropy considerations. The relation of the displacement gradient and deformation gradient tensor is brought via the matrix logarithm function. The micro-dilatation theory constitutive laws are derived using the thermodynamic principles under the zero-centrosymmetric, weakly-centrosymmetric and fully-centrosymmetric cases. These cases have been derived and scrutinized by the numerical experiments. To achieve this assignment, the basic loadings are taken into account, e.g. the hydrostatic loading, simple traction and shear. Some conclusions and outlook pertaining to the above-mentioned cases and variable bulk density have thereafter discussed.

• 出版日期2015-8-15