On Two Kinds Of Cosserat Elasticity And FEM

It has been proved by some experiments focused on micro materials that micro materials may be affected by size when character length is in the level of micron.Traditional elastic and plastic theories can not explain the size effect of materials because there is no characteristic length in these theories.A lot of scholars turn to study gradient/couple-stress theories in recent years.There are parameters that mean the length dimensions in the couple-stress theory,which can explain the size effect of materials.There are meanly two kinds of couple-stress theories, which are non-constrained couple-stress theory and constrained couple-stress theory.The mean way to solve couple-stress theory is the finite element method.Displacement functions of C~0 continuity and C~1 continuity are produced to solve non-constrained couple-stress theory and constrained couple-stress theory respectively.In this paper,non-constrained couple-stress theory is called C~0 theory and constrained couple-stress theory is called C~1 theory.The C~1 theory can also be solved by penalty function.Two kinds of couple-stress theory are described in this paper with their characters respectively.18-DOF plane stain gradient triangular element and 8-node rectangular element are used to compute the stress concentration problem around a circular hole in plane strain condition.Some other examples are also computed.The second shear modulus Ga is discussed in this paper.