Calculation of the elastic strain energy of inclusions by the Greenʹs function and finite element methods

Elastic strain energy of a free-standing body with many inclusions was calculated. In order to consider the effect of surrounding neighborhood inclusions, nonlocal terms of the Greenʹs function were kept. The calculated strain energy by a derived analytic method was compared with that of the finite element method. The prediction of the new analytic method provided a correct tendency of the variation of the strain energy for various sample problems. Deviation of the analytic result from that of the finite element calculation became smaller when the value of the strain energy decreased. As the analytic method does not require solving the field equations, it can be useful for a situation demanding prompt computation of the strain energy.