Energy theorems and bounds in linearized elasticity with residual stress

[摘要] Residual stress is the stress present in a fixed reference placement in which the body is at rest in the absence of external forces. In this work, residual stress is viewed as constitutive information so as to develop nondestructive mechanical tests that provide information about the residual stress fields in bodies that respond in a linearly elastic manner to small deformations from the residually stressed state. In order to construct the necessary background, a number of results from classical linear elastostatics are modified to include the presence of residual stress. Among these results are the Principles of Minimum Potential Energy and Minimum Complementary Energy. These minimum principles are used to derive a bound on the residual stress in terms of experimental data plus solutions to classical problems which correspond to the experiment.

[关键词] Applied Mechanics