On the Development of Survival Criteria for Rate Sensitive Materials

The evaluation and mitigation of injury in the automotive crash environment is often achieved by monitoring and limiting the magnitude of forces and/or moments being applied to or transmitted through dummy structures representing particular portions of the human anatomy. Examples of body areas where this is the practice are the neck, the thoracic and lumbar spine, the pelvis, as well as the upper and lower extremities. Implicit within this process is the assumption that the observed forces are directly proportional to local failure metrics such as stress and/or strain. However, a variety of experimental efforts have demonstrated that many of these anatomical structures exhibit, to various degrees, viscoelastic behavior and time or rate dependent failure properties. This work develops a methodology that generalizes the results of various experimental observations. First, a particular material''s viscoelastic constitutive properties are mathematically characterized by developing a constitutive relationship relating experimentally observed stress time histories to applied strain, and strain rate time histories. This constitutive relationship and a novel technique of "back integration" are employed to develop the material''s creep compliance response. A Duhamel Integral relationship is used to predict the material''s actual strain time history given its observed stress-rate time history and creep compliance characteristic. This then allows casting the material''s loading history into its actual time dependent stress/strain space and determining if failure conditions have been exceeded. Both the theoretical development of this methodology and the effects of its application to real world crash circumstances are presented.