Fracture criterion and mathematical conjectures from fracture mechanics

This paper is written to state mathematical problems which are proved or not proved. Here the term 'proved' means the conjectures hold for weak solutions. These conjecture are already confirmed using special solutions. In fracture mechanics, it will be enough. But the weak solution cover all cases, which give the standard in fracture mechanics. The aim of this paper is to state the historical results in fracture mechanics and to give the conjectures which will be proved (or improved or extended) in later by functional analysis. Because of a singularity of elastic field at crack front, special care should be taken in applying the classical mechanical results. There are huge research on fracture phenomenon, then we cannot state all of them. Mainly, we state here the classical results of brittle fracture which most fracture engineer will agree nearly true. It is impossible to construct one theory which express fracture phenomenon, because the experiment point out that fracture phenomenon is different for materials and in conditions. In general, the results in engineering will not clear from mathematical view-point. There are many conjectures and hypothesis from fracture mechanics that are slightly changed from original papers. (orig.)Available from TIB Hannover: RR 6943(96-18) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman

Eye Gaze and Head Posture Jointly Influence Judgments of Dominance, Physical Strength, and Anger

Social status hierarchies are a universal principle of organization in human societies. Status judgments are often influenced by perceptions of the face and posture. Two important nonverbal cues of social status are head postures and eye gaze. Prior research has shown contradictory results and little is known about the interaction of these two cues. Study 1 investigated how eye gaze (direct vs. averted) and head postures (bowed vs. neutral vs. raised) impact judgments of dominance and physical strength. Judgments of dominance were influenced more than judgments of physical strength. Furthermore, raised heads implied dominance and strength, but in contrast to common assumptions, a bowed head conveyed dominance if the eyes gazed at the observer. Study 2 showed that bowed heads with direct gaze conveyed anger, potentially explaining the increased judgments of dominance. Taken together, the results show that head posture and gaze interactively modulated status-related traits and emotions, namely, dominance, strength, and anger, and help clarify prior incompatible findings on head postures and eye gaze. This is a pre-print of an article published in Journal of Nonverbal Behavior. The final authenticated version is available online at: https://doi.org/10.1007/s10919-018-0276-