On a consistent rod theory for a linearized anisotropic elastic material II. Verification and parametric study

We have derived a rod theory by an asymptotic reduction method for a straight and circular rod composed of linearized anisotropic material in part I of this series. In the current work, we first verify the derived rod theory through five benchmark Saint-Venant’s problems. Then, under a specific loading condition (line force at the lateral surface with two clamped ends), we apply the rod theory to conduct a parametric study of the effects of elastic moduli on the deformation of a rod composed of four types of anisotropic materials including cubic, transversely isotropic, orthotropic, and monoclinic materials. Analytical solutions for the displacement, axial twist angle, stress, and principal stress have been obtained and a systematic investigation of the effects of elastic moduli on these quantities is conducted, which is the main feature of this paper. It is found that these elastic moduli arise in a certain form and in a certain order in the solutions, which gives information about how to appropriately choose moduli to adjust the deformation. Among the four anisotropic materials, it turns out that the monoclinic material presents the most remarkable mechanical behavior owing to the existence of a coupling coefficient: it yields coupled leading-order rod equations, non-trivial axial twist angle, non-negligible transverse shear deformation, and a more adjustable principal stress along the axis.

Opposite asymmetries of face and trunk and of kissing and hugging, as predicted by the axial twist hypothesis

The contralateral organization of the forebrain and the crossing of the optic nerves in the optic chiasm represent a long-standing conundrum. According to the Axial Twist Hypothesis (ATH) the rostral head and the rest of the body are twisted with respect to each other to form a left-handed half turn. This twist is the result, mainly, of asymmetric, twisted growth in the early embryo. Evolutionary selection tends to restore bilateral symmetry. Since selective pressure will decrease as the organism approaches symmetry, we expected a small control error in the form of a small, residual right-handed twist. We found that the mouth-eyes-nose (rostral head) region shows a left-offset with respect to the ears (posterior head) by up to 0.8° (P < 0.01, Bonferroni-corrected). Moreover, this systematic aurofacial asymmetry was larger in young children (on average up to 3°) and reduced with age. Finally, we predicted and found a right-sided bias for hugging (78%) and a left-sided bias for kissing (69%). Thus, all predictions were confirmed by the data. These results are all in support of the ATH, whereas the pattern of results is not (or only partly) explained by existing alternative theories. As of the present results, the ATH is the first theory for the contralateral forebrain and the optic chiasm whose predictions have been tested empirically. We conclude that humans (and all other vertebrates) are fundamentally asymmetric, both in their anatomy and their behavior. This supports the thesis that the approximate bilateral symmetry of vertebrates is a secondary feature, despite their being bilaterians.

Opposite asymmetries of face and trunk and of kissing and hugging, as predicted by the axial twist hypothesis

The contralateral organization of the forebrain and the crossing of the optic nerves in the optic chiasm represent a long-standing conundrum. According to the Axial Twist Hypothesis (ATH) the rostral head and the rest of the body are twisted with respect to each other to form a left-handed half turn. This twist is the result, mainly, of asymmetric, twisted growth in the early embryo. Evolutionary selection tends to restore bilateral symmetry. Since selective pressure will decrease as the organism approaches symmetry, we expected a small control error in the form of a small, residual right-handed twist. We found that the mouth-eyes-nose (rostral head) region shows a left-offset with respect to the ears (posterior head) by up to 0.8° (P<0.01, Bonferroni-corrected). Moreover, this systematic aurofacial asymmetry was larger in young children (on average up to 3°) and reduced with age. Finally, we predicted and found a right-sided bias for hugging (78%) and a left-sided bias for kissing (69%). Thus, all predictions were confirmed by the data. These results are all in support of the ATH, whereas the pattern of results is not explained by existing alternative theories. As of the present results, the ATH is the first theory for the contralateral forebrain and the optic chiasm whose predictions have been tested empirically. We conclude that humans (and all other vertebrates) are fundamentally asymmetric, both in their anatomy and their behavior. This supports the thesis that the approximate bilateral symmetry of vertebrates is a secondary feature, despite their being bilaterians.

Opposite asymmetries of face and trunk and of kissing and hugging, as predicted by the axial twist hypothesis

The contralateral organization of the forebrain and the crossing of the optic nerves in the optic chiasm represent a long-standing conundrum. According to the Axial Twist Hypothesis (ATH) the rostral head and the rest of the body are twisted with respect to each other to form a left-handed half turn. This twist is the result, mainly, of asymmetric, twisted growth in the early embryo. Evolutionary selection tends to restore bilateral symmetry. Since selective pressure will decrease as the organism approaches symmetry, we expected a small control error in the form of a small, residual right-handed twist. We found that the mouth-eyes-nose (rostral head) region shows a left-offset with respect to the ears (posterior head) by up to 0.8° (P<0.01, Bonferroni-corrected). Moreover, this systematic aurofacial asymmetry was larger in young children (on average up to 3°) and reduced with age. Finally, we predicted and found a right-sided bias for hugging (78%) and a left-sided bias for kissing (69%). Thus, all predictions were confirmed by the data. These results are all in support of the ATH, whereas the pattern of results is not explained by existing alternative theories. As of the present results, the ATH is the first theory for the contralateral forebrain and the optic chiasm whose predictions have been tested empirically. We conclude that humans (and all other vertebrates) are fundamentally asymmetric, both in their anatomy and their behavior. This supports the thesis that the approximate bilateral symmetry of vertebrates is a secondary feature, despite their being bilaterians.