ترغب بنشر مسار تعليمي؟ اضغط هنا

A general criterion for solid instability and its application to creases

104   0   0.0 ( 0 )
 نشر من قبل Bin Liu
 تاريخ النشر 2019
  مجال البحث فيزياء
والبحث باللغة English




اسأل ChatGPT حول البحث

A general force-perturbation-based criterion for solid instability is proposed, which can predict instability including crease without priori knowledge of instability configuration. The crease instability is analyzed in detail, we found that the occurrence of solid instability does not always correspond to the non-positive definiteness of global stiffness matrix. An element stiffness-based criterion based on material stiffness is proposed as a stronger criterion in order to fast determine the occurrence of instability. This criterion has been shown to degenerate into the criterion for judging instability of certain known phenomena, such as necking and shear band phenomena. Besides, instability in strongly anisotropic materials is also predicted by the element stiffness-based criterion.



قيم البحث

اقرأ أيضاً

The Whitham equation was proposed as a model for surface water waves that combines the quadratic flux nonlinearity $f(u) = tfrac{1}{2}u^2$ of the Korteweg-de Vries equation and the full linear dispersion relation $Omega(k) = sqrt{ktanh k}$ of uni-dir ectional gravity water waves in suitably scaled variables. This paper proposes and analyzes a generalization of Whithams model to unidirectional nonlinear wave equations consisting of a general nonlinear flux function $f(u)$ and a general linear dispersion relation $Omega(k)$. Assuming the existence of periodic traveling wave solutions to this generalized Whitham equation, their slow modulations are studied in the context of Whitham modulation theory. A multiple scales calculation yields the modulation equations, a system of three conservation laws that describe the slow evolution of the periodic traveling waves wavenumber, amplitude, and mean. In the weakly nonlinear limit, explicit, simple criteria in terms of general $f(u)$ and $Omega(k)$ establishing the strict hyperbolicity and genuine nonlinearity of the modulation equations are determined. This result is interpreted as a generalized Lighthill-Whitham criterion for modulational instability.
We present a general method to unfold energy bands of supercell calculations to primitive Brillouin zone using group theoretical techniques, where an isomorphic factor group is introduced to connect the primitive translation group with the supercell translation group via a direct product. Originating from the translation group symmetry, our method gives an uniform description of unfolding approaches based on various basis sets, and therefore, should be easy to implement in both tight-binding model and existing ab initio code packages using different basis sets. This makes the method applicable to a variety of problems involving the use of supercells, such as defects, disorder, and interfacial reconstructions. As a realistic example, we calculate electronic properties of an monolayer FeSe on SrTiO$_3$ in checkerboard and collinear antiferromagnetic spin configurations, illustrating the potential of our method.
The surfaces of growing biological tissues, swelling gels, and compressed rubbers do not remain smooth, but frequently exhibit highly localized inward folds. We reveal the morphology of this surface folding in a novel experimental setup, which permit s to deform the surface of a soft gel in a controlled fashion. The interface first forms a sharp furrow, whose tip size decreases rapidly with deformation. Above a critical deformation, the furrow bifurcates to an inward folded crease of vanishing tip size. We show experimentally and numerically that both creases and furrows exhibit a universal cusp-shape, whose width scales like $y^{3/2}$ at a distance $y$ from the tip. We provide a similarity theory that captures the singular profiles before and after the self-folding bifurcation, and derive the length of the fold from large deformation elasticity.
The effect of a change of noise amplitudes in overdamped diffusive systems is linked to their unperturbed behavior by means of a nonequilibrium fluctuation-response relation. This formula holds also for systems with state-independent nontrivial diffu sivity matrices, as we show with an application to an experiment of two trapped and hydrodynamically coupled colloids, one of which is subject to an external random forcing that mimics an effective temperature. The nonequilibrium susceptibility of the energy to a variation of this driving is an example of our formulation, which improves an earlier version, as it does not depend on the time-discretization of the stochastic dynamics. This scheme holds for generic systems with additive noise and can be easily implemented numerically, thanks to matrix operations.
We have derived a general separability criterion for a class of two mode non-Gaussian continuous variable systems, obtained earlier using PPT, violation of which provides sufficient condition for entanglement. It has been obtained by utilizing the Ca uchy-Schwarz inequality and from the basic definition of separable states. This criterion coincides with the work of Agarwal and Biswas [4] which involved inequality involving higher order correlation, for testing entanglement in non-Gaussian states.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا