The cochlea, or inner ear, is a space fully enclosed within the temporal bone of the skull, except for two membrane-covered portals connecting it to the middle ear space. One of these portals is the round window, which is covered by the Round Window Membrane (RWM). A longstanding clinical goal is to reliably and precisely deliver therapeutics into the cochlea to treat a plethora of auditory and vestibular disorders. Standard of care for several difficult-to-treat diseases calls for injection of a therapeutic substance through the tympanic membrane into the middle ear space, after which a portion of the substance diffuses across the RWM into the cochlea. The efficacy of this technique is limited by an inconsistent rate of molecular transport across the RWM. A solution to this problem involves the introduction of one or more microscopic perforations through the RWM to enhance the rate and reliability of diffusive transport. This paper reports the use of direct 3D printing via Two-Photon Polymerization (2PP) lithography to fabricate ultra-sharp polymer microneedles specifically designed to perforate the RWM. The microneedle has tip radius of 500 nm and shank radius of 50 μ m, and perforates the guinea pig RWM with a mean force of 1.19 mN. The resulting perforations performed in vitro are lens-shaped with major axis equal to the microneedle shank diameter and minor axis about 25% of the major axis, with mean area 1670 μ m. The major axis is aligned with the direction of the connective fibers within the RWM. The fibers were separated along their axes without ripping or tearing of the RWM suggesting the main failure mechanism to be fiber-to-fiber decohesion. The small perforation area along with fiber-to-fiber decohesion are promising indicators that the perforations would heal readily following in vivo experiments. These results establish a foundation for the use of Two-Photon Polymerization lithography as a means to fabricate microneedles to perforate the RWM and other similar membranes.

Shear bands are material instabilities associated with highly localized intense plastic deformation zones which can form in materials undergoing high strain rates. Determining the onset of shear band localization is a difficult task and past work reported in the literature attempt to detect this instability by computing the eigenvalues of the acoustic tensor or by studying the linear stability of the perturbed governing equations. However, both methods have their limitations and are not suited for general rate dependent materials in multidimensions.In this work we propose a novel approach to determine the onset of shear band localization and alleviate the limitations of the above mentioned methods.Owing to the implicit mixed finite elements discretization employed in this work, we propose to cast the instability analysis as a generalized eigenvalue problem by employing a particular decomposition of the element Jacobian matrix. We show that this approach is attractive, as it is applicable to general rate dependent multidimensional cases where no special simplifying assumptions ought to be made.To verify the accuracy of the proposed eigenvalue analysis, we first extend an analytical criterion by applying linear perturbation techniques to the continuous PDE model, considering an elastoplastic material with thermal diffusion and a nonlinear Taylor-Quinney coefficient. While this extension is novel on its own, it requires strenuous derivations and is not easily extended to general multidimension applications. Hence, herein it is only used for verification purposes in 1D.Numerical results on one-dimensional problems show that the eigenvalue analysis exactly recovers the instability point predicted by the analytical criterion with non-linear Taylor-Quinney coefficient. In addition, the proposed generalized eigenvalue analysis is applied on two-dimensional problems where propagation of the instability can be easily determined.

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a b s t r a c tShear banding, as an unstable process of localization, is a common precursor to fracture in materials under high strain rate loadings, making the detection of the instability point after which localization will occur of significant importance. Stability analysis based on the perturbation method or the acoustic tensor have been employed. However, these methodologies are limited to certain class of problems and are difficult to generalize.In this work we propose an alternative for identifying the instability point by employing the concept of generalized stability analysis. In this framework, a stability measure is obtained by computing the instantaneous growth rate of the vector tangent to the solution. Such an approach is more appropriate for non-orthogonal problems and is easier to generalize to difficult dynamic fracture problems.Under conditions where the local instability triggers the non-homogeneous solution growth, i.e. problems that are homogeneous until the appearance of local instability, the generalized stability analysis and the modal stability analysis will closely match. Therefore, the non-homogeneous growth can be approximated by the Rayleigh Quotient of the vector tangent to the solution, which is easier to compute.We show that for a particular class of problems that respect the aforementioned conditions, in 1D and 2D examples, both quantities successfully find the instability point predicted analytically and validated experimentally in past literature results. This methodology is general and can be applied to a wide array of dynamic fracture problems, for which instability that leads to localization is important.