Reduced integration schemes in micromorphic computational homogenization of elastomeric mechanical metamaterials

AbstractExotic behaviour of mechanical metamaterials often relies on an internal transformation of the underlying microstructure triggered by its local instabilities, rearrangements, and rotations. Depending on the presence and magnitude of such a transformation, effective properties of a metamaterial may change significantly. To capture this phenomenon accurately and efficiently, homogenization schemes are required that reflect microstructural as well as macro-structural instabilities, large deformations, and non-local effects. To this end, a micromorphic computational homogenization scheme has recently been developed, which employs the particular microstructural transformation as a non-local mechanism, magnitude of which is governed by an additional coupled partial differential equation. Upon discretizing the resulting problem it turns out that the macroscopic stiffness matrix requires integration of macro-element basis functions as well as their derivatives, thus calling for higher-order integration rules. Because evaluation of a constitutive law in multiscale schemes involves an expensive solution of a non-linear boundary value problem, computational efficiency of the micromorphic scheme can be improved by reducing the number of integration points. Therefore, the goal of this paper is to investigate reduced-order schemes in computational homogenization, with emphasis on the stability of the resulting elements. In particular, arguments for lowering the order of integration from expensive mass-matrix to a cheaper stiffness-matrix equivalent are outlined first. An efficient one-point integration quadrilateral element is then introduced and a proper hourglass stabilization is discussed. Performance of the resulting set of elements is finally tested on a benchmark bending example, showing that we achieve accuracy comparable to the full quadrature rules, whereas computational cost decreases proportionally to the reduction in the number of quadrature points used

Reduced integration schemes in micromorphic computational homogenization of elastomeric mechanical metamaterials

Exotic behaviour of mechanical metamaterials often relies on an internal transformation of the underlying microstructure triggered by its local instabilities, rearrangements, and rotations. Depending on the presence and magnitude of such a transformation, effective properties of a metamaterial may change significantly. To capture this phenomenon accurately and efficiently, homogenization schemes are required that reflect microstructural as well as macro-structural instabilities, large deformations, and non-local effects. To this end, a micromorphic computational homogenization scheme has recently been developed, which employs the particular microstructural transformation as a non-local mechanism, magnitude of which is governed by an additional coupled partial differential equation. Upon discretizing the resulting problem it turns out that the macroscopic stiffness matrix requires integration of macro-element basis functions as well as their derivatives, thus calling for a higher-order integration rules. Because evaluation of constitutive law in multiscale schemes involves an expensive solution of a non-linear boundary value problem, computational efficiency can be improved by reducing the number of integration points. Therefore, the goal of this paper is to investigate reduced-order schemes in computational homogenization, with emphasis on the stability of the resulting elements. In particular, arguments for lowering the order of integration from the expensive mass-matrix to a cheaper stiffness-matrix equivalent are first outlined. An efficient one-point integration quadrilateral element is then introduced and proper hourglass stabilization discussed. Performance of the resulting set of elements is finally tested on a benchmark bending example, showing that we achieve accuracy comparable to the full quadrature rules.Comment: 21 pages, 8 figures, 3 tables, abstract shortened to fulfill 1920 character limit, small changes after revie

A Theoretical and Experimental Analysis of Radiofrequency Ablation with a Multielectrode, Phased, Duty-Cycled System

Background:   The development of a unique radiofrequency (RF) cardiac ablation system, for the treatment of cardiac arrhythmias, is driven by the clinical need to safely create large uniform lesions while controlling lesion depth. Computational analysis of a finite element model of a three-dimensional, multielectrode, cardiac ablation catheter, powered by a temperature-controlled, multiphase, duty-cycled RF generator, is presented. Methods:   The computational model for each of the five operating modes offered by the generator is compared to independent tissue temperature measurements taken during in vitro ablation experiments performed on bovine myocardium. Results:   The results of the model agree with experimental temperature measurements very closely—the average values for mean error, root mean square difference, and correlation coefficient were 1.9°C, 13.3%, and 0.97, respectively. Lesions are shown to be contiguous and no significant edge effects are observed. Conclusions:   Both the in vitro and computational model results demonstrate that lesion depth decreases consistently as the bipolar-to-unipolar ratio increases—suggesting a clinical application to potentially control lesion depth with higher fidelity than is currently available. The effect of variable design parameters and clinical conditions on RF ablation can now be expeditiously studied with this validated model. (PACE 2010; 33:1089–1100)Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/79205/1/j.1540-8159.2010.02801.x.pd

Auditory chain reaction: Effects of sound pressure and particle motion on auditory structures in fishes

Despite the diversity in fish auditory structures, it remains elusive how otolith morphology and swim bladder-inner ear (= otophysic) connections affect otolith motion and inner ear stimulation. A recent study visualized sound-induced otolith motion;but tank acoustics revealed a complex mixture of sound pressure and particle motion. To separate sound pressure and sound-induced particle motion, we constructed a transparent standing wave tubelike tank equipped with an inertial shaker at each end while using X-ray phase contrast imaging. Driving the shakers in phase resulted in maximised sound pressure at the tank centre, whereas particle motion was maximised when shakers were driven out of phase (180 degrees). We studied the effects of two types of otophysic connections-i.e. the Weberian apparatus (Carassius auratus) and anterior swim bladder extensions contacting the inner ears (Etroplus canarensis)-on otolith motion when fish were subjected to a 200 Hz stimulus. Saccular otolith motion was more pronounced when the swim bladder walls oscillated under the maximised sound pressure condition. The otolith motion patterns mainly matched the orientation patterns of ciliary bundles on the sensory epithelia. Our setup enabled the characterization of the interplay between the auditory structures and provided first experimental evidence of how different types of otophysic connections affect otolith motion

A New Acoustic Portal into the Odontocete Ear and Vibrational Analysis of the Tympanoperiotic Complex

Global concern over the possible deleterious effects of noise on marine organisms was catalyzed when toothed whales stranded and died in the presence of high intensity sound. The lack of knowledge about mechanisms of hearing in toothed whales prompted our group to study the anatomy and build a finite element model to simulate sound reception in odontocetes. The primary auditory pathway in toothed whales is an evolutionary novelty, compensating for the impedance mismatch experienced by whale ancestors as they moved from hearing in air to hearing in water. The mechanism by which high-frequency vibrations pass from the low density fats of the lower jaw into the dense bones of the auditory apparatus is a key to understanding odontocete hearing. Here we identify a new acoustic portal into the ear complex, the tympanoperiotic complex (TPC) and a plausible mechanism by which sound is transduced into the bony components. We reveal the intact anatomic geometry using CT scanning, and test functional preconceptions using finite element modeling and vibrational analysis. We show that the mandibular fat bodies bifurcate posteriorly, attaching to the TPC in two distinct locations. The smaller branch is an inconspicuous, previously undescribed channel, a cone-shaped fat body that fits into a thin-walled bony funnel just anterior to the sigmoid process of the TPC. The TPC also contains regions of thin translucent bone that define zones of differential flexibility, enabling the TPC to bend in response to sound pressure, thus providing a mechanism for vibrations to pass through the ossicular chain. The techniques used to discover the new acoustic portal in toothed whales, provide a means to decipher auditory filtering, beam formation, impedance matching, and transduction. These tools can also be used to address concerns about the potential deleterious effects of high-intensity sound in a broad spectrum of marine organisms, from whales to fish