Premenopausal women exhibit enhanced insulin sensitivity and reduced incidence of type 2 diabetes (T2D) compared with age-matched men, but this advantage disappears after menopause with disrupted glucose homeostasis, in part owing to a reduction in circulating 17b-estradiol (E 2 ). Fasting hyperglycemia is a hallmark of T2D derived largely from dysregulation of hepatic glucose production (HGP), in which Foxo1 plays a central role in the regulation of gluconeogenesis. Here, we investigated the action of E 2 on glucose homeostasis in male and ovariectomized (OVX) female control and liverspecific Foxo1 knockout (L-F1KO) mice and sought to understand the mechanism by which E 2 regulates gluconeogenesis via an interaction with hepatic Foxo1. In both male and OVX female control mice, subcutaneous E 2 implant improved insulin sensitivity and suppressed gluconeogenesis; however, these effects of E 2 were abolished in L-F1KO mice of both sexes. In our use of mouse primary hepatocytes, E 2 suppressed HGP and gluconeogenesis in hepatocytes from control mice but failed in hepatocytes from L-F1KO mice, suggesting that Foxo1 is required for E 2 action on the suppression of gluconeogenesis. We further demonstrated that E 2 suppresses hepatic gluconeogenesis through activation of estrogen receptor (ER)a-phosphoinositide 3-kinase-Akt-Foxo1 signaling, which can be independent of insulin receptor substrates 1 and 2 (Irs1 and Irs2), revealing an important mechanism for E 2 in the regulation of glucose homeostasis. These results may help explain why premenopausal women have lower incidence of T2D than age-matched men and suggest that targeting ERa can be a potential approach to modulate glucose metabolism and prevent diabetes.

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SUMMARYIn this paper, two brittle fracture problems are numerically simulated: the failure of a ceramic ring under centrifugal loading and crack branching in a PMMA strip. A three-dimensional ÿnite element package in which cohesive elements are dynamically inserted has been developed. The cohesive elements' strength is chosen to follow a modiÿed weakest link Weibull distribution. The probability of introducing a weak cohesive element is set to increase with the cohesive element size. This re ects the physically based e ect according to which larger elements are more likely to contain defects. The calculations illustrate how the area dependence of the Weibull model can be used to e ectively address mesh dependency. On the other hand, regular Weibull distributions have failed to reduce mesh dependency for the examples shown in this paper.The ceramic ring calculations revealed that two distinct phenomena appear depending on the magnitude of the Weibull modulus. For low Weibull modulus, the fragmentation of the ring is dominated by heterogeneities. Whereas many cracks were generated, few of them could propagate to the outer surface. Monte Carlo simulations revealed that for highly heterogeneous rings, the number of small fragments was large and that few large fragments were generated.For high Weibull modulus, signifying that the ring is close to being homogeneous, the fragmentation process was very di erent. Monte Carlo simulations highlighted that a larger number of large fragments are generated due to crack branching.

We present a fundamental investigation of the influence of material and structural parameters on the mechanics of fragmentation of brittle materials. First, we conduct a theoretical analysis (similar to Drugan's single wave problem, Drugan, W..) and obtain closed form solutions for a problem coupling stress wave propagation and single cohesive crack growth. Expressions for a characteristic fragment size s 0 and a characteristic strain-rateε 0 are given. Next, we use a numerical approach to analyze a realistic fragmentation process that involves multiple crack interactions. The average fragment size s is calculated for a wide variety of strain-ratesε and a broad range of material parameters. Finally, we derive an empirical function that relates the normalized fragment size s/s 0 to the normalized strain-rateε/ε 0 and that fits all of the numerical results with a single master curve.

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