Mechanical aspects play an important role in brain development, function, and disease. Therefore, continuum-mechanics-based computational models are a valuable tool to advance our understanding of mechanics-related physiological and pathological processes in the brain. Currently, mainly phenomenological material models are used to predict the behavior of brain tissue numerically. The model parameters often lack physical interpretation and only provide adequate estimates for brain regions which have a similar microstructure and age as those used for calibration. These issues can be overcome by establishing advanced constitutive models that are microstructurally motivated and account for regional heterogeneities through microstructural parameters.In this work, we perform simultaneous compressive mechanical loadings and microstructural analyses of porcine brain tissue to identify the microstructural mechanisms that underlie the macroscopic nonlinear and time-dependent mechanical response. Based on experimental insights into the link between macroscopic mechanics and cellular rearrangements, we propose a microstructure-informed finite viscoelastic constitutive model for brain tissue. We determine a relaxation time constant from cellular displacement curves and introduce hyperelastic model parameters as linear functions of the cell density, as determined through histological staining of the tested samples. The model is calibrated using a combination of cyclic loadings and stress relaxation experiments in compression. The presented considerations constitute an important step towards microstructure-based viscoelastic constitutive models for brain tissue, which may eventually allow us to capture regional material heterogeneities and predict how microstructural changes during development, aging, and disease affect macroscopic tissue mechanics.

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The paper considers a two-echelon supply chain inventory model with one manufacturer and multiple buyers in which each buyer's demand is dependent on the selling price of the product. The manufacturer's lead time is composed of several components and each component can be reduced by an additional crashing cost. We develop the proposed model assuming that the lead time demand follows a normal distribution or it is distribution free. The optimal decisions are obtained by maximizing the total expected profit of the supply chain. It is observed from numerical study that the lead time reduction has minor effect on the selling price of the product, but it enhances the profit of the supply chain system.

This paper considers a three-echelon supply chain model with one supplier, one manufacturer and one retailer for trading a single product. We assume that the market demand at the retailer’s end is stochastic, but dependent on price and quality of the product. The final product’s quality depends on the manufacturing process and the raw material’s quality. We first develop models for centralized and decentralized scenarios. Then we try to coordinate the decentralized system with some contract mechanism. We show that revenue sharing contract is not able to coordinate the system, but a composite contract comprised of sales rebate and penalty (SRP) with return is able to coordinate the system. Finally, we illustrate the developed model with a numerical example and show the efficiency of SRP with return policy. We graphically show the effects of various model-parameters on the optimal decisions. Most of the existing literature’s focus on the quality of the finished product, but in this model we incorporate the quality of the raw material as a decision variable along with the finished product quality. We also able to coordinate the three echelon model with a composite contract which is seldom addressed in the existing literatures.

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