Design of optimal material properties for structures composed of nonlinear material

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/76247/1/AIAA-1994-4367-370.pd

Consistent patterns of common species across tropical tree communities

Trees structure the Earth’s most biodiverse ecosystem, tropical forests. The vast number of tree species presents a formidable challenge to understanding these forests, including their response to environmental change, as very little is known about most tropical tree species. A focus on the common species may circumvent this challenge. Here we investigate abundance patterns of common tree species using inventory data on 1,003,805 trees with trunk diameters of at least 10 cm across 1,568 locations1,2,3,4,5,6 in closed-canopy, structurally intact old-growth tropical forests in Africa, Amazonia and Southeast Asia. We estimate that 2.2%, 2.2% and 2.3% of species comprise 50% of the tropical trees in these regions, respectively. Extrapolating across all closed-canopy tropical forests, we estimate that just 1,053 species comprise half of Earth’s 800 billion tropical trees with trunk diameters of at least 10 cm. Despite differing biogeographic, climatic and anthropogenic histories7, we find notably consistent patterns of common species and species abundance distributions across the continents. This suggests that fundamental mechanisms of tree community assembly may apply to all tropical forests. Resampling analyses show that the most common species are likely to belong to a manageable list of known species, enabling targeted efforts to understand their ecology. Although they do not detract from the importance of rare species, our results open new opportunities to understand the world’s most diverse forests, including modelling their response to environmental change, by focusing on the common species that constitute the majority of their trees.Publisher PDFPeer reviewe

Nonlinear computational models for composite materials using homogenization.

The primary objective of this dissertation is to develop computational models that describe the overall mechanical response as well as characterize the microstructure behaviour of composite materials. The models presented are restricted to two different classes: the small deformation of linear elastic composites, and the large deformation of elasto-plastic composites. It is further assumed that the composite materials can be represented by a periodic repetition of a microstructural unit. Based on this assumption the homogenization theory is used to derive models characterizing both the macroscopic and the microscopic mechanical behavior of the composite, and the finite element method used for their computational implementation. For the case of small deformation of linear elastic composites, the accuracy of the finite element method is studied. A priori error estimations are derived and the convergence properties are discussed. After asserting the convergence properties of the method, the ideas of material pre-processor and material post-processor are introduced and examples for local stress analysis are presented. An adaptive finite element method based on the a priori error estimations is also implemented to improve the accuracy of the approximations. For the case of large deformation elasto-plasticity of composites, an incremental method is developed by applying the homogenization technique to the rate form of equilibrium equations. The constitutive equation for the components of the composite assumes time independent plasticity, additive decomposition of the velocity gradient, isotropic and kinematic hardening, and a normal flow rule. The particular case of J\sb2 flow theory of plasticity with isotropic and kinematic hardening is considered. The method is applied to local stress and plasticity analysis of general two dimensional structures, as well as to investigate the macroscopic properties of the composites. The numerical results show that the macroscopic behavior depends significantly on the geometry of the microstructure and is rather different from that of the constituents of the composite material.Ph.D.Applied SciencesEngineeringMechanical engineeringMechanicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/128531/2/9023602.pd

Preprocessing and postprocessing for materials based on the homogenization method with adaptive finite element methods

This paper discusses the homogenization method to determine the effective average elastic constants of linear elasticity of general composite materials by considering their microstructure. After giving a brief theory of the homogenization method, a finite element approximation is introduced with convergence study and corresponding error estimate. Applying these, computer programs PREMAT and POSTMAT are developed for preprocessing and postprocessing of material characterization of composite materials. Using these programs, the homogenized elastic constants for macroscopic stress analysis are obtained for typical composite materials to show their capability. Finally, the adaptive finite element method is introduced to improve the accuracy of the finite element approximation.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/28363/1/0000128.pd

On the prediction of material properties and topology for optimal continuum structures

A new formulation is presented for mathematical modelling to predict material properties for the optimal design of continuum structures. The method is based on an extended form of an already established characterization for continuum design, where the material properties tensor for an arbitrary structural continuum appears as the design variable. The extension is comprised of means to represent an independently specified unit relative cost factor , which appears simply as a weighting function in the argument of the isoperimetric (cost) constraint of the original model. A procedure is demonstrated where optimal black/white topology is predicted out of a sequence of solutions to material properties design problems having this generalized cost formulation form. A systematic adjustment is made in the unit relative cost field for each subsequent solution step in the sequence, and at the stage identified with final topology, no more than a small fraction of a percent of the total element area in the system has material property density off the bounding “black” or “white” levels. This technique is effective for the prediction of optimal black/white topology design for design around obstacles of arbitrary shape, as well as the more unusual topology design problems. Results are presented for 2D examples of both types of problem. In addition to the treatment for (the usual) minimum compliance design, an alternate formulation of the design problem is presented as well, one that provides for the prediction of optimum topology with a generalized measure of compliance as the objective.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46075/1/158_2005_Article_BF01812523.pd

Diagnostic performance of three non-invasive fibrosis scores (Hepamet, FIB-4, NAFLD fibrosis score) in NAFLD patients from a mixed Latin American population

Introduction and aims: Several non-invasive scoring systems have been developed and validated worldwide to predict the risk of liver fibrosis in nonalcoholic fatty liver disease (NAFLD). However, information about the performance of these systems in Latin American populations is scarce. Our aim was to evaluate the performance of the Hepamet Fibrosis Score, Fibrosis-4 (FIB-4) and the NAFLD Fibrosis Score (NFS) in a mixed Latin American group of NAFLD patients. Methods: Clinical, laboratory and liver biopsy data collected from 379 biopsy-proven NAFLD patients from Latin American tertiary health centers were reviewed. Histological fibrosis stages were classified using the Kleiner score. Accuracy was determined, and new fibrosis score thresholds were calculated to better compare the performances of non-invasive tests and to explore their usefulness in excluding fibrosis. Results: The distribution of fibrosis stages among the sample population was as follows: F0 (45%), F1 (27%), F2 (8%), F3 (16%) and F4 (4%). Using modified thresholds, the areas under the ROC curves (AUROC) for Hepamet and FIB-4 (0.73 and 0.74, respectively) to detect significant fibrosis were higher than that of NFS (0.58). However, the AUROCs of the three scores were not significantly different in advanced fibrosis and cirrhosis. To exclude fibrosis, we calculated lower cutoffs than standard thresholds for Hepamet, FIB-4 and NFS with similar performances. Conclusion: Thresholds of non-invasive fibrosis scores (Hepamet, FIB-4 and NFS) can be modified to maximize diagnostic accuracy in Latin American patients with NAFLD