An Optimized, Easy-to-use, Open-source GPU Solver for Large-scale Inverse Homogenization Problems

We propose a high-performance GPU solver for inverse homogenization problems to design high-resolution 3D microstructures. Central to our solver is a favorable combination of data structures and algorithms, making full use of the parallel computation power of today's GPUs through a software-level design space exploration. This solver is demonstrated to optimize homogenized stiffness tensors, such as bulk modulus, shear modulus, and Poisson's ratio, under the constraint of bounded material volume. Practical high-resolution examples with 512^3(134.2 million) finite elements run in less than 32 seconds per iteration with a peak memory of 21 GB. Besides, our GPU implementation is equipped with an easy-to-use framework with less than 20 lines of code to support various objective functions defined by the homogenized stiffness tensors. Our open-source high-performance implementation is publicly accessible at https://github.com/lavenklau/homo3d

Topology Optimization of Differentiable Microstructures

Recent years have seen a growing interest in topology optimization of functionally graded microstructures, characterized by an array of microstructures with varying volume fractions. However, microstructures optimized at slightly different volume fractions do not necessarily connect well when placed adjacently. Furthermore, optimization is commonly performed on a finite set of volume fractions, limiting the number of microstructure configurations. In this paper, we introduce the concept of differentiable microstructures, which are parameterized microstructures that exhibit continuous variations in both geometry and mechanical properties. To construct such microstructures, we propose a novel formulation for topology optimization. In this approach, a series of 2-dimensional microstructures is represented using a height field, and the objective is to maximize the bulk modulus of the entire series. Through this optimization process, an initial microstructure with a small volume fraction undergoes non-uniform transformations, generating a series of microstructures with progressively increasing volume fractions. Notably, when compared to traditional uniform morphing methods, our proposed optimization approach yields a series of microstructures with bulk moduli that closely approach the theoretical limit.Materials and Manufacturin

Dynamic wind turbine wake reconstruction: A Koopman-linear flow estimator

A challenging topic arising in dynamic wind turbine wake is modeling, especially the low-order approximation. The central problem is the fact that it has high-dimensional and nonlinear wake characteristics. In this paper, a Koopman-linear flow estimator is designed according to the Koopman operator theory. Different from the conventional flow reconstruction with the linear stochastic estimation method, a dynamic state-space model with physical states is constructed. The wake dynamics are approximated using a limited number of measurable physical parameters by the dynamic part; then, the full wake flow is reconstructed from the low-order states by the estimation part. The flow estimator is designed into three different forms following Extended Dynamic Mode Decomposition (EDMD) method. Each form has its unique advantages. Precisely, probe sensors are placed in the studied space and provide direct information of the wake, and a few in-directly physical parameters are also included. Nonlinear integer programming is further adopted using a heuristic optimization algorithm, by which the sensor configurations are optimized. Comparisons with the standard Dynamic Mode Decomposition (DMD)-based wake model are adopted in time domain and frequency domain to verify the effectiveness of the proposed flow estimators. The results show acceptable accuracy in typical modeling cases and maintain good estimation accuracy when the measurement noises are involved. Finally, the proposed Koopman-linear flow estimator is compared with related stochastic estimation methods, in which the connections of the proposed estimator with stochastic ones are also discussed.Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.Team Jan-Willem van Wingerde

Biomechanical characterization of normal and pathological human ascending aortic tissues via biaxial testing Experiment, constitutive modeling and finite element analysis

Background: Aortic dissection and atherosclerosis are two common pathological conditions affecting the aorta. Aortic biomechanics are believed to be closely associated with the pathological development of these diseases. However, the biomechanical environment that predisposes the aortic wall to these pathological conditions remains unclear. Methods: Sixteen ascending aortic specimens were harvested from 16 human subjects and further categorized into three groups according to their disease states: aortic dissection group, aortic dissection with accompanied atherosclerosis group and healthy group. Experimental stress-strain data from biaxial tensile testing were used to fit the anisotropic Mooney-Rivlin model to determine material parameters. Computed tomography images or transesophageal echocardiography images were collected to construct computational models to simulate the stress/strain distributions in aortas at the pre-dissection state. Statistical analyses were performed to identify the biomechanical factors to distinguish three groups of aortic tissues. Results: Material parameters of anisotropic Mooney-Rivlin model were fitted with average R2 value 0.9749. The aortic diameter showed no significant difference among three groups. Changes of maximum and average stress values from minimum pressure to maximum pressure (△MaxStress and △AveStress) had significantly difference between dissection group and dissection with accompanied atherosclerosis group (p = 0.0201 and 0.0102). Changes of maximum and average strain values from minimum pressure to maximum pressure (△MaxStrain and △AveStrain) from dissection group were significant different from healthy group (p = 0.0171 and 0.0281). Conclusion: Changes of stress and strain values during the cardiac cycle are good biomechanical factors for predicting potential aortic dissection and aortic dissection accompanied with atherosclerosis.</p