We present a concurrent material and structure optimization framework for multiphase hierarchical systems that relies on homogenization estimates based on continuum micromechanics to account for ...material behavior across many different length scales. We show that the analytical nature of these estimates enables material optimization via a series of inexpensive “discretization-free” constraint optimization problems whose computational cost is independent of the number of hierarchical scales involved. To illustrate the strength of this unique property, we define new benchmark tests with several material scales that for the first time become computationally feasible via our framework. We also outline its potential in engineering applications by reproducing self-optimizing mechanisms in the natural hierarchical system of bamboo culm tissue.
An essential prerequisite for the efficient biomechanical tailoring of crops is to accurately relate mechanical behavior to compositional and morphological properties across different length scales. ...In this article, we develop a multiscale approach to predict macroscale stiffness and strength properties of crop stem materials from their hierarchical microstructure. We first discuss the experimental multiscale characterization based on microimaging (micro-CT, light microscopy, transmission electron microscopy) and chemical analysis, with a particular focus on oat stems. We then derive in detail a general micromechanics-based model of macroscale stiffness and strength. We specify our model for oats and validate it against a series of bending experiments that we conducted with oat stem samples. In the context of biomechanical tailoring, we demonstrate that our model can predict the effects of genetic modifications of microscale composition and morphology on macroscale mechanical properties of thale cress that is available in the literature.
•A micromechanics model for stiffness and strength of hierarchical culm materials is proposed.•Each hierarchical level is characterized by suitable microimaging data.•The model predictions are in ...excellent agreement with experimental measurements.•The model enables a physics-based understanding of the origins of bamboo properties.
Plant materials exhibit a wide range of highly anisotropic mechanical behavior due to a hierarchy of microheterogeneous structures at different length scales. In this article, we present a micromechanics approach that derives a hierarchical microstructure driven model of macroscopic stiffness and strength properties of anisotropic culm materials. As model input, it requires mechanical properties of the base constituents such as cellulose and lignin as well as morphology and volume fractions of all heterogeneous components at each hierarchical level. The latter can be retrieved from imaging data at different length scales, obtained from scanning electron and transmission electron microscopy. We illustrate our modeling approach for the example of bamboo that has gained increasing attention in the last decade due to its role as a sustainable building material. Validating its predictions of macroscopic stiffness moduli and ultimate strength with corresponding experimental measurements, we demonstrate that the micromechanics model provides excellent accuracy without any further phenomenological calibration. We also show that the multiscale modeling approach enables a better physics-based understanding of the origins of bamboo stiffness and strength across different scales.
The concept of concurrent material and structure optimization aims at alleviating the computational discovery of optimum microstructure configurations in multiphase hierarchical systems, whose ...macroscale behavior is governed by their microstructure composition that can evolve over multiple length scales from a few micrometers to centimeters. It is based on the split of the multiscale optimization problem into two nested sub-problems, one at the macroscale (structure) and the other at the microscales (material). In this paper, we establish a novel formulation of concurrent material and structure optimization for multiphase hierarchical systems with elastoplastic constituents at the material scales. Exploiting the thermomechanical foundations of elastoplasticity, we reformulate the material optimization problem based on the maximum plastic dissipation principle such that it assumes the format of an elastoplastic constitutive law and can be efficiently solved via modified return mapping algorithms. We integrate continuum micromechanics based estimates of the stiffness and the yield criterion into the formulation, which opens the door to a computationally feasible treatment of the material optimization problem. To demonstrate the accuracy and robustness of our framework, we define new benchmark tests with several material scales that, for the first time, become computationally feasible. We argue that our formulation naturally extends to multiscale optimization under further path-dependent effects such as viscoplasticity or multiscale fracture and damage.
Lodging impedes the successful cultivation of cereal crops. Complex anatomy, morphology and environmental interactions make identifying reliable and measurable traits for breeding challenging. ...Therefore, we present a unique collaboration among disciplines for plant science, modelling and simulations, and experimental fluid dynamics in a broader context of breeding lodging resilient wheat and oat. We ran comprehensive wind tunnel experiments to quantify the stem bending behaviour of both cereals under controlled aerodynamic conditions. Measured phenotypes from experiments concluded that the wheat stems response is stiffer than the oat. However, these observations did not in themselves establish causal relationships of this observed behaviour with the physical traits of the plants. To further investigate we created an independent finite-element simulation framework integrating our recently developed multi-scale material modelling approach to predict the mechanical response of wheat and oat stems. All the input parameters including chemical composition, tissue characteristics and plant morphology have a strong physiological meaning in the hierarchical organization of plants, and the framework is free from empirical parameter tuning. This feature of our simulation framework reveals the multi-scale origin of the observed wide differences in the stem strength of both cereals that would not have been possible with purely experimental approach.
Hierarchical multiphase systems such as plant structures apply the concept of microheterogeneity repetitively across a hierarchy of well-separated length scales: composite microstructures at a ...smaller scale form the base materials for new microstructures at the next larger scale. Their complex multiphase hierarchical organization in conjunction with physiological, reproductive, and phylogenetic constraints pose significant challenges for understanding their mechanical behavior. A rational understanding of microstructure interdependencies across hierarchical scales is, therefore, essential to pave the way towards more efficient and sustained tailoring with improved properties, for instance in the context of the targeted breeding of agricultural crops. This thesis aims to develop computationally feasible and accurate multiscale analysis and optimization methods that rationally predict the mechanical behavior and self-adapting mechanisms of multiphase hierarchical systems across multiple scales. We focus on three objectives to accomplish the outlined goal. First, we develop a multiscale modeling approach within the continuum micromechanics framework to predict the macroscale stiffness and strength of multiphase hierarchical materials focusing on a broad class of plant materials. Our approach is supported by microimages and chemical analysis data and extensively validated with the reported experiments in the literature and performed experiments by ourselves in the lab. Second, we integrate results from the continuum micromechanics and topology optimization frontiers to establish rigorous theoretical foundations for an efficient concurrent material and structure optimization framework for multiphase hierarchical systems. The framework accounts for the elastoplastic limit behavior across hierarchical scales, while its computational cost does not explode exponentially with the number of hierarchical scales. Finally, working with plant geneticists, we transfer these concepts to rationalize the biotailoring of cereals for improved lodging resistance. This thesis presents a unique opportunity and foundation concepts for the collaborative research efforts of computational mechanics and plant science in a broader context of the biomechanical tailoring of plants.
•A two-stage variational approach for segmenting 3D bone CT data is proposed.•Well-separated regions are identified by a flux-augmented Chan–Vese model.•A phase-field fracture inspired method is ...presented to remove fine-scale contacts.•Accuracy, robustness and automation is demonstrated for 3D femur and vertebra.
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We present a two-stage variational approach for segmenting 3D bone CT data that performs robustly with respect to thin cartilage interfaces. In the first stage, we minimize a flux-augmented Chan–Vese model that accurately segments well-separated regions. In the second stage, we apply a new phase-field fracture inspired model that reliably eliminates spurious bridges across thin cartilage interfaces, resulting in an accurate segmentation topology, from which each bone object can be identified. Its mathematical formulation is based on the phase-field approach to variational fracture, which naturally blends with the variational approach to segmentation. We successfully test and validate our methodology for the segmentation of 3D femur and vertebra bones, which feature thin cartilage regions in the hip joint, the intervertebral disks, and synovial joints of the spinous processes. The major strength of the new methodology is its potential for full automation and seamless integration with downstream predictive bone simulation in a common finite element framework.
In this article, we explore an embedded shell finite element method for the unfitted discretization of solid–shell interaction problems. Its core component is a variationally consistent approach that ...couples a shell discretization on the surface of an embedded solid domain to its unfitted discretization with hexahedral solid elements. Derived via an augmented Lagrangian formulation and the formal elimination of interface Lagrange multipliers, our method depends only on displacement variables, facilitated by a shift of the displacement-dependent traction vector entirely to the solid structure. We demonstrate that the weighted least squares term required for stability of the formulation triggers severe surface locking due to a mismatch in the polynomial spaces of the shell element and the embedding solid element. We show that reduced quadrature of the stabilization term that evaluates the kinematic constraint at the nodes of the embedded shell elements completely mitigates surface locking. For coarse discretizations, our variationally consistent method achieves superior accuracy with respect to a locking-free nodal penalty method. We illustrate the versatility of embedded shell finite elements for image-based analysis, including patient-specific stress prediction in a vertebra and local rind buckling in a plant structure.
•We couple a shell mesh on the surface of an embedded solid domain to its unfitted volumetric mesh.•The variationally consistent formulation depends only on displacement variables.•Its stabilization term triggers surface locking due to a polynomial mismatch between shell and solid elements.•Reduced quadrature of the stabilization term mitigates surface locking.•We present two use cases: patient-specific stress prediction in a vertebra and local rind buckling in a plant structure.
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