Robust and parallel scalable iterative solutions for large-scale finite cell analyses

The finite cell method is a highly flexible discretization technique for numerical analysis on domains with complex geometries. By using a non-boundary conforming computational domain that can be easily meshed, automatized computations on a wide range of geometrical models can be performed. Application of the finite cell method, and other immersed methods, to large real-life and industrial problems is often limited due to the conditioning problems associated with these methods. These conditioning problems have caused researchers to resort to direct solution methods, which signifi- cantly limit the maximum size of solvable systems. Iterative solvers are better suited for large-scale computations than their direct counterparts due to their lower memory requirements and suitability for parallel computing. These benefits can, however, only be exploited when systems are properly conditioned. In this contribution we present an Additive-Schwarz type preconditioner that enables efficient and parallel scalable iterative solutions of large-scale multi-level hp-refined finite cell analyses.Comment: 32 pages, 17 figure

Multi-level Bézier extraction for hierarchical local refinement of Isogeometric Analysis

One of the main topics of research on Isogeometric Analysis is local refinement. Among the various techniques currently studied and developed, one of the most appealing, referred to as hierarchical B-Splines, consists of defining a suitable set of basis functions on different hierarchical levels. This strategy can also be improved, for example to recover partition of unity, resorting to a truncation operation, giving rise to the so-called truncated hierarchical B-Splines. Despite its conceptual simplicity, implementing the hierarchical definition of shape functions into an existing code can be rather involved. In this work we present a simple way to bring the hierarchical isogeometric concept closer to a standard finite element formulation. Practically speaking, the hierarchy of functions and knot spans is flattened into a sequence of elements being equipped with a standard single-level basis. In fact, the proposed multi-level extraction is a generalization of the classical Bézier extraction and analogously offers a standard element structure to the hierarchical overlay of functions. Moreover, this approach is suitable for an extension to non-linear problems and for a parallel implementation. The multi-level extraction is presented as a general concept that can be applied to different kinds of refinements and basis functions. Finally, few basic algorithms to compute the local multi-level extraction operator for knot insertion on spline spaces are outlined and compared, and some numerical examples are presented

Hierarchically refined isogeometric analysis of trimmed shells

This work focuses on the study of several computational challenges arising when trimmed surfaces are directly employed for the isogeometric analysis of Kirchhoff-Love shells. To cope with these issues and to resolve mechanical and/or geometrical features of interest, we exploit the local refinement capabilities of hierarchical B-splines. In particular, we show numerically that local refinement is suited to effectively impose Dirichlet-type boundary conditions in a weak sense, where this easily allows to overcome the issue of over-constraining of trimmed elements. Moreover, we highlight how refinement can alleviate the spurious coupling stemming from disjoint supports of basis functions in the presence of "small" trimmed geometrical features such as thin holes. These phenomena are particularly pronounced in surface models defined by complex trimming patterns and with details at different scales. In this contribution we focus our effort on the analysis of single-patch geometries, where we show through several numerical examples the benefits and computational efficiency of the proposed methodology

Spline- and hp-basis functions of higher differentiability in the finite cell method

In this paper, the use of hpbasis functions with higher differentiability properties is discussed in the context of the finite cell method and numerical simulations on complex geometries. For this purpose, Ck hpbasis functions based on classical Bsplines and a new approach for the construction of C1 hpbasis functions with minimal local support are introduced. Both approaches allow for hanging nodes, whereas the new C1 approach also includes varying polynomial degrees. The properties of the hpbasis functions are studied in several numerical experiments, in which a linear elastic problem with some singularities is discretized with adaptive refinements. Furthermore, the application of the Ck hpbasis functions based on Bsplines is investigated in the context of nonlinear material models, namely hyperelasticity and elastoplasicity with finite strains.(VLID)439440

Spline- and hp-basis functions of higher differentiability in the finite cell method

In this paper, the use of hp-basis functions with higher differentiability properties is discussed in the context of the finite cell method and numerical simulations on complex geometries. For this purpose, Ck hp-basis functions based on classical B-splines and a new approach for the construction of C1 hp-basis functions with minimal local support are introduced. Both approaches allow for hanging nodes, whereas the new C1 approach also includes varying polynomial degrees. The properties of the hp-basis functions are studied in several numerical experiments, in which a linear elastic problem with some singularities is discretized with adaptive refinements. Furthermore, the application of the Ck hp-basis functions based on B-splines is investigated in the context of nonlinear material models, namely hyperelasticity and elastoplasicity with finite strains.Support by the Deutsche Forschungsgemeinschaft in the Priority Program 1748 “Reliable simulation techniques in solid mechanics. Development of non-standard discretization methods, mechanical and mathematical analysis” under the project DU 405/8-2, SCHR 1244/4-2, and RA 624/27-2

An integrated design, material, and fabrication platform for engineering biomechanically and biologically functional soft tissues

We present a design rationale for stretchable soft network composites for engineering tissues that predominantly function under high tensile loads. The convergence of 3D-printed fibers selected from a design library and biodegradable interpenetrating polymer networks (IPNs) result in biomimetic tissue engineered constructs (bTECs) with fully tunable properties that can match specific tissue requirements. We present our technology platform using an exemplary soft network composite model that is characterized to be flexible, yet ∼125 times stronger (E = 3.19 MPa) and ∼100 times tougher (WExt = ∼2000 kJ m–3) than its hydrogel counterpart

Synergizing Algorithmic Design, Photoclick Chemistry and Multi-Material Volumetric Printing for Accelerating Complex Shape Engineering

The field of biomedical design and manufacturing has been rapidly evolving, with implants and grafts featuring complex 3D design constraints and materials distributions. By combining a new coding-based design and modeling approach with high-throughput volumetric printing, a new approach is demonstrated to transform the way complex shapes are designed and fabricated for biomedical applications. Here, an algorithmic voxel-based approach is used that can rapidly generate a large design library of porous structures, auxetic meshes and cylinders, or perfusable constructs. By deploying finite cell modeling within the algorithmic design framework, large arrays of selected auxetic designs can be computationally modeled. Finally, the design schemes are used in conjunction with new approaches for multi-material volumetric printing based on thiol-ene photoclick chemistry to rapidly fabricate complex heterogeneous shapes. Collectively, the new design, modeling and fabrication techniques can be used toward a wide spectrum of products such as actuators, biomedical implants and grafts, or tissue and disease models.ISSN:2198-384

Synergizing Algorithmic Design, Photoclick Chemistry and Multi‐Material Volumetric Printing for Accelerating Complex Shape Engineering

Abstract The field of biomedical design and manufacturing has been rapidly evolving, with implants and grafts featuring complex 3D design constraints and materials distributions. By combining a new coding‐based design and modeling approach with high‐throughput volumetric printing, a new approach is demonstrated to transform the way complex shapes are designed and fabricated for biomedical applications. Here, an algorithmic voxel‐based approach is used that can rapidly generate a large design library of porous structures, auxetic meshes and cylinders, or perfusable constructs. By deploying finite cell modeling within the algorithmic design framework, large arrays of selected auxetic designs can be computationally modeled. Finally, the design schemes are used in conjunction with new approaches for multi‐material volumetric printing based on thiol‐ene photoclick chemistry to rapidly fabricate complex heterogeneous shapes. Collectively, the new design, modeling and fabrication techniques can be used toward a wide spectrum of products such as actuators, biomedical implants and grafts, or tissue and disease models