Articular cartilage from a material science point of view is a soft network composite that plays a critical role in load-bearing joints during dynamic loading. Its composite structure, consisting of a collagen fiber network and a hydrated proteoglycan matrix, gives rise to the complex mechanical properties of the tissue including viscoelasticity and stress relaxation. Melt electrospinning writing allows the design and fabrication of medical grade polycaprolactone (mPCL) fibrous networks for the reinforcement of soft hydrogel matrices for cartilage tissue engineering. However, these fiber-reinforced constructs underperformed under dynamic and prolonged loading conditions, suggesting that more targeted design approaches and material selection are required to fully exploit the potential of fibers as reinforcing agents for cartilage tissue engineering. In the present study, we emulated the proteoglycan matrix of articular cartilage by using highly negatively charged star-shaped poly(ethylene glycol)/heparin hydrogel (sPEG/Hep) as the soft matrix. These soft hydrogels combined with mPCL melt electrospun fibrous networks exhibited mechanical anisotropy, nonlinearity, viscoelasticity and morphology analogous to those of their native counterpart, and provided a suitable microenvironment for in vitro human chondrocyte culture and neocartilage formation. In addition, a numerical model using the p-version of the finite element method (p-FEM) was developed in order to gain further insights into the deformation mechanisms of the constructs in silico, as well as to predict compressive moduli. To our knowledge, this is the first study presenting cartilage tissue-engineered constructs that capture the overall transient, equilibrium and dynamic biomechanical properties of human articular cartilage.

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 (W = ∼2000 kJ m) than its hydrogel counterpart.

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 significantly 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.

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In this contribution we provide benchmark problems in the field of computational solid mechanics. In detail, we address classical fields as elasticity, incompressibility, material interfaces, thin structures and plasticity at finite deformations. For this we describe explicit setups of the benchmarks and introduce the numerical schemes. For the computations the various participating groups use different (mixed) Galerkin finite element and isogeometric analysis formulations. Some programming codes are available open-source. The output is measured in terms of carefully designed quantities of interest that allow for a comparison of other models, discretizations, and implementations. Furthermore, computational robustness is shown in terms of mesh refinement studies. This paper presents benchmarks, which were developed within the Priority Programme of the German Research Foundation ‘SPP 1748 Reliable Simulation Techniques in Solid Mechanics—Development of Non-Standard Discretisation Methods, Mechanical and Mathematical Analysis’.

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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, where we show through several numerical examples the benefits and computational efficiency of the proposed methodology.

Recently, a multi-level hp-version of the finite element method (FEM) was proposed to ease the difficulties of treating hanging nodes, while providing full hp-approximation capabilities. In the original paper, the refinement procedure made use of a-priori knowledge of the solution. However, adaptive procedures can produce discretizations which are more effective than an intuitive choice of element sizes h and polynomial degree distributions p. This is particularly prominent when a-priori knowledge of the solution is only vague or unavailable. The present contribution demonstrates that multi-level hp-adaptive schemes can be efficiently driven by an explicit a-posteriori error estimator. To this end, we adopt the classical residual-based error estimator. The main insight here is that its extension to multi-level hp-FEM is possible by considering the refined-most overlay elements as integration domains. We demonstrate on several two-and three-dimensional examples that exponential convergence rates can be obtained.