Josef Kiendl

• PhD
• Professor (Full) at University of the Bundeswehr Munich

We present a finite element modelling approach for unidirectional Fused Filament Fabrication (FFF)-printed specimens under tensile loading. In this study, the focus is on the fracture behaviour, the goal is to simulate the mechanical behaviour of specimens with different strand orientations until final failure of the specimens. In particular, the a...

We present a finite element modelling approach for unidirectional Fused Filament Fabrication (FFF)-printed specimens under tensile loading. In this study, the focus is on the fracture behaviour, the goal is to simulate the mechanical behaviour of specimens with different strand orientations until final failure of the specimens. In particular, the a...

The application of material extrusion methodologies in the fabrication of thermoplastic components frequently entails many notable challenges, such as shrinkage, warpage, and delamination. During the extrusion process, there is an uneven cooling gradient between the layers. As a result, this causes a component to be distorted. This deformation is o...

The application of fused filament fabrication (FFF) in vacuum changes the heat transfer of the process. This work investigates the influence of the working ambient pressure conditions in FFF-based 3D printing of polyetheretherketone (PEEK) specimens, and its impact on the resulting part strength. Layer adhesion drastically improves with decreasing...

We propose a novel variationally consistent membrane wrinkling model for analyzing the mechanical responses of wrinkled thin membranes. The elastic strain energy density is split into tensile and compressive terms via a spectral decomposition of the strain tensor. Tensile and compressive parts of the stress and constitutive tensors are then obtaine...

We present a fully explicit dynamic formulation for geometrically exact shear-deformable beams. The starting point of this work is an existing isogeometric collocation (IGA-C) formulation which is explicit in the strict sense of the time integration algorithm, but still requires a system matrix inversion due to the use of a consistent mass matrix....

We propose an isogeometric approach to model the deformation of active thin films using layered, nonlinear, Kirchhoff Love shells. Isogeometric Collocation and Galerkin formulations are employed to discretize the electrophysiological and mechanical sub-problems, respectively, with the possibility to adopt different element and time-step sizes. Nume...

This paper presents a large deformation Kirchhoff-Love shell model hierarchically enhanced with through-the-thickness warping functions, arbitrarily chosen by the user. Two unknowns are introduced for each of them, representing its amplitudes in two directions tangent to the shell surface. NURBS are used to approximate reference surface displacemen...

The Isogeometric Analysis is a novel method for the numerical solution of boundary value problems of different types. Since its introduction in 2005, it has successfully been applied to different problems of structural mechanics, among others. It offers significant advantages compared to the classical Finite Element Method. Nevertheless, this metho...

Jellyfish are one of the earliest example of animal that actively regulate swimming, but the mechanisms governing the locomotion are still a matter of research. Jellyfish obtain locomotion by activating the subumbrellar muscle layer. Sensory inputs trigger the contraction of the bell and the fluid-structure interaction effects driving locomotion. T...

This work presents an efficient quadrature rule for shell analysis fully integrated in CAD by means of Isogeometric Analysis (IGA). General CAD-models may consist of trimmed parts such as holes, intersections, cut-offs etc. Therefore, IGA should be able to deal with these models in order to fulfil its promise of closing the gap between design and a...

A good understanding of the heat transfer in fused filament fabrication is crucial for an accurate stress prediction and subsequently for repetitive, high quality printing. This work focuses on two challenges that have been presented when it comes to the accuracy and efficiency in simulating the heat transfer in the fused filament fabrication proce...

Heat transfer simulations of the fused filament fabrication process are an important tool to predict bonding, residual stresses and strength of 3D printed parts. But in order to capture the significant thermal gradients that occur in the FFF printing process, a fine mesh discretization and short time steps are required, leading to extensive computa...

We present an isogeometric method for the analysis of Kirchhoff-Love shell structures which are composed of multiple patches and which possibly possess extraordinary vertices, i.e. vertices with a valency different to four. The proposed isogeometric shell discretization is based on the one hand on the approximation of the mid-surface by a particula...

In this paper, the classical C1-continuous Bogner-Fox-Schmit (BFS) elements are employed to study the buckling behavior of rectangular plates with multiple cutouts. BFS elements are constructed by taking the tensor product of cubic Hermitian polynomials, and thus, arguably constitute one of the simplest approaches to deriving plate/shell elements....

We present a formulation for isogeometric Kirchhoff–Love shell analysis on complex CAD models consisting of multiple trimmed patches. The method is based on the penalty coupling method presented in Herrema AJ, Johnson EL, Proserpio D, Wu MCH, Kiendl J, Hsu MC (Penalty coupling of non-matching isogeometric Kirchhoff–Love shell patches with applicati...

A good understanding of the heat transfer in fused filament fabrication is crucial for an accurate stress prediction and subsequently for repetitive, high-quality printing. This work focuses on two challenges that have been presented when it comes to the accuracy and efficiency in simulating the heat transfer in the fused filament fabrication proce...

Penalty methods have proven to be particularly effective for achieving the required C1-continuity in the context of multi-patch isogeometric Kirchhoff–Love shells. Due to their conceptual simplicity, these algorithms are readily applicable to the displacement and rotational coupling of trimmed, non-conforming surfaces. However, the accuracy of the...

In this paper, a computational framework for simulating ductile fracture in multipatch shell structures is presented. A ductile fracture phase-field model at finite strains is combined with an isogeometric Kirchhoff-Love shell formulation. For the application to complex structures, we employ a penalty approach for imposing, at patch interfaces, dis...

In this paper, the isogeometric formulations of the finite element and boundary element methods are applied to the dynamic analysis of thin-walled structures submerged in an infinite, inviscid, and incompressible fluid medium. This fluid–structure interaction problem is decoupled using the modal analysis technique, and the fluid effect on the struc...

Additive manufacturing provides high design flexibility, but its use is restricted by limited mechanical properties compared to conventional production methods. As technology is still emerging, several approaches exist in the literature for quantifying and improving mechanical properties. In this study, we investigate characterizing materials’ resp...

We propose an isogeometric approximation of the equations describing the propagation of an electrophys-iologic stimulus over a thin cardiac tissue with the subsequent muscle contraction. The underlying method relies on the monodomain model for the electrophysiological sub-problem. This requires the solution of a reaction-diffusion equation over a s...

Penalty methods have proven to be particularly effective for achieving the required $C^1$-continuity in the context of multi-patch isogeometric Kirchhoff-Love shells. Due to their conceptual simplicity, these algorithms are readily applicable to the displacement and rotational coupling of trimmed, non-conforming surfaces. However, the accuracy of t...

This work extends the stress recovery for laminated composite solid plates, proposed in [1, 2], to curved structures. Based on 3D Isogeometric analysis (IGA) computations and equilibrium, this procedure uses a single element through the thickness in combination with a calibrated layer-by-layer integration rule or a homogenized approach, allowing fo...

We present a computational framework for applying the phase-field approach to brittle fracture efficiently to complex shell structures. The momentum and phase-field equations are solved in a staggered scheme using isogeometric Kirchhoff–Love shell analysis for the structural part and isogeometric second- and fourth-order phase-field formulations fo...

Isogeometric Kirchhoff–Love elements have been receiving increasing attention in geometrically nonlinear analysis of thin shells because they make it possible to meet the C1 requirement in the interior of surface patches and to avoid the use of finite rotations. However, engineering structures of appreciable complexity are typically modeled using m...

This work focuses on an efficient stress recovery procedure for laminated composite curved structures, which relies on Isogeometric Analysis (IGA) and equilibrium. Using a single element through the thickness in combination with a calibrated layerwise integration rule or a homogenized approach, the 3D solid isogeometric modeling grants an inexpensi...

We present a nonlinear multiscale modeling and simulation framework for the mechanical design of machine-knitted textiles with functionally graded microstructures. The framework operates on the mesoscale (stitch level), where yarns intermesh into stitch patterns, and the macroscale (fabric level), where these repetitive stitch patterns are composed...

Despite the accelerated deployment of laminated composites in a wide variety of markets due to their peculiar engineering features, the design of those materials is often restrained by the lack of cost-efficient modeling techniques. In fact, the existing strategies allowing for cheap simulations usually fail to directly capture out-of-plane through...

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 particu...

In this paper, we use isogeometric Kirchhoff plates to approximate composite laminates adopting the classical laminate plate theory. Both isogeometric Galerkin and collocation formulations are considered. Within this framework, interlaminar stresses are recovered through an effective post-processing technique based on the direct imposition of equil...

A computational framework is designed to accurately predict the elastic response of thin shells undergoing large displacements induced by local hydrodynamic forces, as well as to resolve the complex fluid pattern arising from its interaction with an incompressible fluid. Within the context of partitioned algorithms, two different approaches are emp...

In this work, we focus on the family of shell formulations referred to as “solid shells”, where the simulation of shell-type structures is performed by means of a mesh of 3D solid elements, with typically only one element through the thickness. We propose a novel approach for alleviating shear and membrane locking phenomena, which typically appear...

We present a nonlinear multiscale modeling and simulation framework for the mechanical design of machine knitted textiles with functionally graded microstructures. The framework operates on the mesoscale (stitch level), where yarns intermesh into stitch patterns, and the macroscale (fabric level), where these repetitive stitch patterns are composed...

In this paper the isogeometric collocation (IGA-C) method is used to solve the dynamic problem of geometrically exact beams. The kinematics of a spatial Timoshenko beam undergoing finite displacements and rotations involves the Lie group \({\mathrm{SO(3)}}\). Most of the computational complexities originate from the presence of such a non-additive...

In this work we employ isogeometric analysis (IGA) in the field of computational homogenization. We present the nonlinear governing equations for the elasticity problem with finite deformations discretized with both IGA Galerkin and collocation methods in a nested multiscale problem and then explore the accuracy and computational performance of the...

Analysis-suitable T-splines (ASTS) including both extraordinary points and T-junctions are used to solve Kirchhoff–Love shell problems. Extraordinary points are required to represent surfaces with arbitrary topological genus. T-junctions enable local refinement of regions where increased resolution is needed. The benefits of using ASTS to define sh...

We propose a novel approach to the implicit dynamics of shear-deformable geometrically exact beams, based on the isogeometric collocation method combined with the Newmark time integration scheme extended to the rotation group SO(3). The proposed formulation is fully consistent with the underlying geometric structure of the configuration manifold. T...

In this work, we focus on the family of shell formulations referred to as "solid shells", where the simulation of shell-type structures is performed by means of a mesh of 3D solid elements, with typically only one element through the thickness. We propose a novel approach for alleviating the various locking phenomena, which typically appear in thin...

We investigate the influence of raster layup on the resulting material properties of FDM 3D-printed materials made of PLA. In particular, we investigate the resulting toughness, strength, and stiffness, with a special focus on toughness. We show that for standard layups with layer orientations alternating by 90°, stiffness and strength are almost i...

Isogeometric Kirchhoff-Love elements have received an increasing attention in geometrically nonlinear analysis of elastic shells. Nevertheless, some difficulties still remain. Among the others, the highly nonlinear expression of the strain measure, which leads to a complicated and costly computation of the discrete operators, and the existence of l...

Architectured materials have attracted much attention in recent years because the specific micro‐nano structure and material combinations of architectured materials can lead to very high performance structures. Topological interlocking material (TIM), as one type of dense architectured materials, shows outstanding performances in mechanical propert...

Early‐stage wind turbine blade design usually relies heavily on low‐fidelity structural models; high‐fidelity, finite‐element‐based structural analyses are reserved for later design stages because of their complex workflows and high computational expense. Yet, high‐fidelity structural analyses often provide design‐governing feedback such as bucklin...

A strain gradient elasticity model for shells of arbitrary geometry is derived for the first time. The Kirchhoff–Love shell kinematics is employed in the context of a one-parameter modification of Mindlin's strain gradient elasticity theory. The weak form of the static boundary value problem of the generalized shell model is formulated within an H3...

Isogeometric analysis (IGA) has been a particularly impactful development in the realm of Kirchhoff–Love thin-shell analysis because the high-order basis functions employed naturally satisfy the requirement of [Formula presented] continuity. Still, engineering models of appreciable complexity, such as wind turbine blades, are typically modeled usin...

We initiate the study of three-dimensional shear-deformable geometrically exact beam dynamics through explicit isogeometric collocation methods. The formulation we propose is based on a natural combination of the chosen finite rotations representation with an explicit, geometrically consistent Lie group time integrator. We focus on extending the in...

An isogeometric thin shell formulation allowing for large-strain plastic deformation is presented. A stress-based approach is adopted, which means that the constitutive equations are evaluated at different integration points through the thickness, allowing the use of general 3D material models. The plane stress constraint is satisfied by iterativel...

An isogeometric analysis formulation for simulating red blood cell (RBC) electro-deformationis presented. Electrically-induced cell deformation experiments are receiving increasing attention as an attractive strategy for single-cell mechanical phenotyping. As the RBC structure consists in a very thin biological membrane enclosing a nearly-incompres...

This paper considers an anisotropic hyperelastic soft tissue model, originally proposed for native valve tissue and referred to herein as the Lee–Sacks model, in an isogeometric thin shell analysis framework that can be readily combined with immersogeometric fluid–structure interaction (FSI) analysis for high-fidelity simulations of bioprosthetic h...

As a first step, variational formulations and governing equations with boundary conditions are derived for a pair of Euler–Bernoulli beam bending models following a simplified version of Mindlin’s strain gradient elasticity theory of form II. For both models, this leads to sixth-order boundary value problems with new types of boundary conditions th...

Physico-mathematical models of shells in the framework of couple stress and strain gradient elasticity theories with variational formulations are developed. The models derived are embedded into a commercial finite element software as user subroutines following the isogeometric paradigm. Practical applications such as modelling of microarchitectured...

Micro Abstract We present a phase-field approach to model brittle fracture in plates and shells. For structural analysis, the discretization of the geometry is performed using an isogeometric Kirchhoff-Love shell formulation, extended to local refinement with LR B-splines in order to properly resolve the mesh in the cracked regions, improving the a...

We present an isogeometric collocation formulation for the Reissner–Mindlin shell problem. After recalling the necessary basics on differential geometry and the shell governing equations, we show that the standard approach of expressing the equilibrium equations in terms of the primal variables is not a suitable way for shells due to the complexity...

We present a reformulation of the classical Timoshenko beam problem, resulting in a single differential equation with the rotation as the only primal variable. We show that this formulation is equivalent to the standard formulation and the same types of boundary conditions apply. Moreover, we develop an isogeometric collocation scheme to solve the...

A frictionless contact formulation for spatial rods is developed within the framework of isogeometric collocation. The structural mechanics is described by the Cosserat theory of geometrically nonlinear spatial rods. The numerical discretization is based on an isogeometric collocation method, where the geometry and solution fields are represented a...

The interaction between thin structures and incompressible Newtonian fluids is ubiquitous both in nature and in industrial applications. In this paper we present an isogeometric formulation of such problems which exploits a boundary integral formulation of Stokes equations to model the surrounding flow, and a non linear Kirchhoff-Love shell theory...

This paper focuses on the employment of analysis-suitable T-spline surfaces of arbitrary degree for performing structural analysis of fully nonlinear thin shells. Our aim is to bring closer a seamless and flexible integration of design and analysis for shell structures. The local refinement capability of T-splines together with the Kirchhoff-Love s...

We present an approach for phase-field modeling of fracture in thin structures like plates and shells, where the kinematics is defined by midsurface variables. Accordingly, the phase field is defined as a two-dimensional field on the midsurface of the structure. In this work, we consider brittle fracture and a Kirchhoff–Love shell model for structu...

The interaction between thin structures and incompressible Newtonian fluids is ubiquitous both in nature and in industrial applications. In this paper we present an isogeometric formulation of such problems which exploits a boundary integral formulation of Stokes equations to model the surrounding flow, and a non linear Kirchhoff-Love shell theory...

Phase-field modeling of brittle and ductile fracture is a modern promising approach that enables a unified description of complicated failure processes (including crack initiation, propagation, branching, merging), as well as its efficient numerical treatment [1-4]. In the present work, we apply this approach to model fracture in shell structures,...

Sixth-order boundary value problems of a one-parameter gradient-elastic Kirchhoff plate model are formulated in a weak form within an Sobolev space setting with the corresponding equilibrium equations and general boundary conditions. The corresponding conforming Galerkin method is proposed with error estimates for discretizations satisfying continu...

Isogeometric collocation mixed methods for spatial rods are presented and studied. A theoretical analysis of stability and convergence is available. The proposed schemes are locking-free, irrespective of the selected approximation spaces.

We study a reformulated version of Reissner–Mindlin plate theory in which rotation variables are eliminated in favor of transverse shear strains. Upon discretization, this theory has the advantage that the "shear locking" phenomenon is completely precluded, independent of the basis functions used for displacement and shear strains. Any combination...

We present formulations for compressible and incompressible hyperelastic thin shells which can use general 3D constitutive models. The necessary plane stress condition is enforced analytically for incompressible materials and iteratively for compressible materials. The thickness stretch is statically condensed and the shell kinematics are completel...

This paper builds on a recently developed immersogeometric fluid-structure interaction (FSI) methodology for bioprosthetic heart valve (BHV) modeling and simulation. It enhances the proposed framework in the areas of geometry design and constitutive modeling. With these enhancements, BHV FSI simulations may be performed with greater levels of autom...

In isogeometric analysis (IGA), the functions used to describe the CAD geometry (such as NURBS) are also employed, in an isoparametric fashion, for the approximation of the unknown fields, leading to an exact geometry representation. Since the introduction of IGA, it has been shown that the high regularity properties of the employed functions lead...

This paper presents a novel approach for isogeometric analysis of thin shells using polynomial splines over hierarchical T-meshes (PHT-splines). The method exploits the flexibility of T-meshes for local refinement. The main advantage of the PHT-splines in the context of thin shell theory is that it achieves C1 continuity, so the Kirchhoff-Love theo...

An isogeometric finite element method is presented for natural frequencies analysis of thin plate problems of various geometries. Non-Uniform Rational B-Splines (NURBS) basis function is applied for approximation of the thin plate deflection field, as for description of the geometry. The governing and discretized equation for the free vibration of...