We present a Riemannian trust-region (RTR) method for a geometrically nonlinear shell model with drilling rotations, based on the stress-resultant shell theory of Ibrahimbegović. Since the rotational degrees of freedom take values in SO(3), the shell problem is naturally formulated as an energy minimization on the configuration manifold C = R³ × SO(3). We derive the Riemannian gradient and Hessian of the total potential energy, employ the exponential map on SO(3) as a retraction, and introduce a constraint-shifting strategy to robustly handle displacement-driven boundary conditions incompatible with the trust region. The trust-region subproblem is solved accurately using the Moré–Sorensen algorithm, which proves essential due to ill-conditioning arising from large length-to-thickness ratios and the coupling between translational and rotational degrees of freedom. The method is evaluated on several benchmarks, including a twisted cable, a release-boundary problem, a cantilever with a C-profile, and an industrially motivated S-shaped flat cable. In all cases, the proposed RTR method is more robust than standard Newton and Newton with line search, requiring fewer load steps and fewer linear solves. For challenging configurations such as the S-shaped cable, Newton-based solvers fail while RTR reliably converges, demonstrating its suitability for realistic engineering applications

This work investigates how curvature, internal pressure and fiber reinforcements affect the deformation behavior of hoses, factors that in combination cannot be adequately represented using geometrically exact rod models. Therefore, we analytically describe the dominant deformation mechanisms in curved hoses, modeled as toroidal components. The coupling between curvature and internal pressure generates an outward shear force and induces characteristic cross-sectional deformations arising from the inherently coupled axial and radial response of the closed-ring toroidal structure. Additionally, curvature changes the local fiber orientation, leading to a variation of the helical wrapping angle. Moreover, we investigate the interaction between internal pressure, curvature and helical reinforcements, showing that the toroidal neutral wrapping angle establishes an isotensoidal stress state by balancing axial and circumferential stresses. The analytical results are assessed through pressurized hose experiments supported by computed tomography (CT)-based fiber structure characterization. The predicted deformation patterns are validated using high-resolution 3D continuum finite-element models with suitable homogenization of the fiber reinforcements and sensitivity-based identification of the material parameters.

This work investigates the role of fiber orientation in the analysis and simulation of a helically reinforced, pressurized torus. Therefore, the concept of the neutral wrapping angle of a straight cylinder is extended to a torus. This specific angle establishes an isotensoidal load condition by balancing axial and circumferential stresses. It varies for a torus along the cross section due to fluctuating circumferential stresses. Because of the curvature of the torus, the geometrical wrapping angle is not constant. Bending a reinforced straight cylinder into a toroidal shape or winding fibers onto a toroidal part inherently creates a varying geometrical wrapping angle, which follows a similar pattern to the toroidal neutral wrapping angle, but differs quantitatively. Using the finite element method and suitable modeling approaches, we analyze this difference as well as the interplay between fiber orientation and curvature effects on toroidal deformations. Specifically, we examine how deviations from the neutral wrapping angle superpose with the Bourdon effect. These interactions emphasize the need for precise modeling of varying wrapping angles, especially in highly curved toroidal geometries.

This contribution investigates and compares different fiber reinforcement paths on a torus subjected to internal pressure. In particular, the following three characteristic trajectories are considered: the toroidal helix, the path of the resultant principal stress, and a geodesic. The objective is to understand the role of fiber orientation on the structural strength and deformation of a pressurized torus. The wrapping angles of these trajectories vary along the cross-section of the torus. The geometrical wrapping angle of the toroidal helix and the toroidal neutral wrapping angle, which represents the orientation of the resultant principal stress path, behave qualitatively similar but quantitatively different, while the geodesic line behaves reciprocally. To characterize the mechanical response, we propose a stress ratio parameter that reflects how fiber paths relate to stress distribution and deformation behavior.

This contribution aims to model and characterize the nonlinear elastic behavior of hoses under internal pressure. A highly resolved 3D continuum model is used to identify relevant effects of preformed hoses under internal pressure. The focus of this work is on the Bourdon effect, which is illustrated by simulating two simplified models, a full torus and a quarter torus. For a full torus, the Bourdon effect can be observed by the fact that the radius of curvature increases in addition to the expansion of the cross-sectional radius. For a quarter torus, which is a simplified example of a curved hose, the Bourdon effect can be observed by the tendency of the hose to straighten under internal pressure. Furthermore it is detected for both examples that the non-constant distribution of the poloidal (hoop) stress over the cross-section leads to an ovalization behavior. In addition, the model of a quarter torus is extended to a more complex model with straight hose sections at both ends.

Significant trends in the vehicle industry are autonomous driving, micromobility, electrification and the increased use of shared mobility solutions. These new vehicle automation and mobility classes lead to a larger number of occupant positions, interiors and load directions. As safety systems interact with and protect occupants, it is essential to place the human, with its variability and vulnerability, at the center of the design and operation of these systems. Digital human body models (HBMs) can help meet these requirements and are therefore increasingly being integrated into the development of new vehicle models. This contribution provides an overview of current HBMs and their applications in vehicle safety in different driving modes. The authors briefly introduce the underlying mathematical methods and present a selection of HBMs to the reader. An overview table with guideline values for simulation times, common applications and available variants of the models is provided. To provide insight into the broad application of HBMs, the authors present three case studies in the field of vehicle safety: (i) in-crash finite element simulations and injuries of riders on a motorcycle; (ii) scenario-based assessment of the active pre-crash behavior of occupants with the Madymo multibody HBM; (iii) prediction of human behavior in a take-over scenario using the EMMA model.

This paper proposes a kinematical reduction for Kirchhoff–Love shells in the special case of developable base surfaces. The resulting model considers a curve and a director field along it, reducing the shell to one-dimensional items and thereby decreasing the number of degrees of freedom involved. The presented overview of the geometry of developable surfaces covers dissolution of two types of singularities: a relatively parallel frame allows for points or segments of zero curvature along the curve and an explicit condition accounts for local self-intersections of the ruled surface description. We generalise earlier results after which the geometric constraints proposed are equivalent to isometric shell deformation. We also give a more general update of the elastic bending energy of the ribbon, which yields equilibrium states as minimisers. Subsequently, we discuss the numerical details of the approach and illustrate the feasibility at hand of several examples, among them the famous Möbius ribbon.

This paper aims at introducing a kinematical reduction for Kirchhoff-Love shells with developable base surfaces that undergo isometric deformations. This framework is appropriate to model, for example, flexible flat cables. In order to decrease the involved number of degrees of freedom, we utilise kinematical reduction to a geodesic line and a vector field along this curve. Application of a relatively parallel frame allows us to generalise this framework to a more general class of curves that may exhibit points or segments of vanishing curvature. We derive the one-dimensional bending energy functional for a rectangular strip, combine it with penalty terms addressing the nonlinear constraints, and compute the equilibrium state as minimiser of this penalised energy. An isogeometric discretisation yields finitely many degrees of freedom for the inner point optimiser. Several example strips clamped at both ends illustrate the feasibility of this approach.

The goal of this paper is to introduce a kinematical reduction for the structural model of Kirchhoff-Love shells with developable base surfaces. The dimensional reduction to a curve and a vector field along it decreases the involved number of degrees of freedom. Local coordinates in form of a relatively parallel frame allow us to simplify the geometric constraints occurring in the model and prevent instabilities caused by points or segments of zero curvature. The core of this work is to prove equivalence of these requirements and the isometry of the transformation. Subsequently, we derive the one-dimensional bending energy functional for rectangular strips. In order to compute the equilibrium state of a static shell, we minimise a penalised version of this functional over the finitely many degrees of freedom stemming from an isogeometric discretisation. Several example strips clamped at both ends illustrate the feasibility of this approach.

In IPS-IMMA the operation sequence planning tool offers an easy and powerful way to construct, analyze, and simulate sequences of human operations. So far, the simulations created using this tool have been quasi-static solutions to the operation sequence. In this paper we present new functionality for motion planning of digital human operation sequences which also takes the dynamics of the human into consideration. The new functionality is based discrete mechanics and optimal control and will be seamlessly integrated into to the IPS-IMMA software through the operation sequence planning tool. First, the user constructs an operation sequence using the operation sequence planning tool in IPS-IMMA. The operation sequence is then converted into a discrete optimal control problem which is solved using a nonlinear programming solver. Finally, the solution can be played back and analyzed in the graphical interface of IPS-IMMA. In order to obtain physically correct solutions to complex sequences consisting of several consecutive and dependent operations, we view the digital human as a hybrid system, i.e. a system containing both continuous and discrete dynamic behavior. In particular, the optimal control problem is divided into multiple continuous phases, connected by discrete events. The variational integrators used in discrete mechanics are particularly well suited for modelling the dynamics of constrained mechanical systems, which is almost always the case when considering complex human models interacting with the environment. To demonstrate the workflow, we model and solve an industrial case where the dynamics of the system plays an important part in the solution.

In this work, a digital human model based on multibody system dynamics is used in a car pre-crash scenario. An optimal control approach is used to generate motion and control signals. The arms of the manikin are actuated by Hill muscles, while the rest of the body is controlled by joint torques. A full braking maneuver is investigated as an application case.

The human hand has a complex musculoskeletal structure which acts as an effective end-effector to perform grasping effectively. Optimal control is a productive method to execute predictive simulations for many biomechanical activities. Optimal control for grasping simulations has been demonstrated for precision grasps for two fingers. However, the procedure to expand it to a full hand is laborious, primarily due to a large computational cost. Furthermore, a full hand performs with a high degree of coordination. These issues can be challenged by the inclusion of kinematic or postural synergies in the multibody framework. In this work, we implement the modelling of kinematic synergies to perform grasping simulations.

Grasping is a complex human movement. During grasping, when the hand closes around the object, the multibody system changes from a kinematic tree structure to a closed loop contact problem. To better understand work-related disorders or optimize execution of activities of daily life, an optimal control simulation to perform grasping is useful. We simulate the grasping action with a three-dimensional rigid multibody model composed of two fingers actuated by joint torques. The grasping movement is composed of a reaching phase (no contacts) and a grasping phase (closed contacts). The contact constraints are imposed first through distances between the fingers and the object surfaces and then through spherical joints. Thus, the dynamics of grasping is described by a hybrid dynamical system with a given switching sequence and unknown switching times. To determine a favourable trajectory for grasping action, we solve an optimal control problem (ocp). The ocp is solved using the direct transcription method DMOCC, leading to a structure preserving approximation of the continuous problem. An objective involving either the contact polygon centroid or the contol torques is minimized subject to discrete Euler-Lagrange equations, boundary conditions and path constraints. The dynamics of the object to grasp along with Coulomb friction is also taken into account.

In this work we will present a novel approach to compute the potential energy and its derivatives of a shell discretized by finite elements. Afterwards a special solution strategy for quasistatic equilibrium problems with moving boundary conditions is presented. At the end numerical examples are shown, which demonstrate the benefits of this methods in simulating flexible flat cables.

We developed a biomechanical digital human model (DHM) simulation framework that uses (synergetic) Hill type muscles as actuators and optimal control (OC) for motion generation. In this work, we start investigating the underlying actuation signals of the Hill type muscles. We have set up a weight lifting test (‘biceps curls’) in the motion lab, where we measure the muscle activation via electromyography (EMG). The via muscles actuated simulation model produces human like trajectories for different types of OC cost functions, whereas the underlying muscle actuations strongly differ from each other. Our first results indicate that a muscle synergy actuation is more robust concerning the variation of activation signals and that a specific mix of cost functions preserves the resulting motion behavior while producing more human like actuation signals.

In this contribution, we focus on a muscle actuated human arm model [1] and discuss the applicability of Reinforcement Learning (RL) [2] in order to control it. The content is divided into five sections. We start with the introduction of the human arm model and continue with the optimization method the authors of the model applied. Afterwards, we bring the optimization problem into a form such that RL can handle it and introduce the RL approach we are planning to apply. Before we close with the conclusion, we have a look at the results of the techniques in the numerics section.

We solve optimal control problems to perform predictive human grasping simulation for a two‐finger rigid multibody model. The quality of the grasp is strongly influenced by the choice of the objective function. We investigate the quality of the grasp using objectives based on grasp matrix and the hand Jacobian. We compare the performance of optimal control grasping simulations by minimising objectives based on these grasp quality measures for a lateral grasp activity.

Grasping is a complex human activity performed with readiness through a complicated mechanical system as an end effector, i.e. the human hand. Here, we apply a direct transcription method of discrete mechanics and optimal control with constraints (DMOCC) to reproduce human-level grasping of an object with a three-dimensional model of the hand, actuated through joint control torques. The equations of motions describing the hand dynamics are derived from a discrete variational principle based on a discrete action functional, which gives the time integrator structure-preserving properties. The grasping action is achieved through a series of constraints, which generate a hybrid dynamical system with a given switching sequence and unknown switching times. To determine a favourable trajectory for grasping action, we solve an optimal control problem (ocp) with an objective involving either the contact polygon centroid or the control torques subject to discrete Euler-Lagrange equations, boundary conditions and path constraints.

ABSTRACT — Modelling and controlling a digital human model (DHM) is a challenging task, and the scope of ergonomic evaluation adds some additio nal requirements to the generated motions. In previous publications, we introduced a multibody sy stem dynamics approach for DHM modelling with an optimal control (OC) framework for motion g eneration that uses different actuation modes (AM). Human bones are modeled as rigid bodies and c onnected via joints, as actuators joint torques (AM-T) or simplified hill type muscles are implemented. The latter can be controlled directly (AM-M) or by using muscle synergies as con trol parameters (AM-S). In this paper, we investigate the characteristics of human reaching m otions measured in the motion lab at a “basic reaching test”. We then simulate the reaching motio ns under similar specifications as done in the experimental setup, and compare the influence of th e different actuation modes to the measured trajectories and velocity profiles.

In this paper, an approach for digital human modell ing and an appropriate simulation environment is pr esented. The human body or parts of it are modeled as a mult ibody system with Hill-type muscle models as actuat ors, and human like motions are created with an optimal cont rol (OC) framework. The focus is on inner (muscle) loads for ergonomic assessment and human like motion gene ration. A basic reaching test is set up in a motion lab where muscle activation signals via EMG and upper b ody trajectories are measured with a motion capture system when performing a multitude of different rea ching tasks. The measured data is used for validati on of the simulation results and additionally muscle synergie s are extracted from the EMG signals. These synergi es can be used as control parameters in the musculoskeletal m odel, whereby the number of actuators is reduced. T his leads to computational speedup, reduction of anatomical r edundancy and captures human muscle activation prof iles.