Accretion and ablation in deformable solids with an Eulerian description: examples using the method of characteristics

Accretion and ablation, i.e., the addition and removal of mass at the surface, are important in a wide range of physical processes, including solidification, growth of biological tissues, environmental processes, and additive manufacturing. The description of accretion requires the addition of new continuum particles to the body, and is therefore challenging for standard continuum formulations for solids that require a reference configuration. Recent work has proposed an Eulerian approach to this problem, enabling side-stepping of the issue of constructing the reference configuration. However, this raises the complementary challenge of determining the stress response of the solid, which typically requires the deformation gradient that is not immediately available in the Eulerian formulation. To resolve this, the approach introduced the elastic deformation as an additional kinematic descriptor of the added material, and its evolution has been shown to be governed by a transport equation. In this work, the method of characteristics is applied to solve concrete simplified problems motivated by biomechanics and manufacturing. Specifically, (1) for a problem with both ablation and accretion in a fixed domain and (2) for a problem with a time-varying domain, the closed-form solution is obtained in the Eulerian framework using the method of characteristics without explicit construction of the reference configuration.

Prediction of the Onset of Failure in Elastomeric Solids with Weld Lines being Represented as Localized Regions of Lower Density

We study the initiation of damage in a polymeric body in which there is a line defect due to the formation of a “weld line” that occurs when two polymer streams join together and then solidify. We show that damage initiates in the region of weakness, namely the “weld line” based on a criterion for damage that was developed earlier in [1]. We also show that if there are other stress concentrators also additionally present, such as a hole, then there is a competition between the stresses induced due to the weakness and the stress as a consequence of the stress concentrator (in this instance a hole). This study adds more credence to the criterion for the initiation of damage that is based completely on knowledge of information at the current configuration of the body, that is, the criterion for damage is not based on the value of quantities that also need information based on a reference configuration such as the stress or strain.

Reference Configurations Versus Optimal Rotations: A Derivation of Linear Elasticity from Finite Elasticity for all Traction Forces

We rigorously derive linear elasticity as a low energy limit of pure traction nonlinear elasticity. Unlike previous results, we do not impose any restrictive assumptions on the forces, and obtain a full $$\Gamma $$ Γ -convergence result. The analysis relies on identifying the correct reference configuration to linearize about, and studying its relation to the rotations preferred by the forces (optimal rotations). The $$\Gamma $$ Γ -limit is the standard linear elasticity model, plus a term that penalizes for fluctuations of the reference configurations from the optimal rotations. However, on minimizers this additional term is zero and the limit energy reduces to standard linear elasticity.

HLFC-optimized retrofit aircraft design of a medium-range reference configuration within the AVACON project

This paper presents an approach for the design of a retrofit aircraft with integrated, optimized hybrid laminar flow control (HLFC). The basis for this research is a medium-range reference configuration derived within the German LuFo project “Advanced Aircraft Concepts” (AVACON). For the aerodynamics, an in-house-developed process chain for flow analysis is used, which requires airfoil shapes at specific sections of a known wing geometry. To improve the accuracy, pressure distributions from the 2D flow solver MSES are first aligned to high-fidelity 3D results from DLR’s TAU code for extracted airfoils. This is done by varying parameters of the transformation methods used. Subsequently, the required suction distributions are optimized based on pre-defined criteria; these include not only the aerodynamic effects but also the needed mass flows. After optimizing the HLFC system architecture concerning mass and power offtakes, a retrofit aircraft is designed with the in-house “Multidisciplinary Integrated Aircraft Design and Optimization” (MICADO) environment. Compared to the turbulent baseline, the promising potential of the HLFC technology is demonstrated. In addition, the actual benefit of the optimization approach is evaluated in the context of overall preliminary aircraft design. This is done by redesigning the aircraft with other suction distributions and HLFC system architectures. Although it is shown that the approach leads to an overall optimum, the optimization benefit remains small. This indicates the limits of the HLFC technology as a pure add-on for initially turbulent aircraft and the need for the application of new laminar wing design methods to tap the full potential of HLFC.

Numerical position optimization of an over-the-wing mounted engine installation

The Collaborative Research Center 880 is investigating different technologies and configurative variants for the purpose of short take-off and landing (STOL) capabilities, ranging from high-lift systems with Coandӑ flaps to unusual but potentially more efficient engine arrangements. The present study focuses on the reference configuration 3 (REF3). This configuration is characterized by an UHBR over-the-wing nacelle (OWN) located above the wing trailing edge. Starting from the wing/body configuration the installation effects of the OWN were investigated. A fully automatized surrogate based optimization was used to evaluate the impact of an engine position variation in vertical and horizontal direction to observe fundamental aerodynamic interactions between wing and OWN in cruise flight conditions. Due to the presence of OWN and pylon, a distinct disturbance on the wing upper surface could be observed leading to significant interference effects. Nevertheless, the overall cruise drag of REF3 could be improved by 37 drag counts or nearly 11% due to the position optimization.

Convergence Characteristics of Geometrically Accurate Spatial Finite Elements

The convergence characteristics of three geometrically accurate spatial finite elements (FEs) are examined in this study using an eigenvalue analysis. The spatial beam, plate, and solid elements considered in this investigation are suited for both structural and multibody system (MBS) applications. These spatial elements are based on geometry derived from the kinematic description of the absolute nodal coordinate formulation (ANCF). In order to allow for an accurate reference-configuration geometry description, the element shape functions are formulated using constant geometry coefficients defined using the position-vector gradients in the reference configuration. The change in the position-vector gradients is used to define a velocity transformation matrix that leads to constant element inertia and stiffness matrices in the case of infinitesimal rotations. In contrast to conventional structural finite elements, the elements considered in this study can be used to describe the initial geometry with the same degree of accuracy as B-spline and nonuniform rational B-spline (NURBS) representations, widely used in the computer-aided design (CAD). An eigenvalue analysis is performed to evaluate the element convergence characteristics in the case of different geometries, including straight, tapered, and curved configurations. The frequencies obtained are compared with those obtained using a commercial FE software and analytical solutions. The stiffness matrix is obtained using both the general continuum mechanics (GCM) approach and the newly proposed strain split method (SSM) in order to investigate its effectiveness as a locking alleviation technique.

Impact of a Composite Trombe Wall Incorporating Phase Change Materials on the Thermal Behavior of an Individual House with Low Energy Consumption

As the heating demands of buildings drop considerably, the use of solar walls makes increasing sense. One of the obstacles to the development of such walls is their need for on-site implementation by specialized companies. On the other hand, a storage wall is generally composed of heavy materials with high inertia, which prevents prefabrication of the solar component. To avoid this problem and allow for solar walls to be prefabricated in the factory, a novel approach to replacing this heavy wall with a lighter storage wall incorporating phase change materials (PCM) has been proposed. This paper aims to demonstrate the impact of PCM on the thermal energy performance once they have been integrated into the storage wall of the composite Trombe wall. Addressed herein will be the heat transfer exchange inside a house located in the northern part of France, where a composite Trombe wall has been fitted without PCM. Three configurations will be investigated—(1) the model house without the solar Trombe wall, defined as the reference configuration; (2) the model house integrating the concrete solar Trombe wall; and (3) the model house integrating the PCM solar Trombe wall. Two setpoint temperatures will be introduced—(a) a constant setpoint of 20 °C, and (b) a variable setpoint of 19 °C (14 h from 7:00 a.m. to 9:00 p.m.) and 16 °C (10 h from 9:00 p.m. to 7:00 a.m.). Furthermore, three different climate conditions will be adopted to run simulations—Paris-Orly, Lyon, and Nice. Dymola/Modelica, a dynamic thermal simulation tool, will be utilized to simulate the thermal performance of these defined configurations. The results obtained, regarding a solar Trombe wall installation that applies two distinct storage walls exposed to the weather of Paris, showed similar minimizations of the one-year energy heating demand inside the bedroom, equal to roughly 20% (i.e., 20.45% of concrete storage wall and 19.90% of PCM storage wall) compared to the reference configuration (i.e., the house with no solar Trombe wall). Based on the imposed setpoint temperature by means of night and day reductions, the resulting heating energy demand in the bedroom, through application of the two storage walls (concrete and PCM) and three different climatic regions could be minimized by 20.34% in Paris, 20.20% in Lyon, and 68.10% in Nice (for the concrete storage wall) vs. the reference configuration; and by 18.79% in Paris, 19.56% in Lyon, and 55.15% in Nice (for the PCM storage wall) vs. the reference configuration.