TY - JOUR A1 - Colombo, Daniele A1 - Drira, Slah A1 - Frotscher, Ralf A1 - Staat, Manfred T1 - An element-based formulation for ES-FEM and FS-FEM models for implementation in standard solid mechanics finite element codes for 2D and 3D static analysis JF - International Journal for Numerical Methods in Engineering N2 - Edge-based and face-based smoothed finite element methods (ES-FEM and FS-FEM, respectively) are modified versions of the finite element method allowing to achieve more accurate results and to reduce sensitivity to mesh distortion, at least for linear elements. These properties make the two methods very attractive. However, their implementation in a standard finite element code is nontrivial because it requires heavy and extensive modifications to the code architecture. In this article, we present an element-based formulation of ES-FEM and FS-FEM methods allowing to implement the two methods in a standard finite element code with no modifications to its architecture. Moreover, the element-based formulation permits to easily manage any type of element, especially in 3D models where, to the best of the authors' knowledge, only tetrahedral elements are used in FS-FEM applications found in the literature. Shape functions for non-simplex 3D elements are proposed in order to apply FS-FEM to any standard finite element. KW - distorted element KW - ES-FEM KW - FS-FEM KW - non-simplex S-FEM elements KW - S-FEM Y1 - 2022 U6 - http://dx.doi.org/10.1002/nme.7126 SN - 1097-0207 VL - 124 IS - 2 SP - 402 EP - 433 PB - Wiley CY - Chichester ER - TY - JOUR A1 - Staat, Manfred T1 - An extension strain type Mohr–Coulomb criterion JF - Rock mechanics and rock engineering N2 - Extension fractures are typical for the deformation under low or no confining pressure. They can be explained by a phenomenological extension strain failure criterion. In the past, a simple empirical criterion for fracture initiation in brittle rock has been developed. In this article, it is shown that the simple extension strain criterion makes unrealistic strength predictions in biaxial compression and tension. To overcome this major limitation, a new extension strain criterion is proposed by adding a weighted principal shear component to the simple criterion. The shear weight is chosen, such that the enriched extension strain criterion represents the same failure surface as the Mohr–Coulomb (MC) criterion. Thus, the MC criterion has been derived as an extension strain criterion predicting extension failure modes, which are unexpected in the classical understanding of the failure of cohesive-frictional materials. In progressive damage of rock, the most likely fracture direction is orthogonal to the maximum extension strain leading to dilatancy. The enriched extension strain criterion is proposed as a threshold surface for crack initiation CI and crack damage CD and as a failure surface at peak stress CP. Different from compressive loading, tensile loading requires only a limited number of critical cracks to cause failure. Therefore, for tensile stresses, the failure criteria must be modified somehow, possibly by a cut-off corresponding to the CI stress. Examples show that the enriched extension strain criterion predicts much lower volumes of damaged rock mass compared to the simple extension strain criterion. Y1 - 2021 U6 - http://dx.doi.org/10.1007/s00603-021-02608-7 SN - 1434-453X N1 - Corresponding author: Manfred Staat VL - 54 IS - 12 SP - 6207 EP - 6233 PB - Springer Nature CY - Cham ER - TY - JOUR A1 - Abel, Alexander A1 - Kahmann, Stephanie Lucina A1 - Mellon, Stephen A1 - Staat, Manfred A1 - Jung, Alexander T1 - An open-source tool for the validation of finite element models using three-dimensional full-field measurements JF - Medical Engineering & Physics N2 - Three-dimensional (3D) full-field measurements provide a comprehensive and accurate validation of finite element (FE) models. For the validation, the result of the model and measurements are compared based on two respective point-sets and this requires the point-sets to be registered in one coordinate system. Point-set registration is a non-convex optimization problem that has widely been solved by the ordinary iterative closest point algorithm. However, this approach necessitates a good initialization without which it easily returns a local optimum, i.e. an erroneous registration. The globally optimal iterative closest point (Go-ICP) algorithm has overcome this drawback and forms the basis for the presented open-source tool that can be used for the validation of FE models using 3D full-field measurements. The capability of the tool is demonstrated using an application example from the field of biomechanics. Methodological problems that arise in real-world data and the respective implemented solution approaches are discussed. Y1 - 2020 U6 - http://dx.doi.org/10.1016/j.medengphy.2019.10.015 SN - 1350-4533 VL - 77 SP - 125 EP - 129 PB - Elsevier CY - Amsterdam ER - TY - JOUR A1 - Pham, Phu Tinh A1 - Staat, Manfred T1 - An Upper Bound Algorithm for Limit and Shakedown Analysis of Bounded Linearly Kinematic Hardening Structures JF - Limit State of Materials and Structures : Direct Methods 2. Saxcé, Géry de (Hrsg.) Y1 - 2013 SN - 978-94-007-5424-9 SP - 71 EP - 87 PB - Springer CY - Dordrecht ER - TY - JOUR A1 - Vu, Duc Khoi A1 - Staat, Manfred A1 - Tran, Ich Thinh T1 - Analysis of pressure equipment by application of the primal-dual theory of shakedown JF - Communications in Numerical Methods in Engineering. 23 (2007), H. 3 Y1 - 2007 SN - 1069-8299 SP - 213 EP - 225 ER - TY - JOUR A1 - Levers, A. A1 - Staat, Manfred A1 - Laack, Walter van T1 - Analysis of the long-term effect of the MBST® nuclear magnetic resonance therapy on gonarthrosis JF - Orthopedic Practice Y1 - 2016 VL - 47 IS - 11 SP - 521 EP - 528 ER - TY - CHAP A1 - Frotscher, Ralf A1 - Raatschen, Hans-Jürgen A1 - Staat, Manfred ED - Eberhardsteiner, J. T1 - Application of an edge-based smoothed finite element method on geometrically non-linear plates of non-linear material T2 - Proceedings European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2012) Y1 - 2012 N1 - 6th European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2012) Vienna, Austria, September 10-14, 2012 ER - TY - JOUR A1 - Staat, Manfred T1 - Basis Reduction for the Shakedown Problem for Bounded Kinematic Hardening Material N2 - Limit and shakedown analysis are effective methods for assessing the load carrying capacity of a given structure. The elasto–plastic behavior of the structure subjected to loads varying in a given load domain is characterized by the shakedown load factor, defined as the maximum factor which satisfies the sufficient conditions stated in the corresponding static shakedown theorem. The finite element dicretization of the problem may lead to very large convex optimization. For the effective solution a basis reduction method has been developed that makes use of the special problem structure for perfectly plastic material. The paper proposes a modified basis reduction method for direct application to the two-surface plasticity model of bounded kinematic hardening material. The considered numerical examples show an enlargement of the load carrying capacity due to bounded hardening. KW - Finite-Elemente-Methode KW - Einspielen KW - Basis Reduktion KW - konvexe Optimierung KW - FEM KW - Druckgeräte KW - Basis reduction KW - Convex optimization KW - FEM KW - Shakedown analysis Y1 - 2000 ER - TY - CHAP A1 - Staat, Manfred A1 - Heitzer, M. T1 - Basis reduction technique for limit and shakedown problems T2 - Numerical Methods for Limit and Shakedown Analysis. Deterministic and Probabilistic Approach. NIC Series Vol. 15 / Ed. by Staat, M.; Heitzer, M. Y1 - 2003 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0001-2018112115 SN - 3-00-010001-6 SP - 1 EP - 55 PB - John von Neumann Institute for Computing (NIC) CY - Jülich ER - TY - JOUR A1 - Horbach, Andreas A1 - Staat, Manfred A1 - Perez-Viana, Daniel A1 - Simmen, Hans-Peter A1 - Neuhaus, Valentin A1 - Pape, Hans-Christoph A1 - Prescher, Andreas A1 - Ciritsis, Bernhard T1 - Biomechanical in vitro examination of a standardized low-volume tubular femoroplasty JF - Clinical Biomechanics N2 - Background Osteoporosis is associated with the risk of fractures near the hip. Age and comorbidities increase the perioperative risk. Due to the ageing population, fracture of the proximal femur also proves to be a socio-economic problem. Preventive surgical measures have hardly been used so far. Methods 10 pairs of human femora from fresh cadavers were divided into control and low-volume femoroplasty groups and subjected to a Hayes fall-loading fracture test. The results of the respective localization and classification of the fracture site, the Singh index determined by computed tomography (CT) examination and the parameters in terms of fracture force, work to fracture and stiffness were evaluated statistically and with the finite element method. In addition, a finite element parametric study with different position angles and variants of the tubular geometry of the femoroplasty was performed. Findings Compared to the control group, the work to fracture could be increased by 33.2%. The fracture force increased by 19.9%. The used technique and instrumentation proved to be standardized and reproducible with an average poly(methyl methacrylate) volume of 10.5 ml. The parametric study showed the best results for the selected angle and geometry. Interpretation The cadaver studies demonstrated the biomechanical efficacy of the low-volume tubular femoroplasty. The numerical calculations confirmed the optimal choice of positioning as well as the inner and outer diameter of the tube in this setting. The standardized minimally invasive technique with the instruments developed for it could be used in further comparative studies to confirm the measured biomechanical results. Y1 - 2020 U6 - http://dx.doi.org/10.1016/j.clinbiomech.2020.105104 VL - 80 IS - Art. 105104 PB - Elsevier CY - Amsterdam ER -