Julia Mergheim

Bio: Julia Mergheim is an academic researcher from University of Erlangen-Nuremberg. The author has contributed to research in topics: Finite element method & Homogenization (chemistry). The author has an hindex of 19, co-authored 80 publications receiving 1296 citations. Previous affiliations of Julia Mergheim include Kaiserslautern University of Technology.

A finite element method for the computational modelling of cohesive cracks

Abstract: The present contribution is concerned with the computational modelling of cohesive cracks in quasi-brittle materials, whereby the discontinuity is not limited to interelement boundaries, but is allowed to propagate freely through the elements. In the elements, which are intersected by the discontinuity, additional displacement degrees of freedom are introduced at the existing nodes. Therefore, two independent copies of the standard basis functions are used. One set is put to zero on one side of the discontinuity, while it takes its usual values on the opposite side, and vice versa for the other set. To model inelastic material behaviour, a discrete damage-type constitutive model is applied, formulated in terms of displacements and tractions at the surface. Some details on the numerical implementation are given, concerning the failure criterion, the determination of the direction of the discontinuity and the integration scheme. Finally, numerical examples show the performance of the method.

A hybrid discontinuous Galerkin/interface method for the computational modelling of failure

Abstract: The present contribution is concerned with the computational modelling of failure along well-defined surfaces, which occur for example in the case of light-weight composite materials. A hybrid method will be introduced which makes use of the discontinuous Galerkin method in combination with a finite element interface approach. As a natural choice interface elements are introduced along the known failure surface. The discontinuous Galerkin method is applied in the pre-failure regime to avoid the unphysical use of penalty terms and instead to enforce the continuity of the solution along the interface weakly. Once a particular failure criterion is fulfilled, the behaviour of the interface is determined constitutively, depending on the displacement jump. The applicability of the proposed method is illustrated by means of two computational model problems. Copyright © 2004 John Wiley & Sons, Ltd.

Isogeometric analysis of 2D gradient elasticity

Abstract: In the present contribution the concept of isogeometric analysis is extended towards the numerical solution of the problem of gradient elasticity in two dimensions. In gradient elasticity the strain energy becomes a function of the strain and its derivative. This assumption results in a governing differential equation which contains fourth order derivatives of the displacements. The numerical solution of this equation with a displacement-based finite element method requires the use of C 1-continuous elements, which are mostly limited to two dimensions and simple geometries. This motivates the implementation of the concept of isogeometric analysis for gradient elasticity. This NURBS based interpolation scheme naturally includes C 1 and higher order continuity of the approximation of the displacements and the geometry. The numerical approach is implemented for two-dimensional problems of linear gradient elasticity and its convergence behavior is studied.

Macroscopic simulation and experimental measurement of melt pool characteristics in selective electron beam melting of Ti-6Al-4V

Abstract: Selective electron beam melting of Ti-6Al-4V is a promising additive manufacturing process to produce complex parts layer-by-layer additively. The quality and dimensional accuracy of the produced parts depend on various process parameters and their interactions. In the present contribution, the lifetime, width and depth of the pools of molten powder material are analyzed for different beam powers, scan speeds and line energies in experiments and simulations. In the experiments, thin-walled structures are built with an ARCAM AB A2 selective electron beam melting machine and for the simulations a thermal finite element simulation tool is used, which is developed by the authors to simulate the temperature distribution in the selective electron beam melting process. The experimental and numerical results are compared and a good agreement is observed. The lifetime of the melt pool increases linearly with the line energy, whereby the melt pool dimensions show a nonlinear relation with the line energy.

Modelling, simulation and experimental validation of heat transfer in selective laser melting of the polymeric material PA12

Abstract: One of the most promising additive manufacturing techniques is selective laser melting of semi-crystalline thermoplastic powders. In this process the powder is fused in defined, locally-restricted points in the current powder layer by the energy input of a laser beam and, thereby, bonded to the already fused material of previous layers. In this way geometrically complex parts are constructed layer-by-layer. The accuracy of the process and the properties of the resulting parts depend on numerous process parameters and their interactions. To improve the process strategy and to reduce, e.g. eigenstresses and warpage a thorough understanding of the influence of various process parameters is required. In the present contribution one step in this direction is done by analysing the laser energy input into a powder bulk for different process parameters by comparing temperature distributions and the size of melting pools. Experiments with single-line specimens are conducted, analysed and compared to numerical results from finite element simulations of the highly nonlinear thermal problem.

Additive manufacturing of metallic components – Process, structure and properties

Abstract: Since its inception, significant progress has been made in understanding additive manufacturing (AM) processes and the structure and properties of the fabricated metallic components. Because the field is rapidly evolving, a periodic critical assessment of our understanding is useful and this paper seeks to address this need. It covers the emerging research on AM of metallic materials and provides a comprehensive overview of the physical processes and the underlying science of metallurgical structure and properties of the deposited parts. The uniqueness of this review includes substantive discussions on refractory alloys, precious metals and compositionally graded alloys, a succinct comparison of AM with welding and a critical examination of the printability of various engineering alloys based on experiments and theory. An assessment of the status of the field, the gaps in the scientific understanding and the research needs for the expansion of AM of metallic components are provided.

The extended/generalized finite element method: An overview of the method and its applications

Abstract: An overview of the extended/generalized finite element method (GEFM/XFEM) with emphasis on methodological issues is presented. This method enables the accurate approximation of solutions that involve jumps, kinks, singularities, and other locally non-smooth features within elements. This is achieved by enriching the polynomial approximation space of the classical finite element method. The GEFM/XFEM has shown its potential in a variety of applications that involve non-smooth solutions near interfaces: Among them are the simulation of cracks, shear bands, dislocations, solidification, and multi-field problems. Copyright © 2010 John Wiley & Sons, Ltd.

3D printing with polymers: Challenges among expanding options and opportunities.

Abstract: Objectives Additive manufacturing, which is more colloquially referred to as 3D printing, is quickly approaching mainstream adoption as a highly flexible processing technique that can be applied to plastic, metal, ceramic, concrete and other building materials. However, taking advantage of the tremendous versatility associated with in situ photopolymerization as well as the ability to select from a variety of preformed processible polymers, 3D printing predominantly targets the production of polymeric parts and models. The goal of this review is to connect the various additive manufacturing techniques with the monomeric and polymeric materials they use while highlighting emerging material-based developments. Methods Modern additive manufacturing technology was introduced approximately three decades ago but this review compiles recent peer-reviewed literature reports to demonstrate the evolution underway with respect to the various building techniques that differ significantly in approach as well as the new variations in polymer-based materials being employed. Results Recent growth of 3D printing has been dramatic and the ability of the various platform technologies to expand from rapid production prototypic models to the greater volume of readily customizable production of working parts is critical for continued high growth rates. This transition to working part production is highly dependent on adapting materials that deliver not only the requisite design accuracy but also the physical and mechanical properties necessary for the application. Significance With the weighty distinction of being called the next industrial revolution, 3D printing technologies is already altering many industrial and academic operations including changing models for future healthcare delivery in medicine and dentistry.

A method for dynamic crack and shear band propagation with phantom nodes

Abstract: A new method for modelling of arbitrary dynamic crack and shear band propagation is presented. We show that by a rearrangement of the extended finite element basis and the nodal degrees of freedom, the discontinuity can be described by superposed elements and phantom nodes. Cracks are treated by adding phantom nodes and superposing elements on the original mesh. Shear bands are treated by adding phantom degrees of freedom. The proposed method simplifies the treatment of element-by-element crack and shear band propagation in explicit methods. A quadrature method for 4-node quadrilaterals is proposed based on a single quadrature point and hourglass control. The proposed method provides consistent history variables because it does not use a subdomain integration scheme for the discontinuous integrand. Numerical examples for dynamic crack and shear band propagation are provided to demonstrate the effectiveness and robustness of the proposed method. Copyright © 2006 John Wiley & Sons, Ltd.