Kerstin Weinberg

University of Siegen · Department of Mechanical Engineering

Lattice structures are increasingly used in various fields of application due to the steady growth of additive manufacturing technology. Depending on the type of lattice, these structures are more or less suitable for energy absorption due to the deformation of diagonal struts. The energy absorption properties depend significantly on the type of th...

Lattice-like cellular materials, with their unique combination of lightweight, high strength, and good deformability, are promising for engineering applications. This paper investigates the energy-absorbing properties of four truss-lattice structures with two defined volume fractions of material in static compression experiments. The mass-specific...

Rupture discs, also known as bursting discs, are indispensable components in fluid-operated systems providing effective protection against hazardous over-pressure or partial vacuum. They belong to a special class of safety devices and are found in a variety of technical applications including pressure vessels, piping systems, reactors and boilers....

Peridynamics is a nonlocal continuum mechanics formulation well suited for simulating dynamic fracture phenomena. Various peridynamic material formulations have been developed in recent years. These models have some differences, particularly regarding the correct handling of elastic deformation. This study investigates the elastic wave propagation...

Peridynamics describes the material in a non-local form and is very suited for the simulation of dynamic fracture. However, one significant effect regarding dynamic fracture is the correct handling of elastic deformation, like the pressure and tension waves inside a body, due to dynamic boundary conditions like an impact or impulse. Many peridynami...

This talk will present the latest developments in Peridynamics.jl, a Julia package designed for dynamic fracture simulations. We rewrote the package from scratch to enhance multithreading and enable MPI support, redesigned the API to catch errors earlier, and implemented new material models to match the state-of-the-art peridynamics research. The t...

Soft hydrogels are widely used to simulate biological tissue. When subjected to an impact, the gels’ typical mechanical response is associated with the cavitation of bubbles. Because of the complexity of the phenomenon and the difficulties related to experimental measurements, cavitation in soft gels is still a subject of investigation. This contri...

When a vehicle leaves the road, crash barriers stop it and prevent significant damage to the vehicle, its environment, and the occupants. Typically, such protection systems are made of simple steel, but fiber-reinforced composites can efficiently absorb and dissipate the impact energy at high-risk locations. In order to design such protective syste...

This paper presents a model‐free data‐driven strategy for linear and non‐linear finite element computations of open‐cell foam. Employing sets of material data, the data‐driven problem is formulated as the minimization of a distance function subjected to the physical constraints from the kinematics and the balance laws of the mechanical problem. The...

To characterize generally valid hyperelastic material parameters, tensile tests at different deformation states are essential. This necessity arises from the hyperelasticity theory for incompressible materials, which is based on the first and second invariants of the right Cauchy–Green tensor. These invariants describe the elongation and surface ch...

Extrusion-based 3D printing has become one of the most common additive manufacturing methods and is widely used in engineering. This contribution presents the results of flexural creep experiments on 3D printed PLA specimens, focusing on changes in creep behavior due to physical aging. It is shown experimentally that the creep curves obtained on ag...

In this work, two non-local approaches to dynamic fracture are investigated: a novel peridynamic formulation and a variational phase-field approach. The chosen continuum-kinematics-based peridynamic model extends the current peridynamic models by introducing surface and volume-based interactions. The phase-field fracture approach optimizes the body...

We resort to game theory in order to formulate Data-Driven methods for solid mechanics in which stress and strain players pursue different objectives. The objective of the stress player is to minimize the discrepancy to a material data set, whereas the objective of the strain player is to ensure the admissibility of the mechanical state, in the sen...

Additive manufacturing of pure copper (Cu) via laser-powder bed fusion (L-PBF) is challenging due to the low energy absorptivity under infra-red laser. As a result, 3-dimensional architectures, known for excellent load-bearing and energy absorption capabilities, have not been fabricated in pure Cu, so far. This study, for the first time, Cu lattice...

This paper aims to investigate multiple large-strain topology-optimized structures, by interpreting their overlay as a probability density function. Such a strategy is suited to finding an optimum design of silicon electrodes subject to a random contact. Using this method, and prescribing a zero net-force constraint on the global system, the optimu...

In this contribution we present analytical results on a model for dynamic fracture in viscoelastic materials at small strains that have been obtained in full depth in [1]. In the model, the sharp crack interface is regularized with a phase‐field approximation, and for the phase‐field variable a viscous evolution with a quadratic dissipation potenti...

Lattice structures are attractive in additive manufacturing technology as they are small, lightweight, and especially scaleable. Closely spaced diagonal elements absorb energy through elastic and plastic deformation within a lattice, but the performance depends on many factors like design, material properties, printing process, post‐treatment, etc....

Polyurethane (PUR) foams are used in various industrial applications, including vibration damping and noise reduction. Because the effective mechanical properties are needed for the engineering design process, this work presents a method to measure the dynamic Poisson's ratio for the typical range of sound frequencies. A hydraulic pulse testing mac...

The notion of dynamic fracture with continuum‐kinematics‐based peridynamics is presented in this work. A geometrically precise version of peridynamics called continuum‐kinematics‐based peridynamics adds surface‐ or volume‐based interactions to the traditional peridynamic bonds, accurately capturing the finite deformation kinematics. The point famil...

Extrusion-based 3D printing has become one of the most common additive manufacturing methods and is widely used in engineering. This contribution presents the results of flexural creep experiments on 3D printed PLA specimens, focusing on changes in creep behavior due to physical aging. It is shown experimentally that the creep curves obtained on ag...

The transient dynamic behavior of soft gels under a sudden impact is often associated with the cavitation of bubbles. This phenomenon has gained rising attention, essentially due to the vast emergence of different biomedical applications and the gels’ use to replicate soft body parts. In this contribution, a variational approach to cavitation is pr...

The phase field approach has proved to be efficient and has received ample attention amongst the available techniques to model fracture. However, high computational cost still imposes substantial difficulties in the phase-field simulation of fractures. This contribution is based on a recently proposed variational approach for spatial adaptivity in...

Lattice structures composed of periodic solid frames and pores can be utilized in energy absorption applications due to their high specific strength and large deformation. However, these structures typically suffer from post-yield softenings originating from the limited plasticity of available material choices. This study aims to resolve such an is...

This paper presents a model-free data-driven strategy for linear and non-linear finite element computations of open-cell foam. Employing sets of material data, the data-driven problem is formulated as the minimization of a distance function subjected to the physical constraints from the kinematics and the balance laws of the mechanical problem. The...

This contribution presents a concept to dynamic fracture with continuum-kinematics-based peridynamics. Continuum-kinematics-based peridynamics is a geometrically exact formulation of peridynamics, which adds surface- or volume-based interactions to the classical peridynamic bonds, thus capturing the finite deformation kinematics correctly. The surf...

In recent years, soft gels, including agarose, have been widely used to mimic soft biological tissues. Hence, such materials’ transient dynamic response has become increasingly relevant. When gels are subjected to an impact, the typical mechanical response is associated with the cavitation of bubbles. This study presents experimental and numerical...

This contribution presents a concept to dynamic fracture with continuum-kinematics-based peridynamics. Continuum-kinematics-based peridynamics is a geometrically exact formulation of peridynamics, which adds surface- or volumetric-based interactions to the classical peridynamic bonds, thus capturing the finite deformation kinematics correctly. The...

Foam is a cellular material whose mechanical properties are strongly determined by its complex microstructure. To study the microstructure, at first a foam characterization based on μ$$ \upmu $$CT image processing is required. Here we present an image segmentation procedure and determine the foam's characteristics using the lattice cell‐based conce...

In multi-field problems, the free energy contributions of different fields are coupled. For the kinematic of deformation, explicit assumptions on the independent fields are necessary, and the intermediate configurations of composed deformations are not uniquely determined. Here, a thermodynamic free energy potential with two primary variables is an...

Experimental and numerical investigations of brittle fracture are of great relevance for many engineering materials. However, numerical methods derived from classical continuum mechanics often encounter difficulties for discontinuities and cracks for unknown paths. Therefore, we employ the theory of peridynamics to study brittle fracture in ultra-h...

Phase-field models of fracture introduce smeared cracks of width commensurate with a regularisation length parameter ε and obeying a minimum energy principle. Mesh adaptivity naturally suggests itself as a means of supplying spatial resolution where needed while simultaneously keeping the computational size of the model as small as possible. Here,...

Phase-field models have been proven to be reliable methods for the simulation of complex crack patterns and crack propagation. In this contribution we investigate the phase-field model in linear and finite elasticity and summarize the influences of model specific parameters. Furthermore, externally driven fracture processes, in particular in the co...

In this study, a peridynamic approach to pneumatic fracture is presented. The examined peridynamic model relies on the classical state-based formulation, where a critical bond-strain damage is assumed for a linear solid material. A penny-shaped initial crack is subjected to internal pressure, and it is found that that the crack tip opening displace...

Phase-field models of fracture allow the prediction of crack propagation and crack patterns. In this contribution, externally driven fracture processes in linear and finite elasticity are investigated. Different approaches to consider pneumatic pressure and materials with non-isotropic crack resistance are studied, combined, and examined in detail....

Phase-field fracture simulations have been established to simulate crack propagation in solid structures. The method employs a variational framework which has been proven to converge to Griffith' classical model for brittle fracture. Here we investigate the predictiveness of phase-field fracture through a four-point bending test in a mixed mode con...

The paper deals with experiments on 3D printed lattices in a Split Hopkinson Pressure Bar. An energy-based evaluation of the measured wave signals enables us to compare the damping properties of two different copper lattice structures.

This contribution explores the ability to conduct polymorphic uncertainty computations within the data-driven finite element framework. The constitutive equation is replaced by data sets that determine the material behavior, and a fuzzy load is used for the polymorphic approach. To conduct many simulations with the discretized variables and to incr...

We present a new numerical approach for wave induced dynamic fracture. The method is based on a discontinuous Galerkin approximation of the first-order hyperbolic system for elastic waves and a phase-field approximation of brittle fracture driven by the maximum tension. The algorithm is staggered in time and combines an implicit midpoint rule for t...

The data-driven finite element method proposed by Kirchdoerfer and Ortiz [1] allows to elude the material modeling step. Instead, a previously obtained data set is used directly in the algorithm to describe the material behavior under deformation. Usually, this data set is expected to be gained experimentally. The following empirical treatment is s...

Phase-field models of fracture introduce smeared cracks of width commensurate with a regularisation length parameter $\epsilon$ and obeying a minimum energy principle. Mesh adaptivity naturally suggests itself as a means of supplying spatial resolution were needed while simultaneously keeping the computational size of the model as small as possible...

The usage of resin-based materials for 3D printing applications has been growing over the past decades. In this study, two types of resins, namely a MMA-based resin and an ABS-based tough resin, are subjected to compression tests on a split Hopkinson pressure bar to deduce their dynamic properties under high strain rate loading. Two Hopkinson bar s...

We analyze the operation of melting probes as a Stefan problem for the liquid/solid interface surrounding the probe. We assume that the liquid layer is thin and, therefore, amenable to analysis by the lubrication theory. The resulting Stefan problem is solvable in the closed form. The solution determines the dependence of the penetration speed on t...

Foamed rubber with a mixed cellular microstructure is a compressible material used for various sealing applications in the automotive industry. For technical optimization, a sufficiently precise material model is required. Here a material description for the porous elastic and viscoelastic response of low density foamed rubber is proposed and adapt...

We present a new numerical approach for wave induced dynamic fracture. The method is based on a discontinuous Galerkin approximation of the first-order hyperbolic system for elastic waves and a phase-field approximation of brittle fracture driven by the maximum tension. The algorithm is staggered in time and combines an implicit midpoint rule for t...

In the data-driven finite element analysis proposed by Kirchdoerfer and Ortiz (2016) the material data are a direct part of the optimization problem. The mechanical problem is rewritten as a minimization problem of a distance function subject to the conservation laws. For every material point of the finite element geometry nearest neighbor searches...

Fabrication of polymeric components with complex geometry has been increased in the recent years. As additive manufacturing (AM) showed its unique capabilities, it has been widely used in production of geometrically-complex parts. Although various types of bonding have been developed, utilizing adhesive joints is common in different polymeric struc...

An electrochemical–thermomechanical model for the description of charging and discharging processes in lithium electrodes is presented. Multi-physics coupling is achieved through the constitutive relations, obtained within a consistent thermodynamic framework based on the definition of the free energy density, sum of distinct contributions from dif...

We compare the accuracy, convergence rate and computational cost of eigenerosion (EE) and phase-field (PF) methods. For purposes of comparison, we specifically consider the standard test case of a center-crack panel loaded in biaxial tension and assess the convergence of the energy error as the length scale parameter and mesh size tend to zero simu...

We compare the accuracy, convergence rate and computational cost of eigenerosion (EE) and phase-field (PF) methods. For purposes of comparison, we specifically consider the standard test case of a center-crack panel loaded in biaxial tension and assess the convergence of the energy error as the length scale parameter and mesh size tend to zero simu...

The Split‐Hopkinson Pressure Bar (SHPB) is a common experimental setup to investigate the dynamic properties of materials. For soft materials the SHPB setup has to be customize using plastic bars. Because such bars show wave attenuation and dispersion, the measured wave signals have to be corrected. In this study a method of signal correction by me...

In a data‐driven finite element analysis the experimental data are directly employed as an input for computational analysis, thus evading any state of matter modeling. The essential physical principles, such as balance laws and continuity, remain unchanged, as do all the numerical schemes used in their discretization. In addition, uncertainties and...

Phase‐field models have already been proven to predict complex fracture patterns for brittle fracture at small strains. In this paper we discuss a model for phase‐field fracture at finite deformations in more detail. Among the identification of crack location and projection of crack growth the numerical stability is one of the main challenges in so...

Aim Solder joints of microelectronic devices are subjected to a wide range of loadings. They affect the microstructural evolution of the alloy. Long term investigations are commonly performed under thermally accelerated conditions, but are not available for real-life environmental conditions in literature yet. Therefore, the solder bumps of ten-yea...

Numerical techniques to simulate crack propagation can roughly be divided into sharp and diffuse interface methods. Two prominent approaches to quantitative dynamic fracture analysis are compared here. Specifically, an adaptive cohesive element technique and a phase-field fracture approach are applied to simulate Hopkinson bar experiments on the fr...

We analyze the operation of melting probes as a Stefan problem for the liquid/solid interface surrounding the probe. We assume that the liquid layer is thin and, therefore, amenable to analysis by lubrication theory. The resulting Stefan problem is solvable in closed form. The solution determines the dependence of the penetration speed on the tempe...

We analyze the operation of melting probes as a Stefan problem for the liquid/solid interface surrounding the probe. We assume that the liquid layer is thin and, therefore, amenable to analysis by lubrication theory. The resulting Stefan problem is solvable in closed form. The solution determines the dependence of the penetration speed on the tempe...

Ultra-High Performance Concrete (UHPC) is an innovative cement based material with superior strength for engineering structures. The mechanical properties of the cementitious composite depend on its exact composition and need to be determined experimentally. Whereas several standard tests for the static loading regime exist, dynamic data such as te...

The wave propagation in a group of soft resin based (3d printed) materials is investigated by using a Split Hopkinson Bar test. The principal assumptions and the role of pulse shaping, as an approach to achieve constant strain rates and dispersion reduction, is discussed. The experimental stress‐strain curves, gained by aluminium Split Hopkinson ba...

The latest battery developments focus on the design of the anode and try to ensure a safe charging of the electrical device. Here an anode is studied which is made of graphite or silicon and subjected to several physical effects like thermal expansion, electrical current conductivity, and mechanical deformation. Typical design objectives like compl...

Phase‐field fracture simulations have been established to simulate crack propagation in fracture mechanics. This contribution sets the focus on different driving forces for crack growth and on the simulation of waves propagating along the fractured interfaces. Typically, phase‐field methods for brittle fracture employ a variational framework which...

In data driven modeling the constitutive model is replaced by a data set and therefore yields a model‐free computation. In this context the data set also can be the input for noisy material data and describe material uncertainty. This contribution presents a juxtaposition of different finite element trechniques to describe material uncertainties, n...

In the classical Euler‐Bernoulli cantilever beam theory the deflection w depends on different parameters. On the one hand we have material and geometric parameters, like the Young's Modulus E, the second moment of area I and the length of the beam L. On the other hand there are different loading types like point loads F, distributed loads, or varyi...

The tensile strength of brittle and tension-sensitive materials can be determined experimentally by the Brazilian test. To complement the experimental results numerical methods are required which predict the effective properties of the material as an outcome of the calculations. Here a modified phase-field approach to fracture is presented which is...

Phase‐field approaches to fracture are gaining popularity to compute a priori unknown crack paths. In this work the sensitivity of such phase‐field approaches with respect to its model specific parameters, that is, the critical length of regularization, the degradation function and the mobility, is investigated. The susceptibility of the computed c...

The presence of voids or cavities inside a material plays an important role in several applications. Recently, their investigation has gained attention to understand the effect of such inhomogeneities on 3D‐printed structures. Such structures could be already weakened due to the procedure of additive manufacturing. Voids can be visualized by comput...

Applications of sandwich-structured composites gained increasing interest in aviation and aerospace industries as well as in modern lightweight design. In order to improve the reliability of computational models for the dimensioning of such structures, experimental data are indispensable prerequisites. In the current manuscript, the essential outco...

The phase-field approach to fracture has been proven to be a mathematically sound and easy to implement method for computing crack propagation with arbitrary crack paths. Hereby crack growth is driven by energy minimization resulting in a variational crack-driving force. The definition of this force out of a tension-related energy functional does,...

In this contribution, several case studies with data uncertainties are presented which have been performed in individual projects as part of the DFG (German Research Foundation) Priority Programme SPP 1886 “Polymorphic uncertainty modelling for the numerical design of structures.” In all case studies numerical models with uncertainties are derived...

In many applications the experimental results are not sufficient for material characterization. Nonetheless, predictive numerical simulations require to harness the available stress–strain data and to use them, e.g., as input parameters for finite element computations. In this contribution two strategies, a stochastic and a data-driven finite eleme...

In the light of today’s extensive research on rechargeable batteries a electro-chemically diffusion model for a temperature sensitive multi-phase solid is presented. The derivation of the model is based on the framework of the Thermodynamics of Irreversible Processes with the assumption of a local equilibrium. The physical effects which are account...

Repair and replacement of damaged composites are costly and time-consuming processes, therefore a prediction of fracture is highly beneficial, and may enhance structure reliability. In this study, a case-based reasoning (CBR) methodology as a problem-solving method of artificial intelligence is utilized to predict fracture occurrence in adhesively...

Open‐cell structures like open‐pore foams have several applications, e.g. as acoustic damping material in civil engineering. Most models for such materials capture the static but not the dynamic behavior correctly. In order to develop a model which is able to describe the static and the dynamic properties, an analysis of the microstructure is requi...

In lithium batteries, multicomponent compositions like LiCoO2 or LiFePO4 are used as cathode material and single substances like graphite are employed as anode material. In the latest battery developments anodes of silicon are introduced. Unfortunately, by now the high volumetric changes of silicon during intercalation — sometimes a factor of four...

Phase‐field methods have been proven to address the main challenges in fracture mechanics – the identification of crack initiation and the simulation of the unknown crack paths – in an elegant way. This approach has therefore become very popular recently. Our contribution sets the focus on different ways to capture anisotropy in the phase‐field mod...

The wave propagation in a group of soft resin based (3d printed) materials is investigated by using a Split Hopkinson Bar setup. The principal assumptions and the role of pulse shaping, as an approach to achieve constant strain rates and dispersion reduction, is discussed. The measured dynamic elastic modulus is presented and indicates that flexibl...

Additive manufacturing, also known as 3D printing, has become a well‐established method in many different fields of fabrication. It is a preferred method to produce small series or even individual parts of components. The present work aims at the experimental identification of the hyper‐ and viscoelastic properties of two different kinds of highly...

Recently Kirchdoerfer and Ortiz proposed a new computing paradigm, called data‐driven computing [1]. It is a new approach to overcome uncertainties in the modeling process of the material law. The aim of this work is to compare the solutions of the data‐driven method with classical finite element solutions and an analytic solution. A simple elastic...

Our living standards are substantially influenced by the advent and development of new materials. The need for stronger building materials has led to useful innovations such as the fortification of concrete to produce Ultra-High-Performance Concrete (UHPC). Since numerous structures constructed by various types of concrete and UHPC, experience high...

Injection molding has been a preferred production process in the fabrication of complex components. In this technique not only the injection machine and mold play important roles, but also different process parameters have strong effects on the quality of the final products. The production process might be stopped because of different types of faul...

Ultra-High Performance Concrete (UHPC) is a new class of concrete which shows high strength and durability. In this paper experimental investigations on the dynamic properties of a low-silica UHPC are presented. By means of Hopkinson Pressure Bar experiments the dynamic elastic modulus and the tensile resistance of the material are determined. Addi...

The phase-field approach to fracture has been proven to be a mathematically sound and easy to implement method for computing crack propagation with arbitrary crack paths. Hereby crack growth is driven by energy minimization resulting in a variational crack-driving force. The definition of this force out of a tension-related energy functional does,...

High-tech demands of the aviation industry require a detailed knowledge of the mechanical and structural response of composite structures. This contribution presents experimental investigations on composite honeycomb sandwich T-joint connections. To understand the effect of loading and ageing on the adhesively bonded joints, quasistatic tension exp...

Split Hopkinson bar experiments are fundamental test arrangements to determine elastic, plastic, and fracture properties of materials under high strain rates. A specimen is considered to be in a well‐defined state of uniaxial stress, and depending on the specific device, limit loads or high strains can be achieved through purely elastic loading in...

The de-mixing properties of heterogeneous viscous fluids are determined by an interplay of diffusion, surface tension and a superposed velocity field. In this contribution a variational model of the decomposition, based on the Navier–Stokes equations for incompressible laminar flow and the extended Korteweg–Cahn–Hilliard equations, is formulated. A...

In this work we provide an extended Cahn–Hilliard equation describing separation processes in binary alloys affected by temperature gradients coupled with a heat equation. The three important material parameters used in the model, namely the Gibbs’ configurational free energy density, the mobility of atoms and their heats of transport, are modelled...

We present recent results on the mathematical analysis of phase‐field model for anisotropic fracture at finite strains. It is based on a modification of the Ambrosio‐Tortorelli model, formulated for polyconvex energy densities in terms of the modified invariants of the right Cauchy‐Green strain tensor and augmented by a viscous dissipation for the...

The functional properties of multi-component materials are often determined by a rearrangement of their different phases and by chemical reactions of their components. In this contribution, a material model is presented which enables computational simulations and structural optimization of solid multi-component systems. Typical Systems of this kind...