Multiscale modeling of cancellous bone considering full coupling of mechanical, electric and magnetic effects

Modeling of cancellous bone has important applications in the detection and treatment of fatigue fractures and diseases like osteoporosis. In this paper, we present a fully coupled multiscale approach considering mechanical, electric and magnetic effects by using the multiscale finite element method and a two-phase material model on the microscale. We show numerical results for both scales, including calculations for a femur bone, comparing a healthy bone to ones affected by different stages of osteoporosis. Here, the magnetic field strength resulting from a small mechanical impact decreases drastically for later stages of the disease, confirming experimental research

On the effects of a surrounding medium and phase split in coupled bone simulations

In our previous contributions we established a multiscale, multiphase material model for the simulation of cancellous bone with the novel idea of including the full coupling of mechanical, electric and magnetic effects, which could be used for example, for the early detection of osteoporosis. While our calculations have already shown promising results, our previous approach lacks very important aspects, strongly limiting the applicability of our findings. In this paper we extend our base model by considering the effect of a surrounding medium on our bone specimen, using improved boundary conditions and differentiating between cortical bone, bone marrow and spongy bone to better reflect the physiological properties of bone. We show numerical results and compare our calculations to our previous modeling

Data-driven simulation of inelastic materials using structured data sets and tangential transition rules

Data-driven computational mechanics replaces phenomenological constitutive functions by performing numerical simulations based on data sets of representative samples in stress-strain space. The distance of modeling values, e.g. stresses and strains in Gauss-points of a finite element calculation, from the data set is minimized with respect to an appropriate metric, subject to equilibrium and compatibility constraints, see [1]. Although this method operates well for non-linear elastic problems, there are challenges dealing with history-dependent materials, since one point in stress-strain space might correspond to different material behaviour. In [2], this issue is treated by including local histories into the data set. However, there is still the necessity to include models for the evolution of internal variables. Thus, a mixed formulation is obtained consisting of a combination of classical and data-driven modeling. In the presented approach, the data set is augmented with directions in the tangent space of points in stress-strain space. Moreover, the data set is classified into subsets corresponding to different material behaviour, e.g. elastic and inelastic. Based on the classification, transition rules map the modeling points to the various subsets. The approach and its performance will be demonstrated by applying it to a model of small strain elasto-plasticity with isotropic hardening

Model-free data-driven simulation of inelastic materials using structured data sets, tangent space information and transition rules

Model-free data-driven computational mechanics replaces phenomenological constitutive functions by numerical simulations based on data sets of representative samples in stress-strain space. The distance of strain and stress pairs from the data set is minimized, subject to equilibrium and compatibility constraints. Although this method operates well for non-linear elastic problems, there are challenges dealing with history-dependent materials, since one and the same point in stress-strain space might correspond to different material behaviour. In recent literature, this issue has been treated by including local histories into the data set. However, there is still the necessity to include models for the evolution of specific internal variables. Thus, a mixed formulation of classical and data-driven modeling is obtained. In the presented approach, the data set is augmented with directions in the tangent space of points in stress-strain space. Moreover, the data set is divided into subsets corresponding to different material behaviour. Based on this classification, transition rules map the modeling points to the various subsets. The approach will be applied to non-linear elasticity and elasto-plasticity with isotropic hardening

A model for the evolution size and composition of olivine crystals

In this proceeding, a material model to describe the evolution of olivine crystals, in particular iron-based Fayalite crystals, which are affected by the diffusion of magnesium ions, is introduced. These crystals are present in magma and understanding their behavior is an important aspect in improving prediction tools for volcanic eruptions. The model describes the development of the dislocation density, the concentration of magnesium over location and time, as well as the development of the size of the crystal over time. We discuss the model and the corresponding parameters. Furthermore, we present a numerical implementation of the model employing the platform Julia as well as a study on the influence of the various model parameters on the results. The results show a clear threshold between stable and unstable crystals

Topology and material optimization of anisotropic materials including a filter to smooth fiber pathways

A three-dimensional topology optimization of anisotropic materials including the optimization of the local material orientation based on thermodynamic principles is presented. To this end, the topology is parameterized by a continuous density variable with penalization of intermediate densities (SIMP) [1]. The material orientation is defined by the rotation of a given anisotropic base material and the rotation is parameterized by a set of three Euler angles. A novel filtering technique is presented to provide a smoothing of the material orientation, i.e. the fiber paths. The influence of the filter parameter on the maximum allowed fiber path curvature is shown. The constraint on the maximum fiber curvature also influences the results for the optimal topology. Corresponding numerical results for the simultaneous optimization of the topology and local material optimization for the two-dimensional and three-dimensional case will be presented

Variational regularization of damage models based on the emulated RVE

Material models exhibiting softening effects due to damage or localization share the problem of leading to ill-posed boundary value problems that lead to physically meaningless, mesh-dependent finite element results. It is thus necessary to apply regularization techniques that couple local behavior, described, e.g., by internal variables, at a spatial level. The common way to do this is to take into account higher gradients of the field variables, thus introducing an internal length scale. In this paper, we suggest a different approach to regularization that does not make use of any nonlocal enhancement like the inclusion of higher gradients or integration over local sub-domains nor of any classical viscous effects. Instead we perform an appropriate relaxation of the (condensed) free energy in a time-incremental setting which leads to a modified energy that is coercive and satisfies quasiconvexity in an approximate way. Thus, in every time increment a regular boundary value problem is solved. The proposed approach holds the same advantage as other methods, but with less numerical effort. We start with the theoretical derivation, discuss a rate-independent version of the proposed model and present details of the numerical treatment. Finally, we give finite element results that demonstrate the efficiency of this new approach

Seismic exploration in tunneling using full waveform inversion with a frequency domain model

With the knowledge of the geology in front of a tunnel, the excavation process can be optimized to avoid damage at the tunnel boring machine and settlements on the surface. Therefore, dwell times can be decreased and additional expenses can be avoided. Transmitted seismic waves will be spread, reflected and refracted due to geological changes. By utilizing geophones, the seismic waves will be captured and information about the geological structure in front of the tunnel can be extracted from the measured seismograms using e.g. the concept of full waveform inversion. A frequency domain model has been employed to demonstrate the potential of full waveform inversion for seismic reconnaissance in a tunnel environment. The success of the inversion procedure depends strongly on the positions of the utilized sender and receiver stations, the chosen initial material parameter distribution, and on the selected frequency groups for the inversion. Further challenges are an accurate representation of the reflecting surfaces and the application of absorbing borders to oppress reflections from the artificial boundaries, which delimit the analyzed domain. The results of the performed full waveform inversion for synthetic models of a 3D tunnel configuration with different disturbances ahead of the front tunnel face will be discussed. Additionally, the influence of different locations of the sender and receiver stations will be analyzed

Numerical investigation of wear processes by a gradient-enhanced damage-plasticity model

The prediction of failure mechanism in structures are always an important topic in the field of computational mechanics.Finite element computations of an inelastic material involving softening behavior (e.g. softening plasticity or damage) cansuffer from strongly mesh-dependent results. Therefore, such continuum models should be equipped with a regularization(localization limiter) strategy to overcome the above-mentioned problem.In this study, we present a framework for gradient-enhancement for coupled damage-plasticity material model derived bymeans of Hamilton’s principle for non-conservative continua. This model is applied for the numerical investigation of wearprocesses as they occur, e.g. in the case of mechanized tunneling. These investigations require a fine resolution of the involvedconstituents (cut sheet and abrasive particles in the soil). Consequently, a numerical strategy for the damage-plasticity modelis demanded that allows for time-efficient simulations.In this paper, we present a first step to the mentioned ultimate goal. To this end, a numerical framework for gradient-enhanced damage-plasticity coupling is proposed that is based on a combination of the finite element method with strategiesfrom meshless methods. We demonstrate that this framework keeps the computational effort limited and for each load stepclose to the purely elastic problems. Several numerical examples prove the elimination of the pathological mesh dependencyof the results. Furthermore, first results to the simulation of wear in tunneling machines are presented