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The micro-sphere modeling framework provides a popular means by which one-dimensional mechanical models can easily and quickly be generalized into three-dimensional stress-strain models. The essential notion of the framework, similar to homogenization theory, is that one allows the microstructural kinematic fields to relax subject to a constraint connected to a macroscopic deformation measure. In its standard presentation, the micro-sphere modeling framework is strictly applicable to elastic materials. Presentations considering inelastic phenomena invariably, and inconsistently, assume an affine relation between inelastic macroscopic and microscopic phenomena. In this work we present a methodology by which one can lift this modeling restriction using two formally different approaches. In particular, we show how one can construct and apply a homogenization with Biot theory to generate fully-relaxed variationally-consistent macroscopic models for inelastic materials within the context of the micro-sphere model. The primary application example will be finite deformation viscoelasticity.

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. [ABSTRACT FROM AUTHOR]

As damage occurs in the context of high stresses that are also related to the presence of plastic strains, it is natural to investigate the effect of plasticity on damage evolution and to thus achieve a more realistic model. In this work, the existing and new damage model presented in [Junker P, Schwarz S, Makowski J, Hackl K. Continuum Mech. Therm. 2017, 29 (1), 291–310] is enhanced with plasticity and isotropic hardening. The damage model is based on a relaxation-based approach and does not require additional complex regularization techniques besides considering viscous effects. The benefit of the model are mesh-independent results for the rate-dependent case, even without considering, e.g. gradient terms for mathematical regularization. The enhancement with plasticity and isotropic hardening was investigated for a representative volume element that considerd a damaging matrix material and non-damaging hard precipitates. Two different loading types, pure tension and pure shear, yielded the homogenized stress/strain response for the material at various loading rates. Hereto, several finite discretizations in terms of finite-element meshes were used. The results underline the mesh-independence for physically reasonable loading rates and viscosities.

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. [ABSTRACT FROM AUTHOR]

This work presents a variational material model for transformation-induced plasticity in steels. We will use the principle of the minimum of the dissipation potential to develop a coupled material model for plastic deformations and phase transformations that simultaneously accounts for the hardening effects that play an important role. We will use a polycrystalline approach and introduce a combined Voigt/Reuß bound and a coupled ansatz for the dissipation functional to model the simultaneous effects of plastic deformations and phase transformations. Finally, we will present the first numerical results for a tension/compression test.

Metamaterials are artificially created multiscale materials with many different applications [1]. We assume periodic microstructure. No specific length scale is demanded for the differentiation between the scales. Instead, we consider the microscale as consisting of repeating unit cells, whereas the macroscale is the scale, where desired and sometimes unusual physical effects occur. The precise arrangement and geometry at the microscale level is responsible for the macroscopic material behavior, which can substantially differ from the original components it is made from. This way, unique material properties otherwise not found in nature (e.g. negative refractive materials [2]) are possible. Most previous research regarding metamaterials concentrated only on a single physical branch in each case, e.g. electromagnetic or acoustic metamaterials [3,4]. In this contribution we present a class of theoretical electro‐mechanical metamaterials by combining insulating and conducting materials. Our aim is to directly control and reduce the resulting total stress of insulating materials by counteracting the mechanical stress through the application of an electric field, which is created by a conducting material. The solution of the resulting minimization problem is related to the eigenvalues of the mechanical stress tensor. Additionally, we discuss the constrained cases of tension and compression and cover the plane stress case. We show numerical results for all cases and discuss the limits of such a material. [ABSTRACT FROM AUTHOR]

In mechanized tunneling, so‐called tunnel boring machines (TBMs) drill through the ground in an automatized manner. Therefore, the drilling process is very efficient but the maintenance costs are high. Seismic exploration seems appropriate to identify changing ground conditions in front of the TBM to reduce costs from damages of the TBM and from the corresponding dwell times. Today's seismic exploration techniques are using only a small amount of the information, which is contained in the seismic records from field observations, whereas full waveform inversion (FWI) tries to use the whole content. The potential of different FWI approaches for the application in mechanized tunneling has been investigated. An analysis of the performance of FWI not only employing synthetic examples but additionally measured waveforms is essential. Since seismic surveys at the construction side are not performed with FWI in mind, the data sets are usually not appropriate for testing the developed algorithms. Nevertheless, a validation of FWI approaches by measured waveforms is possible by using waveform recordings from a small‐scale experimental setup. A small‐scale super high strength grout specimen is constructed for validating an adjoint frequency domain FWI approach. Frequency domain models compute the seismic response of a system for an infinite time interval. The attenuation of the material as well as the attenuation effects at the free surfaces are hard to quantify over an infinite time interval. Therefore, the specimen is designed in a way that four of the six borders can be modeled as absorbing boundaries. For this purpose, the displacement recordings are truncated just before the waves that are reflected at the excluded borders arrive at the measurement points. This design in combination with a notch representing a rectangular tunnel makes the measurements more similar to data from a tunnel construction side. A rectangular hole is embedded in the specimen and acts as material discontinuity, which the FWI approach is aiming to detect. [ABSTRACT FROM AUTHOR]

We derive an energy-based material model for thermomechanically coupled phase transformations in polycrystalline shape memory alloys. For the variational formulation of the model, we use the principle of the minimum of the dissipation potential for nonisothermal processes for which only a minimal number of constitutive assumptions has to be made. By introducing a condensed formulation for the representative orientation distribution function, the resulting material model is numerically highly efficient. For a first analysis, we present the results of material point calculations, where the evolution of temperature as well as its influence on the mechanical material response is investigated.

Experiments conducted in granular media like clay, silt, or sand show complex structures which cannot be explained as simple shear bands. Materials in this class are usually heterogeneous mixtures of fluids, usually air and water, and particles that have little to no cementation. The shear strength is provided by friction and interlocking of the particles. This generally leads to pressure dependent plastic behavior. Consequently, models in soil mechanics require pressure‐dependent yield surfaces resulting, in contrast to models in crystal plasticity, in non‐associated flow rules, which have not been studied as extensively as associated ones. In this study, we introduce a model capable of explaining the occurrence of the complex structures mentioned above starting from a time‐incremental variational formulation. We consider a basic model giving a reduced description for plasticity in soil mechanics with as few parameters as possible while retaining the essential features of the full model. The goal is to capture the complexity seen in experiments by considering the stability properties of the emerging microstructures. As expected, these complex structures lead to challenging questions concerning numerical simulations, which can be resolved employing a relaxed model in the implementation. [ABSTRACT FROM AUTHOR]