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The Cut Finite Element Method (CutFEM) is recently shown to be a versatile approach for tunnel construction modeling and settlement analysis. The CutFEM can significantly simplify the computational workflow by facilitating the discretization and coupling of different components in structural analysis, while maintaining the same accuracy as the standard boundary-fitted method. In this work, three surrogate models based on the Proper Orthogonal Decomposition and Radial Basis Functions (POD-RBF), Artificial Neural Networks (ANN) and Gradient Boosting (GBoost) are proposed and compared for tunnel alignment design. The flexibility of generating multiple designs quickly and conveniently using CutFEM, to provide snapshot data for surrogate model construction, is exploited. As an illustration of the concept, the surrogate model resulting from the linear analysis, involving linear elastic material with compatible parameters, is presented. This approach can be extended to the analysis including a city model, which leads to efficient damage assessment analysis on the existing infrastructure. The resulting surrogate model is used for tunnel track design, where the settlement field can be determined quickly in seconds , which allows real-time applications. The surrogate model is integrated into an interactive platform, named as TunAID, that can be used for real-time design of the tunnel alignment in urban area.

Waveform inversion is an approach used to find an optimal model for the velocity field of a ground structure such that the dynamic response is close enough to the given seismic data. First, a suitable numerical approach is employed to establish a realistic forward computer model. The forward problem is solved in the frequency domain using higher-order finite elements. The velocity field is inverted over a specific number of discrete frequencies, thereby reducing the computational cost of the forward calculation and the nonlinearity of the inverse problem. The results are presented for different frequency sets and with different source and receiver locations for a two-dimensional model. The influence of attenuation effects is also investigated. The results of two blind tests are presented where only the seismic records of an unknown synthetic model with an inhomogeneous material parameter distribution are provided to mimic a more realistic case. Finally, the result of the inversion in a three-dimensional space is illustrated.

This study presents numerical and experimental models for the analysis of the excavation of soft soils by means of a cutting tool. The computational model is constructed using an Updated Lagrangean (UL) velocity-based Finite Element approach. A hypoplastic formulation is employed to describe the constitutive behavior of soft soils. Large displacements and deformations of the ground resulting from the cutting tool-soil interaction are handled by means of the Particle Finite Element method, characterized by a global re-meshing strategy and a boundary identification procedure called α-shape technique. The capabilities and performance of the proposed model are demonstrated through comparative analyses between experiments and simulations of cutting tool-soft soil interactions. The experiments are performed using an excavation device at Ruhr-Universität Bochum (RUB), Germany. The main details concerning the setup and calibration and evolution of the measured draft forces are discussed. Selected computational results characterizing the cutting tool-soft soil interaction including the topology of the free surface, void ratio distribution ahead of the tool, spatio-temporal evolution of the reaction forces and abrasive wear behavior are evaluated.

The phenomenon of functional fatigue occurs during cyclic loading of pseudoelastic shape memory alloys. We model this effect by considering an irreversible martensitic volume fraction in addition to the reversible amounts of austenite and martensite based on variational principles. The inclusion of irreversible martensitic volume fractions coincides with experimental observations and enables the model to be easily calibrated without any fitting functions. In our previous studies, we modeled the polycrystalline material structure by static discretization of a relatively large number of randomly chosen grain orientations, which required much numerical effort. In contrast, we now apply a dynamic representation of the orientation distribution function to the modeling of functional fatigue which has proven to be beneficial regarding the numerical performance. To this end, we take into account an averaged grain orientation parameterized by three Euler angles that serve as additional internal variables. This results in an extremely reduced numerical effort. The model derivation is given along with the numerical implementation and computer experiments on the cyclic behavior of shape memory alloys.

Numerical simulations are a powerful tool to analyze the complex thermo-mechanically coupled material behavior of shape memory alloys during product engineering. The benefit of the simulations strongly depends on the quality of the underlying material model. In this contribution, we discuss a variational approach which is based solely on energetic considerations and demonstrate that unique calibration of such a model is sufficient to predict the material behavior at varying ambient temperature. In the beginning, we recall the necessary equations of the material model and explain the fundamental idea. Afterwards, we focus on the numerical implementation and provide all information that is needed for programing. Then, we show two different ways to calibrate the model and discuss the results. Furthermore, we show how this model is used during real-life industrial product engineering.

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.

AbstractWe 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.

We develop a framework for a variational analysis of microstructural evolution during inelastic high‐temperature deformation accommodated by dislocation mechanisms and diffusive mass transport. A polycrystalline aggregate is represented by a distribution function characterizing the state of individual grains by three variables, dislocation density, grain size, and elastic strain. The aggregate's free energy comprises elastic energy and energies of lattice distortions due to dislocations and grain boundaries. The work performed by the external loading is consumed by changes in the number of defects and their migration leading to inelastic deformation. The variational approach minimizes the rate of change of free energy with the evolution of the state variables under constraints on the aggregate volume, on a relation between changes in plastic strain and dislocation density, and on the form of the dissipation functionals for defect processes. The constrained minimization results in four basic evolution equations, one each for the evolution in grain size and dislocation density and flow laws for dislocation and diffusion creep. Analytical steady state scaling relations between stress and dislocation density and grain size (piezometers) are derived for quasi‐homogeneous materials characterized by a unique relation between grain size and dislocation density. Our model matches all currently available experimental observations regarding high‐temperature deformation of olivine aggregates with plausible values for the involved micromechanical model parameters. The relation between strain rate and stress for olivine aggregates maintaining a steady state microstructure is distinctly nonlinear in stark contrast to the majority of geodynamical modeling relying on linear relations, i.e., Newtonian behavior. Analytical derivation of steady-state piezometers using variational analysisMatches observations for olivine rocks with plausible micromechanical parametersProvides insight into rheology of olivine aggregates, e.g., lifetime of grains

A mathematical model for a finite–strain elastoplastic evolution problem is proposed in which one time–step of an implicit time–discretization leads to generally non–convex minimization problems. The elimination of all internal variables enables a mathematical and numerical analysis of a reduced problem within the general framework of calculus of variations and nonlinear partial differential equations. The results for a single slip–system and von Mises plasticity illustrate that finite–strain elastoplasticity generates reduced problems with non–quasiconvex energy densities and so allows for non–attainment of energy minimizers and microstructures.

A very general class of shell theories is established, based on a unified variational principle and on expansions with respect to biorthogonal function systems. The shell models derived are able to accommodate the flow theory of large strain thermoelastoplasticity including the effects due to unloading. The specific case of a compressible neo-Hookean material with a von Mises yield condition is discussed in detail.

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.