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This work addresses an efficient neural network (NN) representation for the phase-field modeling of isotropic brittle fracture. In recent years, data-driven approaches, such as neural networks, have become an active research field in mechanics. In this contribution, deep neural networks—in particular, the feed-forward neural network (FFNN)—are utilized directly for the development of the failure model. The verification and generalization of the trained models for elasticity as well as fracture behavior are investigated by several representative numerical examples under different loading conditions. As an outcome, promising results close to the exact solutions are produced.

This paper deals with the mathematical modeling of bacterial co-aggregation and its numerical implementation in a FEM framework. Since the concept of co-aggregation refers to the physical binding between cells of different microbial species, a system composed of two species is considered in the modeling framework. The extension of the model to an arbitrary number of species is straightforward. In addition to two-species (multi-species growth) dynamics, the transport of a nutritional substance and the extent of co-aggregation are introduced into the model as the third and fourth primary variables. A phase-field modeling approach is employed to describe the co-aggregation between the two species. The mathematical model is three-dimensional and fully based on the continuum description of the problem without any need for discrete agents which are the key elements of the individual-based modeling approach. It is shown that the use of a phase-field-based model is equivalent to a particular form of classical diffusion-reaction systems. Unlike the so-called mixture models, the evolution of each component of the multi-species system is captured thanks to the inherent capability of phase-field modeling in treating systems consisting of distinct multi-phases. The details of numerical implementation in a FEM framework are also presented. Indeed, a new multi-field user element is developed and implemented in ANSYS for this multiphysics problem. Predictions of the model are compared with the experimental observations. By that, the versatility and applicability of the model and the numerical tool are well established.

In this work a Dirichlet pressure boundary condition for incompressible Smoothed Particle Hydrodynamics (SPH) is presented for free surfaces under surface tension. These free surfaces occur when the surrounding phase in simulations is neglected for computational reasons while the effects of the surface tension shall remain. We demonstrate capabilities of the boundary condition by comparing it to an approach from the literature. The simulations show that our approach provides a higher stability to the free surface, being capable of capturing static and transient processes as much as bubble coalescence. Furthermore a new approach is presented to compute the curvature more exactly for three-dimensional cases in order to stabilize the simulation, which is applicable for weakly compressible SPH and incompressible SPH simulations.

Hyperelasticity is a common modeling approach to reproduce the nonlinear mechanical behavior of rubber materials at finite deformations. It is not only employed for stand-alone, purely elastic models but also within more sophisticated frameworks like viscoelasticity or Mullins-type softening. The choice of an appropriate strain energy function and identification of its parameters is of particular importance for reliable simulations of rubber products. The present manuscript provides an overview of suitable hyperelastic models to reproduce the isochoric as well as volumetric behavior of nine widely used rubber compounds. This necessitates firstly a discussion on the careful preparation of the experimental data. More specific, procedures are proposed to properly treat the preload in tensile and compression tests as well as to proof the consistency of experimental data from multiple experiments. Moreover, feasible formulations of the cost function for the parameter identification in terms of the stress measure, error type as well as order of the residual norm are studied and their effect on the fitting results is illustrated. After these preliminaries, invariant-based strain energy functions with decoupled dependencies on all three principal invariants are employed to identify promising models for each compound. Especially, appropriate parameter constraints are discussed and the role of the second invariant is analyzed. Thus, this contribution may serve as a guideline for the process of experimental characterization, data processing, model selection and parameter identification for existing as well as new materials.

Cryopreservation can be used to store equine oocytes for extended periods so that they can be used in artificial reproduction technologies at a desired time point. It requires use of cryoprotective agents (CPAs) to protect the oocytes against freezing injury. The intracellular introduction of CPAs, however, may cause irreversible osmotic damage. The response of cells exposed to CPA solutions is governed by the permeability of the cellular membrane towards water and the CPAs. In this study, a mathematical mass transport model describing the permeation of water and CPAs across an oocyte membrane was used to simulate oocyte volume responses and concomitant intracellular CPA concentrations during the exposure of oocytes to CPA solutions. The results of the analytical simulations were subsequently used to develop a phenomenological finite element method (FEM) continuum model to capture the response of oocytes exposed to CPA solutions with spatial information. FEM simulations were used to depict spatial differences in CPA concentration during CPA permeation, namely at locations near the membrane surface and towards the middle of the cell, and to capture corresponding changes in deformation and hydrostatic pressure. FEM simulations of the multiple processes occurring during CPA loading of oocytes are a valuable tool to increase our understanding of the mechanisms underlying cryopreservation outcome.

Purpose - The paper aims to introduce an efficient contact detection algorithm for smooth convex particles.Design methodology approach - The contact points of adjacent particles are defined according to the common-normal concept. The problem of contact detection is formulated as 2D unconstrained optimization problem that is solved by a combination of Newton's method and a Levenberg-Marquardt method.Findings - The contact detection algorithm is efficient in terms of the number of iterations required to reach a high accuracy. In the case of non-penetrating particles, a penetration can be ruled out in the course of the iterative solution before convergence is reached.Research limitations implications - The algorithm is only applicable to smooth convex particles, where a bijective relation between the surface points and the surface normals exists.Originality value - By a new kind of formulation, the problem of contact detection between 3D particles can be reduced to a 2D unconstrained optimization problem. This formulation enables fast contact exclusions in the case of non-penetrating particles.

Assumed stress finite elements are known for their extraordinary good performance in the framework of linear elasticity. In this contribution we propose a mixed variational formulation of the Hellinger–Reissner type for hyperelasticity. A family of hexahedral shaped elements is considered with a classical trilinear interpolation of the displacements and different piecewise discontinuous interpolation schemes for the stresses. The performance and stability of the new elements are investigated and demonstrated by the analysis of several benchmark problems. In addition the results are compared to well known enhanced assumed strain elements.

Magnesium has mechanical properties similar to those of bone and is being considered as a potential bone substitute. In the present study, two different pore sized scaffolds of the Mg alloy LAE442, coated with magnesium fluoride, were compared. The scaffolds had interconnecting pores of either 400 (p400) or 500 µm (p500). ß-TCP served as control. Ten scaffolds per time group (6, 12, 24, 36 weeks) were implanted in the trochanter major of rabbits. Histological analyses, µCT scans, and SEM/EDX were performed. The scaffolds showed slow volume decreases (week 36 p400: 9.9%; p500: 7.5%), which were accompanied by uncritical gas releases. In contrast, ß-TCP showed accelerated resorption (78.5%) and significantly more new bone inside (18.19 ± 1.47 mm3). Bone fragments grew into p400 (0.17 ± 0.19 mm3) and p500 (0.36 ± 0.26 mm3), reaching the centrally located pores within p500 more frequently. In particular, p400 displayed a more uneven and progressively larger surface area (week 36 p400: 253.22 ± 19.44; p500: 219.19 ± 4.76 mm2). A better osseointegration of p500 was indicated by significantly more trabecular contacts and a 200 µm wide bone matrix being in the process of mineralization and in permanent contact with the scaffold. The number of macrophages and foreign body giant cells were at an acceptable level concerning resorbable biomaterials. In terms of ingrown bone and integrative properties, LAE442 scaffolds could not achieve the results of ß-TCP. In this long-term study, p500 appears to be a biocompatible and more osteoconductive pore size for the Mg alloy LAE442.

Forming of hybrid bulk metal components might include severe membrane mode deformation of the joining zone. This effect is not reflected by common Traction Separation Laws used within Cohesive Zone Elements that are usually applied for the simulation of joining zones. Thus, they cannot capture possible damage of the joining zone under these conditions. Membrane Mode Enhanced Cohesive Zone Elements fix this deficiency. This novel approach can be implemented in finite elements. It can be used within commercial codes where an implementation as a material model is beneficial as this simplifies model preparation with the existing GUIs. In this contribution, the implementation of Membrane Mode Enhanced Cohesive Zone Elements as a material model is presented within MSC Marc along with simulations showing the capabilities of this approach.

A sharp-interface model employing the extended finite element method is presented. It is designed to capture the prominent γ-γ′ phase transformation in nickel-based superalloys. The novel combination of crystal plasticity and sharp-interface theory outlines a good modeling alternative to approaches based on the Cahn–Hilliard equation. The transformation is driven by diffusion of solute γ′-forming elements in the γ-phase. Boundary conditions for the diffusion problem are computed by the stress-modified Gibbs–Thomson equation. The normal mass balance of solute atoms at the interface yields the normal interface velocity, which is integrated in time by a level set procedure. In order to capture the influence of dislocation glide and climb on interface motion, a crystal plasticity model is assumed to describe the constitutive behaviour of the γ-phase. Cuboidal equilibrium shapes and Ostwald ripening can be reproduced. According to the model, in low γ′ volume-fraction alloys with separated γ′-precipitates, interface movement does not have a significant effect on tensile creep behaviour at various lattice orientations.