Mesoscopic Modeling for Continua with Pores: Dynamic Void Growth in Viscoplastic Materials

Dieser Beitrag ist mit Zustimmung des Rechteinhabers aufgrund einer (DFG geförderten) Allianz- bzw. Nationallizenz frei zugänglich.This publication is with permission of the rights owner freely accessible due to an Alliance licence and a national licence (funded by the DFG, German Research Foundation) respectively.The temporal development of arbitrarily distributed voids in a viscoplastic material under different loading regimes is investigated. For this reason, we make use of a mesoscopic continuum model extending the classical space–time domain of continuum mechanics. This extended domain requires a reformulation of the classical balance equations as well as the consideration of additional constitutive quantities. Furthermore, a mesoscopic distribution function is formulated to describe the temporal evolution of different void regimes. Here, we assume a spherical shell model for the porous composites and elaborate all required steps in order to describe load-induced void growth in a metal-like matrix. We conclude with some exemplary results that confirm experimental observations of dynamical fracture

Mesoscopic Modeling for Continua with Pores: Application in Biological Soft Tissue

Dieser Beitrag ist mit Zustimmung des Rechteinhabers aufgrund einer (DFG geförderten) Allianz- bzw. Nationallizenz frei zugänglich.This publication is with permission of the rights owner freely accessible due to an Alliance licence and a national licence (funded by the DFG, German Research Foundation) respectively.In this work, the damage in biological soft tissue induced by bubble cavitation is investigated. A typical medical procedure with such damaging side effects is the kidney stone fragmentation by shock-wave lithotripsy. We start with a mesoscopic continuum model that allows the consideration of microstructural information within the macroscopic balance equations. An evolution equation for the temporal development of the bubble distribution function is derived. Furthermore, the constitutive relations of bubble expansion are deduced by means of a spherical shell model. Numerical simulations are presented for a typical soft tissue material and different definitions for a damage parameter are discussed

B-Spline meshing for high-order finite element analyses of multi-physics problems

Multi-physics problems often involve differential equations of higher-order, which cannot be solved with standard finiteelement methods. B-splines as finite element basis functions provide the required continuity and smoothness. However, the meshgeneration for arbitrarily shaped domains is non-intuitively and traditional techniques often lead to distorted elements.Here a strategy is presented to design isoparametric B-spline based meshes for curves, surfaces, and volumes. The error of thehomeomorphic transformation into curved boundaries is estimated. For selected two and three-dimensional shapes, the knotvectors and the control points are calculated.Exemplarily, a finite element analysis of a helical structure subjected to a chemo-mechanical deformation with phase decompositionis performed

Effect of physical aging on the flexural creep in 3D printed thermoplastic

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 aged specimens are shifted to each other on the logarithmic time scale in a way that the theory of physical aging can explain. The reason for the physical aging of 3D printed thermoplastics is assumed to be the special heat treatment that the polymer undergoes during extrusion. Additionally, results of a long-term flexural creep experiment are shown, demonstrating that non-negligible creep over long periods can be observed even at temperatures well below the glass transition temperature. Such creep effects should be considered for designing components made of 3D printed thermoplastics.Comment: This is a preprint of the following chapter: Fischbach, M., Weinberg, K., Effect of Physical Aging on the Flexural Creep in 3D Printed Thermoplastic, published in Creep in Structures VI, edited by Altenbach, H., Naumenko, K., 2023, Springer reproduced with permission of Springer Nature Switzerland A

Origins of Bulk Viscosity at RHIC

A variety of physical phenomena can lead to viscous effects. Several sources of shear and bulk viscosity are reviewed with an emphasis on the bulk viscosity associated with chiral restoration and with chemical non-equilibrium. We show that in a mean-field treatment of the limiting case of a second order phase transition, the bulk viscosity peaks in a singularity at the critical point.Comment: submitted to PR

Dynamic fracture with continuum-kinematics-based peridynamics

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 surfaces and volumes considered for these non-local interactions are constructed using the point families derived from the material points' horizon. For fracture, the classical bond-stretch damage approach is not sufficient in continuum-kinematics-based peridynamics. Here it is extended to the surface- and volume-based interactions by additional failure variables considering the loss of strength in the material points' internal force densities. By numerical examples, it is shown that the approach can correctly handle crack growth, impact damage, and spontaneous crack initiation under dynamic loading conditions with large deformations

Analysis and simulations for a phase-field fracture model at finite strains based on modified invariants

Phase-field models have already been proven to predict complex fracture patterns in two and three dimensions 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 solid mechanics. We here present a phase-field model at finite strains, which takes into account the anisotropy of damage by applying an anisotropic split and the modified invariants of the right Cauchy-Green strain tensor. We introduce a suitable weak notion of solution that also allows for a spatial and temporal discretization of the model. In this framework we study the existence of solutions and we show that the time-discrete solutions converge in a weak sense to a solution of the time-continuous formulation of the model. Numerical examples in two and three space dimensions are carried out in the range of validity of the analytical results

Continuum-kinematics-based peridynamics and phase-field approximation of non-local dynamic fracture

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’s potential energy and provides a reliable method for predicting fracture in finite element computations. Both methods are able to efficiently compute crack propagation even when the cracks have arbitrary or complex patterns. We discuss the relations of critical fracture parameters in the two methods and show that our novel damage model for the continuum-kinematics-based peridynamics effectively manages fracture under dynamic loading conditions. Numerical examples demonstrate a good agreement between both methods in terms of crack propagation, fracture pattern, and in part, critical loading. We also show the limitations of the methods and discuss possible reasons for deviations