Inverse form finding with h-adaptivity and an application to a notch stamping process

The aim is to determine the optimized semi-finished workpiece geometry to its given target geometry after a forming process. Hereby, a novel approach for inverse form finding, a type of a shape optimization, is applied to a notch stamping process. As a special feature, h-adaptive mesh refinement is considered within the iteratively performed forming simulation

Homogenization of heterogeneous, fibre structured materials

This contribution presents a multi-scale homogenization method to model fibre structured materials. On the macroscopic level textiles are characterized by a large area-to-thickness ratio, such that a discretization with shell elements is numerically efficient. The material behavior is strongly influenced by the heterogeneous micro structure. To capture the contact on the micro level, the RVE is explicitly modelled by means of a volumetric micro sample and a shell specific homogenization scheme is applied to transfer the microscopic response to the macro level. Theoretical aspects are discussed and a numerical example for contact behavior of a periodic knitted structure is give

On Potential Energy Shifts in Hyperelastic Energy-Momentum Tensors

The invariance of the so-called energy-momentum format of the (spatial motion) Cauchy and the (material motion) Eshelby stress tensors of hyperelasticity is discussed with respect to shifts of the potential energy density. As an noteworthy result it turns out that the duality of the spatial and the material motion problem renders the corresponding energy-momentum tensors either invariant or equipped with an additional pressure-like contribution, respectively. This additional pressure like contribution captures the different total potential energy content due to the shift in potential energy density

Some properties of the dissipative model of strain-gradient plasticity

A theoretical and computational investigation is carried out of a dissipative model of rate-independent strain-gradient plasticity and its regularization. It is shown that the flow relation, when expressed in terms of the Cauchy stress, is necessarily global. The most convenient approach to formulating the flow relation is through the use of a dissipation function. It is shown, however, that the task of obtaining the dual version, in the form of a normality relation, is a complex one. A numerical investigation casts further light on the response using the dissipative theory in situations of non-proportional loading. The elastic gap, a feature reported in recent investigations, is observed in situations in which passivation has been imposed. It is shown computationally that the gap may be regarded as an efficient path between a load-deformation response corresponding to micro-free boundary conditions, and that corresponding to micro-hard boundary conditions, in which plastic strains are set equal to zero.Comment: 26 pages, 10 figure

James Sdrales and Virginia Zambukos v. Sam Rondos : Brief of Respondents

This paper deals with shape optimization for anisotropic elastoplasticity in logarithmic strain space. We aim to find an appropriate undeformed configuration of a workpiece knowing in advance its deformed configuration, the boundary conditions and the applied loads. The node coordinates of the finite element (FE) domain are chosen as design variables. A discrete sensitivity analysis is presented and analytical gradients are performed. A numerical example illustrates the theoretical aspects

On a recursive algorithm for avoiding mesh distortion in inverse form finding

A challenge in the design of functional parts is the determination of the initial, undeformed shape such that under a given load a part will obtain the desired deformed shape. A shape optimization formulation might be used to determine the initial shape in the sense of an inverse problem via successive iterations of a direct mechanical problem. In this paper, we present a shape optimization formulation for elastoplastic materials with a constitutive model for anisotropic additive elastoplasticity in the logarithmic strain space. A discrete sensitivity analysis is performed and gives the analytical gradient of the objective function needed in the optimization algorithm. We found that the use of the coordinates of the functional component as design variables led to mesh distortions. Without a split of the total force applied on the component and an update of the undeformed configuration between two steps the optimization algorithm is not able to find an appropriate minimum. Three numerical examples in isotropic and anisotropic elastoplasticity illustrate the structure of such a recursive algorithm for avoiding mesh distortions

Lower variability of radionuclide activities in upland dairy products compared to soils and vegetation: Implication for environmental survey

Contamination of the environment by radionuclides is usually estimated using soil and grass sampling. However, radionuclides are often not homogeneously distributed in soils. In the alpine Mercantour region (Western Alps, France) a large heterogeneity in Chernobyl 137Cs deposition has been previously observed. Here we report additional 137Cs results together with new 90Sr and Pu data for soil, grass, milk, and cheese samples. The results show that radioisotopes from nuclear weapons tests fallout are more homogeneously distributed than Chernobyl 137Cs. Further, we observe that the 137Cs and 90Sr contents are less variable in milk samples than in grass or soil samples. This can be attributed to the homogenization effect of cow vagrancy during grazing. Hence milk seems to be a more robust sample than soil or grass to evaluate the extent of contamination on a regional scale. We explore this idea by comparing own unpublished 90Sr results and 90Sr results from the literature to establish the relationship between altitude of grazing and contamination of soil and milk for Western Europe. There is a significant positive correlation between soil contamination and altitude and an even closer correlation between milk 90Sr activity (A) and altitude (h): A = A0 + ek·h where A0 is the expected activity of milk sampled at sea level (A0 = 0.064 ± 0.014 Bq g-1 Ca) and h is the altitude of grazing, k being a constant (k = 0.95 × 10-3 ± 0.11 × 10-3 m-1 Bq g-1 Ca). The fact that there is less scattering in the relationship for the 90Srmilk-altitude than for 90Srsoil-altitude suggests, again, that milk is a well-suited sample for environmental survey. The relationship between the altitude of grazing and the 90Sr content of milk and cheese can also be used to assess the authenticity of dairy products. © 2006 Elsevier Ltd. All rights reserved

On the simulation of cohesive fatigue effects in grain boundaries of a piezoelectric mesostructure

AbstractFerroelectric materials offer a variety of new applications in the field of smart structures and intelligent systems. Accordingly, the modelling of these materials constitutes an active field of research. A critical limitation of the performance of such materials is given when electrical, mechanical, or mixed loading fatigue occurs, combined with, for instance, microcracking phenomena. In this contribution, fatigue effects in ferroelectric materials are numerically investigated by utilisation of a cohesive-type approach. In view of finite element-based simulations, the geometry of a natural grain structure, as observed on the so-called meso-level, is represented by an appropriate mesh. While the response of the grains themselves is approximated by coupled continuum elements, grain boundaries are numerically incorporated via so-called cohesive-type or interface elements. These offer a great potential for numerical simulations: as an advantage, they do not result in bad-conditioned systems of equations as compared with the application of standard continuum elements inhering a very high ratio of length and height. The grain boundary behaviour is modelled by cohesive-type constitutive laws, designed to capture fatigue phenomena. Being a first attempt, switching effects are planned to be added to the grain model in the future. Two differently motivated fatigue evolution techniques are applied, the first being appropriate for low-cycle-fatigue, and a second one adequate to simulate high-cycle-fatigue. Subsequent to a demonstration of the theoretical and numerical framework, studies of benchmark boundary value problems with fatigue-motivated boundary conditions are presented