How Fear of Future Outcomes Affects Social Dynamics

Journal of Statistical Physics - Mutualistic relationships among the different species are ubiquitous in nature. To prevent mutualism from slipping into antagonism, a host often invokes a...     

Prediction of elastic strain recovery of a formed steel sheet considering stiffness degradation

The aim of this work is to show first, how the springback of a steel sheet drawn part is affected by the stiffness degradation, as it results from the damage evolved during forming process, and second, to build a respective modeling approach to take this degradation into account. For the consideration of the orthotropic elastic properties degradation we develop an approach, based on the Mori-Tanaka theory, where damage is considered by inclusion of ellipsoidal cavities. The respective void shape evolution is proposed to be identified with the measurements of elastic modulus in two perpendicular directions during the uniaxial tensile test of a flat specimen at different loading stages. The proposed approach is coupled with the Gurson-Tvergaard-Needleman (GTN) plastic potential, though it could be substituted by almost any other continuum damage model. At the end the presented approach is experimentally validated by a simple springback test, developed by authors. A very good agreement between by calculation predicted and measured springback amount is observed.     

Integration of self-consistent polycrystal plasticity with dislocation density based hardening laws within an implicit finite element framework: Application to low-symmetry metals

We present an implementation of the viscoplastic self-consistent (VPSC) polycrystalline model in an implicit finite element (FE) framework, which accounts for a dislocation-based hardening law for multiple slip and twinning modes at the micro-scale grain level. The model is applied to simulate the macro-scale mechanical response of a highly anisotropic low-symmetry (orthorhombic) crystal structure. In this approach, a finite element integration point represents a polycrystalline material point and the meso-scale mechanical response is obtained by the mean-field VPSC homogenization scheme. We demonstrate the accuracy of the FE-VPSC model by analyzing the mechanical response and microstructure evolution of α-uranium samples under simple compression/tension and four-point bending tests. Predictions of the FE-VPSC simulations compare favorably with experimental measurements of geometrical changes and microstructure evolution. Specifically, the model captures accurately the tension–compression asymmetry of the material associated with twinning, as well as the rigidity of the material response along the hard-to-deform crystallographic orientations.     

Shear stress analysis in engineering beams using deplanation field of special 2-D finite elements

This paper deals with the 2-D finite element shear stress analysis in beams, loaded by bending with shear and St. Venant’s torsion. The properties of these finite elements, like stiffness matrices as well as load vectors, are derived on the basis of their axial nodal displacements, e.g. by warping field. Proposed finite elements enable stress analysis independently of both cross-sectional member shape and material properties. Stiffness matrices and load vectors are derived for several finite element types. Material is assumed to be isotropic and linear elastic. For justification of the proposed stress analysis procedure, some examples are presented.     

Higher-order beam elements based on the absolute nodal coordinate formulation for three-dimensional elasticity

This study thoroughly examines various higher-order three and four-node beam elements for use in the absolute nodal coordinate formulation (ANCF). The paper carefully investigates which potential benefits and drawbacks the utilization of higher-order ANCF beam elements without in-slope vectors has in the case of the usage of full three-dimensional elasticity. When the elastic forces for shear-deformable ANCF beam elements are calculated using full three-dimensional elasticity—especially in the form of the St. Venant–Kirchhoff material law—Poisson locking severely deteriorates the accuracy of the numeric results. As shown in this paper, an existing approach to preventing this locking phenomenon for three-node beam elements can still produce unsatisfying results in load cases involving bidirectional bending. The results of this study show that enriching the polynomial basis used to approximate the beam kinematics provides a natural solution to this issue. As will be seen, these findings for three-node elements can also be extended to four-node elements. When using a sufficient approximation order in transverse directions, satisfying accuracy can be achieved both in conventional one-dimensional bending and in the above-mentioned bidirectional load case.     

Wave equation for generalized Zener model containing complex order fractional derivatives

We study waves in a viscoelastic rod whose constitutive equation is of generalized Zener type that contains fractional derivatives of complex order. The restrictions following from the Second Law of Thermodynamics are derived. The initial boundary value problem for such materials is formulated and solution is presented in the form of convolution. Two specific examples are analyzed.     

Existence of weakly efficient solutions in vector optimization

In this paper, we present an existence result for weak efficient solution for the vector optimization problem. The result is stated for invex strongly compactly Lipschitz functions.     

Non-Stationary Abstract Friedrichs Systems

Inspired by the results of Ern et al. (Commun Partial Differ Equ 32:317–341, 2007) on the abstract theory for Friedrichs symmetric positive systems, we give the existence and uniqueness result for the initial- (boundary) value problem for the non-stationary abstract Friedrichs system. Despite the absence of the well-posedness result for such systems, there were already attempts for their numerical treatment by Burman et al. (SIAM J Numer Anal 48:2019–2042, 2010) and Bui-Thanh et al. (SIAM J Numer Anal 51:1933–1958, 2013). We use the semigroup theory approach and prove that the operator involved satisfies the conditions of the Hille–Yosida generation theorem. We also address the semilinear problem and apply the new results to a number of examples, such as the symmetric hyperbolic system, the unsteady div–grad problem, and the wave equation. Special attention was paid to the (generalised) unsteady Maxwell system.     

Optimal orthogonalization processes

Two optimal orthogonalization processes are devised toorthogonalize,possibly approximately,the columns of a very large and possiblysparse matrix A∈C^n×k.Algorithmically the aim is,at each step,to optimallydecrease nonorthogonality of all the columns of A.One process relies on using translated small rank corrections.Another is a polynomial orthogonalization process forperforming the L?wdin orthogonalization.The steps rely on using iterative methods combined,preferably,with preconditioning which can have a dramatic effect on how fast thenonorthogonality decreases.The speed of orthogonalization depends on howbunched the singular values of A are,modulo the number of steps taken.These methods put the steps of the Gram-Schmidt orthogonalizationprocess into perspective regardingtheir(lack of)optimality.The constructions are entirely operatortheoretic and can be extended to infinite dimensional Hilbert spaces.