A regularization technique for the XFEM: extension to finite deformations,inelastic material behaviour and multifield problems

Within the XFEM often near linear dependencies between the standard degrees of freedom and enriched degrees of freedom and also among enriched degrees of freedom occur. During the last years, several remedies to that problem have been presented. Here, an extension of the regularization technique described in [1] to finite deformation problems and inelastic material behaviour as well as to multifield problems is proposed. © 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Mathematical modeling of flows through inelastic porous solids

We propose a framework, based on classical mixture theory, to describe the isothermal flow of an incompressible fluid through a deformable inelastic porous solid. The modeling of the behavior of the inelastic solid takes into account changes in the elastic response due to evolution in the microstructure of the material. We apply the model to a compression layer problem. The mathematical problem generated by the model is a free boundary problem.     

Microinhomogeneity of a medium as the basis for general methods of modeling the inelastic deformation of a material and a structure

We construct a structural mathematical model for describing the process of inelastic deformation of structural alloys with an arbitrary repeated-variable loading.Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 27, 1988, pp. 67–71.     

Formulation of the material force approach for elastic and inelastic materials

Fracture mechanical investigations are important for the durability of fracture sensitive products. Fracture mechanical simulations help to shorten the product development cycle and to decrease product costs. The so-called material force approach as an efficient tool is used to determine fracture mechanical parameters for elastic and inelastic materials. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Micro-mechanical modeling of anisotropic inelastic response of soft tissues under supra-physiological loading

Under supra-physiological loading, soft tissues exhibit many inelastic phenomena, such as stress softening, hysteresis and permanent set [1]. Knowledge of the mechanical response of soft tissues under such a large range of deformation is vital for optimizations of vascular medical devices or improvement of injury prevention techniques. In this work, a micro-mechanical model is proposed for soft collagenous tissues. Besides the anisotropy the model can also describe the aforementioned inelastic effects under extremal loadings. To this end, the dispersion of collagen fibers in the soft tissues is captured by a probability distribution of fiber orientations around preferred directions. The deformation induced damage inside the tissue is assumed to take place between collagen fibrils and is included within a statistical mechanical framework. Finally, the accuracy of the model is assessed by comparison with experimental data available in the literature. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On quasistatic inelastic models of gradient type with convex composite constitutive equations

This article defines and presents the mathematical analysis of a new class of models from the theory of inelastic deformations of metals. This new class, containing so called convex composite models, enlarges the class containing monotone models of gradient type defined in [1]. This paper starts to establish the existence theory for models from this new class; we restrict our investigations to the coercive and linear self-controlling case.     

Creep damage modeling of a polycrystalline material

A polycrystalline material is investigated under creep conditions within the framework of continuum micromechanics. Geometrical 3D model of a polycrystalline microstructure is represented as a unit cell with grains of random crystallographical orientation and shape. Thickness of the plains, separating neighboring grains in the unit cell, can have non-zero value. Obtained geometry assigns a special zone in the vicinity of grain boundaries, possessing unordered crystalline structure. A mechanical behavior of this zone should allow sliding of the adjacent grains. Within the grain interior crystalline structure is ordered, what prescribes cubic symmetry of a material. The anisotropic material model with the orthotropic symmetry is implemented in ABAQUS and used to assign elastic and creep behavior of both the grain interior and grain boundary material. Appropriate parameters set allows transition from the orthotropy to the cubic symmetry for the grain interior. Material parameters for the grain interior are identified from creep tests for single crystal copper. Model parameters for the grain boundary are set from the physical considerations and numerical model validation according to the experimental data of the grain boundary sliding in a polycrystalline copper [2]. As the result of analysis representative number of grains and grain boundary thickness in the unit cell are recommended. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

One dynamic model of a composite material

A model has been constructed for the propagation of waves orthogonally to the layers or fibers of a composite material and based on the Voltaire equation of state with oscillating kernels. The results of treatment of experimental data are presented.M. V. Lomonosov Moscow State University. Translated from Mekhanika Polimerov, No. 2, pp. 364–367, March–April, 1976.     

On the variationally consistent modeling of material failure

Material failure associated with cracks or shear bands is frequently analyzed by utilizing so-called cohesive models. Such models are based on traction-separation laws. Within such approaches, the stress vector of the considered crack or shear band is related to its conjugate variable being the respective displacement jump (such as the material separation or the crack opening). In the present work, a framework suitable for the analysis of shear bands is discussed. All models belonging to that framework are consistently derived from thermodynamical principles. Hence, the second law of thermodynamics is automatically fulfilled. Furthermore, a variational principle strongly relying on the postulate of maximum dissipation is elaborated leading finally to a variationally consistent implementation. More precisely, all state variables, together with the unknown deformation mapping, follow naturally from minimizing an incrementally defined potential within the presented algorithmic formulation. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)