An asymptotic method in contact problems

A modification of the “smal λ” singular asymptotic method of solving the integral equations of mixed problems in continuum mechanics [1] is proposed in the case of a special behaviour of the symbol of the kernel encountered, for example, in contact problems of the theory of elasticity for cylindrical and conical bodies [2–4]. Contact problems for elastic cylindrical bodies are considered as an example.     

连续体力学中有限变形与转动的计算增量法

目前在非线性弹塑性力学计算中常用的经典非线性大变形理论由于内在的数学缺点,当变形量与转动很大时.往往误差达到不许可的程度.本文采用作者的有限变形力学理论表述了增量法.在作者与尚勇、谢和平联合研究的另二篇论文中,详细叙述这个新方法在工程中的应用,结果证明从微小变形过渡到大变形,计算结果总是可以满意地符合实验.     

The effect of crack faces contact interaction on the critical strain in composites under compressive loading

Aviation and aerospace structural components made of composite laminates due to their internal structure and manufacturing methods often contain a number of inter- and intra-component defects which size, dispersion and interaction alter significantly the critical compression strain level [1]. The current study investigates the effect of the cracks interaction and crack faces contact interaction on the critical strain in laminar transversally isotropic material (cross-ply) compressed in a static manner along interlaminar defects. The frictionless Hertzian contact and the shear and extensional mode of stability loss are considered for the interacting crack faces. The statement of the problem is based on the most accurate approach, the model of piecewise-homogenous medium and the 3-D stability theory [2]. The moment of stability loss in the microstructure of material is treated as the onset of the fracture process. The complex non-classical fracture mechanics problem is solved utilizing the finite elements analysis. The results are obtained for the typical dispositions of cracks. It was found that the crack faces contact interaction alter significantly the critical strain level of the composite. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Rotationless formulation for large deformations in flexible multibody dynamics

Especially for specific applications, such as contact problems, computer methods for flexible multibody dynamics that are able to treat large deformation phenomena are important. Classical formalisms for multibody dynamics are based on rigid bodies. Their extension to flexible multibody systems is typically restricted to linear elastic material behavior whereas large deformation phenomena are formulated in the framework of the nonlinear finite element method. In the talk we address computer methods that can handle large deformations in the context of multibody systems. In particular, the link between nonlinear continuum mechanics and multibody systems is facilitated by a specific formulation of rigid body dynamics [1]. It makes possible the incorporation of state-of-the-art computer methods for large deformation problems. In the talk we focus on the treatment of large deformation contact whithin flexible multibody dynamics [2]. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Different weak FE‐formulations for 2‐D frictionless Large Deformation Contact based on the Mortar Method

The application of the mortar method in contact mechanics is motivated by the limited use of well known elements, for example the node‐to‐segment (NTS) element, see [1]. The NTS element contains a strong projection of the displacements from one contacting body to the next. Coupling of this element type with higher order shape functions leads to a loss of accuracy of contact stresses. In contrast to this, the mortar element has the advantage of a weak projection. Therefore, consistent coupling with continuum elements of higher order is possible. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Simulation of ice under mechanical and thermal load

The contact physics of the wheel-rail contact of a railway vehicle under presence of water and ice at low temperatures is still not completely understood. For the investigation of the particular process in the contact zone a simulation is required, which is able to calculate the normal and tangential contact, the temperature field and the fluid-structural interaction between wheel and rail at low temperatures under presence of snow and ice. For that purpose the behaviour of ice under wheel-rail contact conditions is an important part. In this paper the thermal dynamic model of TSHIJOV [1], [3] for an adiabatic ice probe is updated by the new IAPWS equations of state for water [5] and ice phase Ih [4]. In a first approximation an ice specimen is loaded by specific wheel-rail contact pressure distributions calculated by the half-space formulation to clarify if phase transitions of ice can exist. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Poincaré非线性振动理论在连续介质力学中的推广(Ⅱ)——若干应用

文本是文[1]的继续.文[1]中,提出和建议使用非线性偏微分方程直接摄动与加权积分方程法,计算连续介质系统的共振与非共振周期解.本文中,应用该方法计算了定跨度弹性梁在各种常见边界条件下强迫振动的共振与非共振周期解,方板在集中周期荷载作用下的共振周期解.指出了,非主振型对非线性振动周期解的影响及静荷载对幅频特性曲线的影响.     

Towards Phase Field Modeling of Ductile Fracture in Gradient-Extended Elastic-Plastic Solids

The modeling of failure in ductile metals must account for complex phenomena at a micro-scale as well as the final rupture at the macro-scale. Within a top-down viewpoint, this can be achieved by the combination of a micro-structure-informed elastic-plastic model with a concept for the modeling of macroscopic crack discontinuities. In this context, it is important to account for material length scales and thermo-mechanical coupling effects due to dissipative heating. This can be achieved by the construction of non-standard, gradient-enhanced models of plasticity with a full embedding into continuum thermodynamics [1,2]. The modeling of macroscopic cracks can be achieved in a convenient way by recently developed continuum phase field approaches to fracture based on regularized crack discontinuities. This avoids the use of complex discretization methods for crack discontinuities, and can account for complex crack patterns within a pure continuum formulation. Moreover, the phase field modeling of fracture is related to gradient theories of continuum damage mechanics, and fits nicely the structure of constitutive models for gradient plasticity. The main focus of this work is the extensions to gradient thermoplasticity and phase field formulation of ductile fracture, conceptually in line with the work [3]. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A thermodynamically consistent model of shape-memory alloys

This contribution presents a non-isothermal mesoscopic model of single-crystalline shape-memory alloys within the framework of continuum mechanics. We briefly recall static mesoscopic modeling concepts as presented in e.g. [4, 5] and propose a thermomechanically consistent model featuring the heat equation and thermo-mechanical coupling. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Molecular statical calculation of graphene sheet buckling

We study the buckling behaviour of a single rectangular graphene layer by a molecular mechanics force field approach. The so called MM3–Potential [1] is used to model the atomistic interactions. The global minimum of the total potential energy is calculated for a prescribed linear displacement field at the edges of the plate. Various buckled configurations depending on the dimension of the plate are calculated and are compared with results from continuum mechanics. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Three-dimensional continuum mechanical modeling of the Portevin-Le Châtelier effect

In many Al, Cu, Fe and Ni based alloys jerky flow associated with the Portevin-Le Châtelier (PLC) effect occurs within a specific range of temperatures and strain-rates. This effect which reduces the ductility and the surface quality of sheet materials is caused by dynamic interaction of mobile dislocations with solute atoms [1]. A three-dimensional continuum mechanical model of this effect, also known as dynamic strain ageing, is presented. Furthermore, the predictions of the three-dimensional model are compared with experimental data. Special emphasis is put on the determination of the instability region in the strain and strain-rate space [2]. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The theory of infinite-dimensional lie groups and its applications

The purpose of this paper is to survey the theory of regular Fréchet-Lie groups developed in [1–10]. Such groups appear and are useful in symplectic geometry and the theory of primitive infinite groups of Lie and Cartan [11]. From the group theoretical standpoint, general relativistic mechanics is a more closed system than Newtonian mechanics. Quantized objects of these classical groups are closely related to the group of Fourier integral operators [12]. These can also be managed as regular Fréchet-Lie groups. However, there are many Fréchet-Lie algebras which are not the Lie algebras of regular Fréchet-Lie groups [13]. Thus, the enlargeability of the Poisson algebra is discussed in detail in this paper. Enlargeability is relevant to the global hypoellipticity [14, 15] of second-order differential operators.     

Regularization of 2D frictional contacts for rigid body dynamics

Classic rigid body mechanics does not provide frictional forces acting in a 2D contact interface between two bodies during sticking. This is due to the statical undeterminacy related with this problem. Many technical systems, e.g. disk clutches, have such surface-to-surface contacts and it is sometimes desirable to treat them as rigid body systems despite the 2D contact. Alternatively it is possible to model the systems using elastic instead of rigid bodies, but this might lead to certain drawbacks. Here a new regularization model of such 2D contacts between rigid bodies is proposed. It is derived from a material model for elasto-plasticity in continuum mechanics. Only dry friction is taken into account. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On coupled problems in geomechanics

Geomechanical problems are generally based on the category of granular, cohesive-frictional materials with a fluid pore content. At the macroscopic scale of continuum mechanics, these materials can be successfully described on the basis of the well-founded Theory of Porous Media (TPM) [1]. The present contribution touches fundamental problems of coupled media by investigating the interacting behaviour of an elasto-viscoplastic porous solid skeleton, the soil, and two pore fluids, water and air. Furthermore, electro-chemical reactions are considered in order to include the swelling behaviour of active soil. In conclusion, this leads to a system of strongly coupled partial differential equations (PDE) that can be solved by use of the finite element method (FEM). In particular, the presentation includes fluid-flow situations in the fully or the partially saturated range, swelling phenomena of active clay [3] as well as localisation phenomena [2] as a result of fluid flow or heavy rainfall events. The computations are carried out by use of the single-processor FE tool PANDAS [4] and, in case of large 3-d problems, by coupling PANDAS with the multi-processor solver M++. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Towards thermomechanics of fractal media

Hans Ziegler’s thermomechanics [1,2,3], established half a century ago, is extended to fractal media on the basis of a recently introduced continuum mechanics due to Tarasov [14,15]. Employing the concept of internal (kinematic) variables and internal stresses, as well as the quasiconservative and dissipative stresses, a field form of the second law of thermodynamics is derived. In contradistinction to the conventional Clausius–Duhem inequality, it involves generalized rates of strain and internal variables. Upon introducing a dissipation function and postulating the thermodynamic orthogonality on any lengthscale, constitutive laws of elastic-dissipative fractal media naturally involving generalized derivatives of strain and stress can then be derived. This is illustrated on a model viscoelastic material. Also generalized to fractal bodies is the Hill condition necessary for homogenization of their constitutive responses.     

Towards thermomechanics of fractal media

Hans Ziegler’s thermomechanics [1,2,3], established half a century ago, is extended to fractal media on the basis of a recently introduced continuum mechanics due to Tarasov [14,15]. Employing the concept of internal (kinematic) variables and internal stresses, as well as the quasiconservative and dissipative stresses, a field form of the second law of thermodynamics is derived. In contradistinction to the conventional Clausius–Duhem inequality, it involves generalized rates of strain and internal variables. Upon introducing a dissipation function and postulating the thermodynamic orthogonality on any lengthscale, constitutive laws of elastic-dissipative fractal media naturally involving generalized derivatives of strain and stress can then be derived. This is illustrated on a model viscoelastic material. Also generalized to fractal bodies is the Hill condition necessary for homogenization of their constitutive responses.