On higher complexity for interface/contact laws with arbitrary anisotropy - development of numerical models and their experimental validations.

在最一般的情况下，在物体的接触相互作用中观察到各种性质的力，例如弹性力、粘弹性力、塑性力。这些力反映了粗糙表面的真实结构和属性。滑动摩擦力和所谓的粘附力是描述接触相互作用的主要力学特征。它们表示2D表面本构关系，类似于3D连续体的弹塑性。建立各种界面接触定律(除了众所周知的库仑摩擦定律之外)的一个关键是基于弹性、塑性、粘性等已知本构关系以完全非线性形式的适当组合。这些组合可以根据导致以协变形式的任意表面度规表示的最大耗散原理的主要热力学原理来获得。这导致了一套先验稳定的数值算法，包括法向和切向解耦相互作用的各种组合。该项目的重点将放在切向本构关系上，其中弹性区域的方程--以非线性形式--表示切向粘结--反映表面结构--塑性定律，也是以非线性形式，表示摩擦相互作用。该项目的一个重要问题是基于均化和多尺度技术的验证。对于微观层面，采用具有一定全局几何结构的具有精确粗糙度的模型，而将所得到的表面界面模型作为宏观层面的平均模型，以实现可用于大规模计算的模型。将提供一系列实验，以确定所开发的平均模型的全局宏观特征，如粘着张量和摩擦张量的结构。

Forces of various nature, e.g. elastic, viscoelastic, plastic forces, are observed during the contact interaction of bodies in the most general case. These forces are reflecting the real structure and the properties of a rough surface. Sliding friction forces and so-called adhesion forces are the main me-chanical characteristics to describe contact interaction. They are representing 2D surface constitutive laws in analogy to elasto-plasticity for 3D continuum. A key to the generalization of the construction of various interface contact laws (besides e.g. the well known Coulomb friction law) is based on proper combinations of known constitutev relations for elasticity, plasticity, viscosity etc. in completely nonlinear form. These combinations can be obtained with regards to main thermodynamical principles leading to the principle of maximum dissipation expressed in the arbitrary surface metrics in covariant form. This leads to a set of a-priory stable numerical algorithms including various combinations of the decoupled interaction in both normal and tangential directions. The focus in the project will be on constitutive relations in the tangential direction, where equations for the elastic region – in nonlinear form – represent the tangential adhesion – reflecting the surface structure – and plastic laws, also in nonlinear form, represent frictional interaction. An important issue of the project is the verification based on homogenization and multi-scale tchniques. For the micro-level a model with exact asperities possessing a certain global geometrical structure is taken while the derived surface interface model is taken as an average model for the macro-level to achieve a model usable in large scale computations. A set of experiments will be provided to define global macro-characteristics of the developed averaged model such as the structures of the adhesion tensor as well as of the friction tensor.