I am a mathematician.I want to understand the physical setting of my problem.
Physical setting. A large variety of situations involving contact phenomena can be cast in the following general physical setting. Let $\Omega$ be a domain in $\mathbb{R}^{d}$ representing the reference configuration of a deformable body which, as a result of actions of body forces and boundary tractions, may come in contact with a rigid or a deformable foundation.
The surface of the body $\Gamma=\partial \Omega$ is assumed to be composed of three parts $\Gamma_{1}, \Gamma_{2}$, and $\Gamma_{3}$, relatively closed with mutually disjoint relatively open interiors. Let $\nu$ be the unit outward normal vector on $\Gamma$. In this chapter we assume that the boundary $\Gamma$ is piecewise smooth so that $\nu$ exists everywhere except at corner points and relations involving $\boldsymbol{\nu}$ are understood to be valid where $\boldsymbol{\nu}$ exists. On $\Gamma_{1}$ the body is held fixed (clamped), on $\Gamma_{2}$ known tractions act and $\Gamma_{3}$ is the potential contact surface. At each time instant $\Gamma_{3}$ is divided into two parts: one part where the body and the foundation are in contact, and the other part where they are separated. The boundary of the contact part is a free boundary, determined by the solution of the problem. For the sake of generality, we assume that in the
reference configuration there exists a gap, denoted by $g=g(\boldsymbol{x})$, between $\Gamma_{3}$ and the foundation, which is measured along the outer normal $\nu$. The setting is depicted in Figure $1.1$.
We are interested in mathematical models that describe the evolution of the mechanical state of the body during the time interval $[0, T], T>0$. To this end, we denote by $\boldsymbol{u}=\boldsymbol{u}(\boldsymbol{x}, t), \boldsymbol{\sigma}=\boldsymbol{\sigma}(\boldsymbol{x}, t)$, and $\boldsymbol{\varepsilon}=\boldsymbol{\varepsilon}(\boldsymbol{u})$ the displacement vector, the stress tensor, and the linearized strain tensor, respectively. The state of the system is completely determined by $(\boldsymbol{u}, \boldsymbol{\sigma})$,
the same problem but without gap
My questions are:
1- they say that the body is clamped on $\Gamma_{1}$ so how the body can move?
2- the forces of tractions , we imagine that there is a person who tracts this body from the side $\Gamma_{2}$ (picture2)?
3-Why the arrow are oriented like that ($f_0$ is is the density of applied forces, such as gravity orelectromagnetic forces)?
4- the body moves from right to left?
