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Theory of Stress
Published in Prasun Kumar Nayak, Mijanur Rahaman Seikh, Continuum Mechanics, 2022
Prasun Kumar Nayak, Mijanur Rahaman Seikh
Surface force: Those forces which act upon and are distributed in some fashion over a surface element of the body, regardless of whether that element is part of the bounding surface, or an arbitrary element of surface within the body, are called surface forces or contact forces. Surface forces, expressed as force per unit area, can act either on the bounding surface of the body, as a result of mechanical contact with other bodies, or on imaginary internal surfaces that bound portions of the body, as a result of the mechanical interaction between the parts of the body to either side of the surface.
Fundamentals of Elasto-Plastic Mechanics
Published in Yichun Zhou, Li Yang, Yongli Huang, Micro- and MacroMechanical Properties of Materials, 2013
Yichun Zhou, Li Yang, Yongli Huang
Surface forces are forces acting on a free body at its bounding surface, such as fluid pressure and contact force. The surface force at each point on the surface of the object is usually different.
Conservation Equations
Published in Krishnan Murugesan, Modeling and Simulation in Thermal and Fluids Engineering, 2023
In the momentum equations, the left-hand side of the equation indicates the force due to the acceleration of the fluid flowing through the control volume. In that, the first term corresponds to the rate of change of momentum of the fluid with time within the control volume, and the second term refers to the next efflux of momentum of fluid in the control volume. The total change of momentum of the fluid on the left-hand side must be equal to the net forces acting on the fluid control volume. The net forces acting on the fluid are shown on the right-hand side of the equation. These forces are surface forces and body force. Surface forces consist of forces due to normal and tangential stresses. The normal stress is equated to the pressure of fluid in motion and the tangential forces to viscous forces developed by the viscosity of the fluid and its velocity gradient in the flow field. The body force is directly proportional to the volume of the fluid, and hence forces such as buoyancy due to thermal and concentration gradients or magnetic force contribute to this term. The solution of Equations (2.65) and (2.66) confirms velocity and pressure fields which are obtained after satisfying mass conservation and momentum balance of the fluid in the control volume in all three directions. It is worth considering the units of these equations. For the continuity equation, the density term is ignored in the equation because it is constant. Hence if Equation (2.65) is multiplied by density of fluid, then the unit comes to be kgs(m3), the mass flow rate per unit volume of the control volume. In the momentum Equation (2.66), all the terms on the left-hand side of the equation correspond to Nm3, that is force per unit volume. Similarly, all the terms on the right-hand side of the equation give rise to Nm3, thus the momentum conservation equation simply indicates the force balance on the fluid element in a given flow domain. It has to be noted that only through force balance in the fluid domain is the velocity field obtained, however, all the force terms appearing in the momentum balance equations are written in terms of velocities and velocity gradients with knowledge of some of the relevant and measurable fluid characteristics.
Thermomechanical response of nonlinear viscoelastic materials
Published in Journal of Thermal Stresses, 2023
A. Khoeini, A. Imam, M. Najafi
In addition, an external body force acting on the body and an internal surface force are assumed to exist. It is noted here that is called the traction vector acting on the boundary at the particle at time but measured per unit area of with outward unit normal vector Adopting the ordinary conservation laws of the single-phase continuum mechanics for momentum and moment of momentum for every material part of occupying a region in the reference configuration, it follows that [25], where is the area element of .
Thermomechanical coupling multi-objective topology optimization of anisotropic structures based on the element-free Galerkin method
Published in Engineering Optimization, 2022
Jianping Zhang, Tingxian Liu, Shusen Wang, Shuguang Gong, Jiangpeng Peng, Qingsong Zuo
The governing equation of linear elastic problems for anisotropic structures is given as where is the prescribed body force in domain , is the prescribed surface force on , is the prescribed displacement on , is the surface force boundary, and is the displacement boundary.
Seepage analysis of a diversion tunnel with high pressure in different periods: a case study
Published in European Journal of Environmental and Civil Engineering, 2018
Tao Wang, Wanrui Hu, Hegao Wu, Wei Zhou, Kai Su, Long Cheng
Understanding the behaviour of inner water is a critical problem in the investigation of the seepage field around a high-pressure tunnel. To address this problem, two major theories are proposed, namely, the surface force theory and the body force theory. To calculate the stress in the lining and the surrounding rock, the former theory is based on the assumptions that the lining is impermeable and considers the internal water pressure to be a surface force, whereas the latter theory assumes that the lining is permeable and considers the internal water pressure to be a body force. According to the observed results from the practical projects, the lining is cracked when the internal water pressure exceeds 1.5 MPa (Wei, 2010); the resulting permeability increases significantly. The inner water is driven into the crack due to high water pressure and directly acts on the lining and surrounding rock. The basic assumptions in the surface force theory do not satisfy the facts, whereas the body force theory is a more appropriate choice (Schleiss, 1997). Therefore, the calculations in this paper are based on the body force theory.