PSI - Issue 25

G.M. Eremina et al. / Procedia Structural Integrity 25 (2020) 470–476

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G.M. Eremina et al./ Structural Integrity Procedia 00 (2019) 000–000

the treatment of severe stages, in which local areas of cartilage destruction appear, endoprosthesis is used (Brennan Olsen et al., 2017). Endoprosthetic hip arthroplasty can be total, in which the proximal part of the femur bone is removed and then replaced with an implant (Evans et al., 2019). With resurfacing arthroplasty, only the damaged layer of the femoral head is turned over and the casing cap is put on. Resurfacing arthroplasty is preferable for young people with an active lifestyle (Koutras et al., 2015). To select a design of the endoprosthesis, it is necessary to take into account the personalized characteristics of the patient; however, it is not possible to do this in the laboratory. Also, it is necessary to accurately determine the range of physical activity that should not damage the composition of the bone tissue and the implant, and will also contribute to good osteointegration of the implant into a living human body (Naal et al., 2007). In the modern world, computer modeling has been actively using for studying the mechanical behavior of the bone endoprosthesis system. Using this research method, the implant design can be selected taking into account all the characteristics of a person without health risks. Many papers are devoted to modeling the mechanical behavior of the system “bone - endoprosthesis”. But most of them consider total hip replacement endoprosthesis; the resurfacing endoprosthesis remains an area that still has been poorly studied using theoretical approaches. In these works, much attention is paid to the selection of design; however, the loading conditions are set quite abstractly, which in turn does not make it possible to study the mechanical behavior at different physical activities (Putzer et. Al., 2018, Todo et al., 2018). Besides, most works consider bone tissue just as an elastic body (Shieh et al., 2012, Kuhl et al., 2005). However, in reality, living bone tissue is a fluid-saturated material. The presence of physiological liquid has a great influence on the mechanical behavior of the material. The first consideration of bone tissue as a fluid-saturated poroelastic medium is given by Cowin (1999). Since that time such an approach has been actively being developed. The goal of this work is a numerical study of the mechanical behavior of the system “femur bone-endoprosthesis” under low-intensity physiological loads in the framework of computer simulation based on a poroelastic bone tissue model. 2. Simulation 2.1. Movable cellular automaton method for poroelastic body For simulating the mechanical behavior of the bone materials, we use the particle-based method of movable cellular automata (Shilko et al., 2015, Smolin et al., 2018) A simulated body is represented by an ensemble of bonded equiaxial discrete elements of the same size (called movable cellular automata), which position, orientation, and state can change due to interaction with neighbors. Automata interact with each other through their contacts. The initial value of the contact area, as well as the volume, is determined by the size of automata and their packing. When describing the kinematics and dynamics of an automaton motion, its shape is approximated by an equivalent sphere. This approximation is the most widely used in the discrete element method and allows one to consider the forces of central and tangential interaction of elements as formally independent. This makes also possible to use the simplified Newton-Euler equations of motion. Movable automata are treated as deformable. Strains and stresses are assumed to be uniformly distributed in the volume of each automaton. Within the framework of this approximation, the values of averaged stresses in the automaton volume may be calculated as the superposition of forces applied to different parts of the automaton surface. In other words, averaged stress tensor components are expressed in terms of the interaction forces with neighbors:           i N j ij ij ij ij i i ij i t f n Ω R S 1 0 0        (1)

where i is the automaton number, i

  is the component  of the averaged stress tensor,  ,  = x , y,z ( XYZ is the

global coordinate system), ij S is the initial value of the contact area between the automata i and j , R i is the radius of the equivalent sphere (semi-size of automaton i ), f ij and  ij are specific values of central and tangential forces of interaction between the automata i and j ,    ij n  and    ij t  are the projections 0 i  is the initial volume of the automaton i , 0