Modeling of cancellous bone has important applications in the detection and treatment of fatigue fractures and diseases like osteoporosis. In this paper, we present a fully coupled multiscale approach considering mechanical, electric and magnetic effects by using the multiscale finite element method and a two-phase material model on the microscale. We show numerical results for both scales, including calculations for a femur bone, comparing a healthy bone to ones affected by different stages of osteoporosis. Here, the magnetic field strength resulting from a small mechanical impact decreases drastically for later stages of the disease, confirming experimental research.
Modeling and simulation have quickly become equivalent pillars of research along with traditional theory and experimentation. The growing realization that most complex phenomena of interest span many orders of spatial and temporal scales has led to an exponential rise in the development and application of multiscale modeling and simulation over the past two decades. In this perspective, the associate editors of the International Journal for Multiscale Computational Engineering and their co-workers illustrate current applications in their respective fields spanning biomolecular structure and dynamics, civil engineering and materials science, computational mechanics, aerospace and mechanical engineering, and more. Such applications are highly tailored, exploit the latest and ever-evolving advances in both computer hardware and software, and contribute significantly to science, technology, and medical challenges in the 21st century.
An important application of simulating wave propagation in bone is the early detection of osteoporosis. During the course of this bone disease cortical bone is reduced and replaced by bone marrow, weakening the bone and increasing the likelihood of fractures [1]. Commonly, in modeling the problem is reduced to only mechanical effects. Recent research includes electrical and magnetic effects as well [2][3][4]. In our previous contributions we introduced a two-phase material model for bone, which considers mechanical, electrical and magnetic effects [5,6].In this contribution we use the introduced material model to perform multiscale simulations of bone. For this purpose we resort to the multiscale finite element method (FE 2 ). To apply this method, we constructed a representative volume element (RVE) incorporating both material phases. We show numerical results of a cylinder model and a true to scale model of a human femur bone.
We outline the mathematical model of the ultrasonic response of wet cortical bone and its time‐harmonic formulation. We employ an energetic approach based on the Reuss bound of the free energy of a porous material consisting of a piezo‐electric solid and a conducting fluid part. Magnetic effects are taken into consideration. Corresponding boundary value problems are stated, and associated theorems are established. A conclusion is included concerning future developments of this formulation.
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