Abstract
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.
Highlights
We develop a multiscale model for cancellous bone taking mechanical, electric and magnetic effects into account
Electric and magnetic effects are coupled via the Maxwell equations
We present a fully coupled multiscale model for cancellous bone considering mechanical, electric and magnetic effects
Summary
We develop a multiscale model for cancellous bone taking mechanical, electric and magnetic effects into account. Applications of the finite element method (FEM) on the topic of bone modeling include the simulation of mechanical properties of bone (Gardner et al 2000; Miller et al 2002) and the simulation of osteogenic effects (Wang et al 2017). We present a fully coupled multiscale approach for modeling cancellous bone considering mechanical, electric and magnetic effects and using two scales, the macro- and microscale. Based on energy methods in mechanics, we establish a thermodynamically consistent material model and derive the weak and strong form of the corresponding boundary value problem. 4 we present numerical results, starting with microscale calculations, on to multiscale simulations for a cylindrical body and a true to scale model of a human femur bone.
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