Related papers: A phase field approach to trabecular bone remodeli…
Phase-field models of fracture introduce smeared cracks of width commensurate with a regularisation length parameter $\epsilon$ and obeying a minimum energy principle. Mesh adaptivity naturally suggests itself as a means of supplying…
The present endeavor numerically exploits the use of a phase-field model to simulate and investigate fracture patterns, deformation mechanisms, damage, and mechanical responses in a human vertebra after the incision of pedicle screws under…
A new class of micromechanically motivated chain network models for soft biological tissues is presented. On the microlevel, it is based on the statistics of long chain molecules. A wormlike chain model is applied to capture the behavior of…
This contribution presents a diffuse framework for modeling cracks in heterogeneous media. Interfaces are depicted by static phase-fields. This concept allows the use of non-conforming meshes. Another phase-field is used to describe the…
We study dendritic microstructure evolution using an adaptive grid, finite element method applied to a phase-field model. The computational complexity of our algorithm, per unit time, scales linearly with system size, rather than the…
Fracture is a ubiquitous phenomenon in most composite engineering structures, and is often the responsible mechanism for catastrophic failure. Over the past several decades, many approaches have emerged to model and predict crack failure.…
A continuum density-field formulation with particle-scale resolution is constructed to simultaneously incorporate the orientation dependence of interparticle interactions and the rotational invariance of the system, a fundamental but…
The multiscale simulation of heterogeneous materials is a popular and important subject in solid mechanics and materials science due to the wide application of composite materials. However, the classical FE2 (finite element2) scheme can be…
Many bone shapes in the human skeleton are characterized by profiles that can be associated to equations of algebraic curves. Fixing the parameters in the curve equation, by means of a classical pattern recognition procedure like the Hough…
Pharmaceutical treatments can slow bone degradation, thus reducing the fracture risk inherent in osteoporosis. Antiresorptive treatments block the over-activation of osteoclasts vs osteoblasts, but the resulting decrease in bone remodeling…
We apply recently introduced measures of complexity for the structural quantfication of distal tibial bone. For the first time, we are able to investigate the temporal structural alteration of trabecular bone. Based on four patients, we…
The phase field model is a widely used mathematical approach for describing crack propagation in continuum damage fractures. In the context of phase field fracture simulations, adaptive finite element methods (AFEM) are often employed to…
Bone is a biomaterial undergoing continuous renewal. The renewal process is known as bone remodelling and is operated by bone-resorbing cells (osteoclasts) and bone-forming cells (osteoblasts). Both biochemical and biomechanical regulatory…
This paper addresses the modeling of fracture in quasi-brittle materials using a phase-field approach to the description of crack topology. Within the computational mechanics community, several studies have treated the issue of modeling…
A cost functional involving the eigenvalues of an elastic structure, that is described by a multi-phase-field equation, is optimized. This allows us to handle topology changes and multiple materials. We prove continuity and…
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, electrical and…
We consider a simple one-dimensional time-dependent model for bone regeneration in the presence of a bio-resorbable polymer scaffold. Within the framework of the model, we optimize the effective mechanical stiffness of the polymer scaffold…
This paper deals with the simulateneous optimization of a subset $\mathcal{O}_0$ of some domain $\Omega$ and its complement $\mathcal{O}_1 = \Omega \setminus \overline{\mathcal{O}}_0$ both considered as separate elastic objects subject to a…
A moving mesh finite element method is studied for the numerical solution of a phase-field model for brittle fracture. The moving mesh partial differential equation approach is employed to dynamically track crack propagation. Meanwhile, the…
We propose a multiscale mechanobiological model of bone remodelling to investigate the site-specific evolution of bone volume fraction across the midshaft of a femur. The model includes hormonal regulation and biochemical coupling of bone…