Analysis of Damage Models for Cortical Bone

Abstract

Bone tissue is a material with a complex structure and mechanical properties. Diseases or even normal repetitive loads may cause microfractures to appear in the bone structure, leading to a deterioration of its properties. A better understanding of this phenomenon will lead to better predictions of bone fracture or bone-implant performance. In this work, the model proposed by Frémond and Nedjar in 1996 (initially for concrete structures) is numerically analyzed and compared against a bone specific mechanical model proposed by García et al. in 2009. The objective is to evaluate both models implemented with a finite element method. This will allow us to determine if the modified Frémond–Nedjar model is adequate for this purpose. We show that, in one dimension, both models show similar results, reproducing the qualitative behaviour of bone subjected to typical engineering tests. In particular, the Frémond–Nedjar model with the introduced modifications shows good agreement with experimental data. Finally, some two-dimensional results are also provided for the Frémond–Nedjar model to show its behaviour in the simulation of a real tensile test.

A Damage Model to Trabecular Bone and Similar Materials: Residual Resource, Effective Elasticity Modulus, and Effective Stress under Uniaxial Compression

“…This means that the models of damage and destruction of concrete and other brittle materials [29] can be adapted to analyze the evolution of bone tissue damage. Baldonedo et al [30] draw attention to this possibility. In turn, models of the evolution of damage and destruction of the trabecular bone can be adapted to the analysis of the behavior of bone-like materials [31].…”

“…However, another question remains open: How are the load-displacement, apparent stress-strain, and effective stress-strain dependencies related? To answer this question, we need a corresponding computational model, an acceptable version of which could not be found in the review [4] or in other articles [12,13,19,[30][31][32][33]. The answers to these questions are presented below.…”

Special Issue on “Biomaterials for Bone Tissue Engineering”

“…The authors concluded that the parameters used in the numerical studies shall be applied in future in in vivo validation studies. Baldonedo et al [12] compared the different mathematical models which included the mechanical evolution of bone tissue damage. The models were numerically implemented, using the finite element method, and compared in 1D and 2D geometries.…”

Modelo estocástico de hueso cortical de costilla humana para la predicción de fracturas mediante emisión acústica

“…De esta forma, la longitud de la fisura no podrá ser muy superior al propio espesor cortical 12 que típicamente es de 0,70,9 mm aproximadamente. 79,93 Siendo el tamaño promedio de una osteona de 190 𝜇m, 91 son una media de 4 o 5 las osteonas que tienen cabida en el espesor cortical (en una muestra de tracción uniaxial de geometría coupon, la sección es de 2 mm de ancho y 0,5 mm de espesor).…”