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In this study, we have been working within the framework of mathematical characterization of materials with complex behavior, and we used this characterization as input data for simulations in finite elements codes. We have researched the behavior of hyperelastic materials with viscoelastic qualities. There are models for the characterization of this type of materials; however, they lean on parameters that have to be previously determined for each material, and only then, their calculation models can estimate an answer for each material under specific loading conditions. We have focused on the viscoelastic characterization applying Prony series for finite elements simulations. We have developed a procedure to obtain the adequate number of terms of the series as well as the coefficients of characterization from a relaxation spectrum generated by a rheological model. We expect that this new procedure can effectively help researchers in the characterization of materials using Prony series and hence be implemented for later use of it in programs of finite elements.

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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.

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