Multiplicative, Non-Newtonian Viscoelasticity Models for Rubber Materials and Brain Tissues: Numerical Treatment and Comparative Studies

In many aspects, elastomers and soft biological tissues exhibit similar mechanical properties such as a pronounced nonlinear stress–strain relation and a viscoelastic response to external loads. Consequently, many models use the same rheological framework and material functions to capture their behavior. The viscosity function is thereby often assumed to be constant and the corresponding free energy function follows that one of the long-term equilibrium response. This work questions this assumption and presents a detailed study on non-Newtonian viscosity functions for elastomers and brain tissues. The viscosity functions are paired with several commonly used free energy functions and fitted to two different types of elastomers and brain tissues in cyclic and relaxation experiments, respectively. Having identified suitable viscosity and free energy functions for the different materials, numerical aspects of viscoelasticity are addressed. From the multiplicative decomposition of the deformation gradient and ensuring a non-negative dissipation rate, four equivalent viscoelasticity formulations are derived that employ different internal variables. Using an implicit exponential map as time integration scheme, the numerical behavior of these four formulations are compared among each other and numerically robust candidates are identified. The fitting results demonstrate that non-Newtonian viscosity functions significantly enhance the fitting quality. It is shown that the choice of a viscosity function is even more important than the choice of a free energy function and the classical neo-Hooke approach is often a sufficient choice. Furthermore, the numerical investigations suggest the superiority of two of the four viscoelasticity formulations, especially when complex finite element simulations are to be conducted

Effect of the yield surface evolution on the earing defect prediction

Although the prediction of earing in the cup drawing process is considerably related to the yield surface shape, the yield surface evolution is also essential for the final ear form. The bending-unbending issue is a fundamental subject occurring on the die and punch shoulders. Since the yield stress is loading path dependent in reversal loadings, the conventional hardening models used in the monotonic loading conditions bring about inaccurate outcomes for predicting the ultimate earing profile, and a kinematic hardening model should be incorporated into the constitutive equations. This study elucidates the yield surface evolution effect involving expansion and translation simultaneously on the ear formation. A sixth-order polynomial yield function was employed to precisely characterize the yield surface shape, while a combined isotropic-kinematic hardening model was implemented to represent the evolution of the yield surface. The translation of the yield surface position was defined by the Armstrong-Frederic hardening model. Punch force-stroke responses and the ear form profiles were predicted by the implemented plasticity model in Marc using the Hypela2 user subroutine and compared with the experimental results. The combined hardening assumption yielded an increase in the mean cup height when compared to the isotropic hardening assumption. Moreover, The HomPol6 coupled with the combined hardening showed a better agreement with the experimental results

STRESS COMPUTATION ALGORITHM FOR TEMPERATURE DEPENDENT NON-LINEAR KINEMATIC HARDENING MODEL

In this work, we derive a stress algorithm for a non-linear kinematic hardening model. The algorithm is implemented in a FEM code. On a simple shear test, we compare the numerical results with the analytical ones

Modelação numérica do comportamento assimétrico do betão

Mestrado em Engenharia CivilEste trabalho descreve um modelo de simulação do comportamento do betão, por analogia a testes tecnológicos com o magnésio, uma vez que são materiais com comportamento mecânico semelhante. O critério de cedência de Cazacu tem sido muito utilizado na modelação numérica de estruturas com ligas de Magnésio, apresentando, do mesmo modo, um comportamento assimétrico para estados de tração e de compressão. Deste modo, pretende-se implementar o critério de cedência de Cazacu em programa de elementos finitos (através de “user subroutines”) e avaliar a capacidade do critério em reproduzir o comportamento de estruturas em betão. A validação numérica do critério será primeiro verificada pela comparação entre os resultados experimentais provenientes de ensaios de tração e compressão do betão e a simulação numérica de elementos estruturais isolados e estruturas mais complexas de betão.This work describes a model for the simulation of the concrete behaviour using the analogy equivalent studies performed with magnesium, given that goth materials exhibit a similar mechanical behaviour. For the purpose, the Cazacu yield criterion was used in the numerical modelling of structures in magnesium alloys, also presenting a nonsymmetric constitutive behaviour in tensile or compression testing. This way, the objective is to implement a Cazacu yield criterion in a Finite element program, as a “user defined” subroutine and investigate the capacity of the so designed criterion in reproducing the behaviour at the structures. The numerical validation of this criterion needs a first comparison with experimental data from standard tensile or compression testing and the numerical simulation of single structural elements from more complex concrete structures

Geometry- and load-specific optimization of the collagen network's fibre orientation in the lumbar spine's annulus fibrosus

In Europe, low back pain (LBP) affects the quality of life of up to 30% of the active population. Although the origin of LBP is not well identified and is probably not unique, epidemiological studies suggest that the severity of the disease is correlated with mechanical factors. The lumbar spine is a complex structure where bone, cartilage, ligaments, and muscles have specific and functional mechanical interactions that depend on the shape and structure of each tissue. Thus, any local tissue abnormality may generate non-physiological loadings on surrounding tissues, extending or catalysing a pre-existing degenerative process. To date, lumbar spine finite element modelling is one of the most promising methods to thoroughly investigate functional load transfers between the different spine tissues. However, many geometrical or mechanical parameters used for tissue modelling are still not quantified and need to be assumed. Previous computational studies demonstrated that the intervertebral disc (IVD) plays a key role in distributing the internal forces across the lumbar spine structure. Within the IVD, together with the nucleus pulposus (NP) pressure, the annulus fibrosus (AF) collagen organization is one of the most influential parameter for the disc stabilization. However, AF collagen organization is not unique and seems to depend on the particularity of spine morphologies. Therefore, any lumbar spine model based on particular geometrical data would require specific definitions of fibre-induced AF anisotropy. Unfortunately, particular AF anisotropies are hardly measurable. Thus, the present project aims to investigate the stabilization of a L4-L5 lumbar spine bi-segment finite element model as a function of the AF fibre orientations. For this, a mathematical function, based on local AF matrix shear strains, fibre stresses and fibre stress distribution has been proposed. In this function was implemented and was partially validated on smaller AF model. Enhancements could be proposed and be applied to the L4-L5 model. Methods and procedure to optimize annulus AF orientations could be validated. The proposed evaluation function had to be changed. It was found that an optimal orientation depends mainly on fibre stress and matrix shear stress. The optimizations converged to average angles between 32 and 68 and radial gradients between 10 and 17 degree. Tangential gradients could not be found. Moreover a critical fibre angle could be determined where fibre under uni-axial load are not loaded any more. Using literature data it was possible to solve one of the main issues of collagen fibre orientations in the AF and to bring together the two hypothesis of either a only radial or only a tangential gradient. Moreover it was concluded that pre-stress respectively hoop stress is an nonnegligible factor which has to be accounted for in IVD finite element models