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FRIEDEL, L. F. O. Analysis of plane structures reinforced with active viscoelastic fibers and matrix with hyperelastic constitutive model: general applications in engineering and biomechanics. 2016. 213p. Dissertação (Mestrado em Engenharia Civil (Estruturas)) Escola de Engenharia de São Carlos, Universidade de São Paulo, São Carlos, 2016. This work presents a formulation for material and geometrical nonlinear analysis of composite materials by immersion of truss finite elements into triangular 2D solid ones using a novel formulation of the finite element method based on positions. This positional formulation uses the shape functions to approximate some quantities defined in the Nonlinear Theory of Elasticity and proposes to describe the specific strain energy and the potential of the external loads as function of nodal positions which are set from a deformation function. Because the nodal positions have current values in each node, this method naturally considers the geometric nonlinearities while the nonlinear relationships between stress and strain may be considered by a pure nonlinear elastic theory called hyperelasticity which allows to obtain linearized constitutive laws in its variational form. If independent meshes are used for the truss elements and for the 2D solid elements, the immersion technique of the trusses adopts shape functions to write the position of any point of a truss as a function of the nodal positions of the 2D solid elements, therefore there is neither an increase in the number of degrees of freedom nor the need that the nodes of the trusses elements coincide with the nodes of the 2D solid elements. Moreover, this work also proposes a positional formulation for the truss elements using a so called nonlinear engineering strain which allows to easily introduce both active and viscous behavior in the immersed truss elements. The proposed formulations are idealized for muscle tissue modeling, however they are not limited only to this type of application. The first 4 chosen examples are simple cases, some of them even with analytical solutions, mainly for validation purposes of the presented formulations. By modeling a structure formed by an arm and an forearm, the 5 and last example shows the potentialities of the concepts and proposed formulations during this work.

Análise de estruturas planas reforçadas com fibras ativas viscoelásticas e matriz com modelo constitutivo hiperelástico: aplicações gerais em engenharia e biomecânica