SUMMARYThe mechanical properties of soft biological tissues vary depending on how the internal structure is organized. Classical examples of tissues are ligaments, tendons, skin, arteries, and annulus fibrous. The main element of such tissues is the fibers which are responsible for the tissue resistance and the main mechanical characteristic is their viscoelastic anisotropic behavior. The objective of this paper is to extend an existing model for isotropic viscoelastic materials in order to include anisotropy provided by fiber reinforcement. The incorporation of the fiber allows the mechanical behavior of these tissues to be simulated. The model is based on a variational framework in which its mechanical behavior is described by a free energy incremental potential whose local minimization provides the constraints for the internal variable updates for each load increment. The main advantage of this variational approach is the ability to represent different material models depending on the choice of suitable potential functions. Finally, the model is implemented in a finite-element code in order to perform numerical tests to show the ability of the proposed model to represent fiber-reinforced materials. The material parameters used in the tests were obtained through parameter identification using experimental data available in the literature.

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Summary Fibrous soft biological tissues such as skin, ligaments, tendons, and arteries are non‐homogeneous composite materials composed of fibers embedded in a ground substance. Cyclic tensile tests on these type of materials usually show a hysteretic stress–strain behavior in which strain rate dependence (viscoelasticity) and softening (Mullins' effect) play a coupled role. The main contribution of the present paper is to present unified variational approach to model both coupled phenomena: nonlinear viscoelasticity and Mullins‐like softening behavior. The approach is labeled as variational because viscous‐strain and damage internal variables are updated based on the minimization of a hyperelastic‐like potential that takes a renewed value at each time step. Numerical examples explores (a) the versatility of the proposed model to account for the two described phenomena according to the chosen functions for the free‐energy and dissipative potentials, (b) the ability of the time‐integration scheme embedded in the incremental potential definition to allow for large time increments, and (c) the capability of the model to mimic experimentally obtained stress–strain cyclic curves of soft tissues. The model implementation on standard finite elements is also tested in which symmetric analytic tangent matrices are used as a natural consequence of the variational nature of the proposed approach. Copyright © 2016 John Wiley & Sons, Ltd.

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Structural adhesives are frequently used for applications (mostly in the automotive field) in which they are exposed to dynamic loads at high strain rates, that can cause plastic straining. Thus, such plastic behavior must be included and correctly reproduced by finite element simulations, for instance, to predict the worthiness of the structure against crash conditions. This work makes use of a recently developed general framework for non-linear constitutive models, based on a variational formulation in which, at every load increment, the updates satisfy a minimum principle. The problem is faced in general terms, operating on potentials from which the constitutive equations are obtained; thus different behaviors can be treated by the specific models which are implemented in the potentials. This paper describes the application of this approach to the case of a structural bi-component epoxy adhesive, with the aim of describing its behavior under compression at different test velocities. A widely available data set on compression tests (at strain rate up to 10 3 s −1 ) has been utilized to identify the parameters of the potentials and to evaluate the capability of the models to reproduce the measurements.