Journal
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
Volume 268, Issue -, Pages 801-842Publisher
ELSEVIER SCIENCE SA
DOI: 10.1016/j.cma.2013.10.013
Keywords
Gradient-enhanced damage; Large deformations; Finite element method; Anisotropic biological tissues; Abaqus UEL; Arc-length method
Funding
- Spanish Ministry of Science and Innovation [DPI-2008-03130/DPI]
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A non-local gradient-based damage formulation within a geometrically non-linear setting is presented. The hyperelastic constitutive response at local material point level is governed by a strain energy which is additively composed of an isotropic matrix and of an anisotropic fibre-reinforced material, respectively. The inelastic constitutive response is governed by a scalar [1-d]-type damage formulation, where only the anisotropic elastic part is assumed to be affected by the damage. Following the concept in Dimitrijevic and HackI [28], the local free energy function is enhanced by a gradient-term. This term essentially contains the gradient of the non-local damage variable which, itself, is introduced as an additional independent variable. In order to guarantee the equivalence between the local and non-local damage variable, a penalisation term is incorporated within the free energy function. Based on the principle of minimum total potential energy, a coupled system of Euler-Lagrange equations, i.e., the balance of linear momentum and the balance of the non-local damage field, is obtained and solved in weak form. The resulting coupled, highly non-linear system of equations is symmetric and can conveniently be solved by a standard incremental-iterative Newton-Raphson-type solution scheme. Several three-dimensional displacement- and force-driven boundary value problems-partially motivated by biomechanical application-highlight the mesh-objective characteristics and constitutive properties of the model and illustratively underline the capabilities of the formulation proposed. (C) 2013 Elsevier B.V. All rights reserved.
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