A gradient-enhanced large-deformation continuum damage model for fibre-reinforced materials

By Tobias Waffenschmidt, César Polindara, Andreas Menzel, S. Blanco. 2014

140 citations recorded by the source corpus.

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 Hackl [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.

Subfields: Biomedical Engineering, Materials Chemistry, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/2d4bc86a5f325aaed6805653e32a46af110057eb

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In Biomedical Engineering

1. Tobias Waffenschmidt
2. L. Sprave
3. B. Kiefer
4. Andreas Menzel

In Materials Chemistry

1. L. Sprave
2. B. Kiefer
3. Andreas Menzel
4. Tobias Waffenschmidt

In Mechanics of Materials

1. Tobias Waffenschmidt
2. L. Sprave
3. B. Kiefer
4. Andreas Menzel

Citations in the corpus

• A gradient-enhanced damage model coupled to plasticity—multi-surface formulation and algorithmic concepts (2018, methodology): “Moreover, alternative approaches of deriving thermodynamically constitutive equations in the generalized setting (Waffenschmidt et al., 2014), start from the non-negativity of the total temperature-weighted production of entropy for an isothermal process”