# Composite material with random wrinkle ## Overview This model implements the 3D anisotropic linear elasticity equations for a composite part with randomised wrinkle. The maximum deflection of the part is estimated by embedding a wrinkle into a high fidelity FE simulation using the high performance toolbox dune-composites. ![Composite-Model](https://raw.githubusercontent.com/UM-Bridge/benchmarks/main/docs/source/images/femodel_new.png "Composite part with wrinkle") ## Authors [Anne Reinarz](mailto:anne.k.reinarz@durham.ac.uk) ## Run ``` docker run -it -p 4242:4242 linusseelinger/model-dune-composites:latest ``` ## Properties Model | Description ---|--- forward | Linear elasticity ### forward Mapping | Dimensions | Description ---|---|--- input | [346000] | Coefficients of a Karhunen Loeve expansion of a wrinkle. output | [1] | Maximum deflection of the composite part. Feature | Supported ---|--- Evaluate | True Gradient | False ApplyJacobian | False ApplyHessian | False Config | Type | Default | Description ---|---|---|--- ranks | int | 2 | Number of MPI ranks (i.e. parallel processes) to be used. stack | string | "example2.csv" | Path to the stacking sequence to be run. ## Mount directories Mount directory | Purpose ---|--- None | ## Source code [Model sources here.](https://github.com/UM-Bridge/benchmarks/tree/main/models/dune-composites) ## Description In the simulation the composite strength of a corner part with a wrinkle is modeled and the maximum deflection is returned. The stacking sequence of the composite corner part can be set using the "stack" configuration parameter, by default a 12 layer setup is used. A simplified model for a 3D bending test was used. The curved composite parts were modelled with shortened limbs of length 10 mm. A unit moment was applied to the end of one limb using a multi-point constraint, with homogeneous Dirichlet conditions applied at the end of the opposite limb. This gives the same stress field towards the apex of the curved section as a full 3D bending test. The analysis assumes standard anisotropic 3D linear elasticity and further details on the numerical model and discretisation can be found in [1]. The wrinkle defect is defined by a deformation field $W:\Omega \rightarrow \mathbb R^3$ mapping a composite component from a pristine state to the defected state. The wrinkles are defined by the wrinkle functions $$ W(x,\xi) = g_1(x_1)g_3(x_3)\sum_{i=1}^{N_w} a_i f_i(x_1,\lambda), $$ where $g_i(x_i)$ are decay functions , $f_i(x_1,\lambda)$ are the first $N_w$ Karhunen-Lo\'{e}ve (KL) modes parameterized by the length scale $\lambda$ and $a_i$ the amplitudes. The amplitude modes and the length scale can be taken as random variables, so that the stochastic vector is defined by $\boldsymbol \xi = [a_1,a_2,\ldots,a_{N_w},\lambda]^T$. The wrinkles are prismatic in $x_2$, e.g. the wrinkle function is assumed to have no $x_2$ dependency. For more details on the wrinkle representation see [2]. ## References - [1] Anne Reinarz, Tim Dodwell, Tim Fletcher, Linus Seelinger, Richard Butler, Robert Scheichl, *Dune-composites – A new framework for high-performance finite element modelling of laminates*, Composite Structures, 2018. - [2] Anhad Sandhu and Anne Reinarz and Tim Dodwell, *A Bayesian framework for assessing the strength distribution of composite structures with random defects*, Composite Structures, 2018.