16 research outputs found
Efficient data structures for model-free data-driven computational mechanics
The data-driven computing paradigm initially introduced by Kirchdoerfer & Ortiz (2016) enables finite element computations in solid mechanics to be performed directly from material data sets, without an explicit material model. From a computational effort point of view, the most challenging task is the projection of admissible states at material points onto their closest states in the material data set. In this study, we compare and develop several possible data structures for solving the nearest-neighbor problem. We show that approximate nearest-neighbor (ANN) algorithms can accelerate material data searches by several orders of magnitude relative to exact searching algorithms. The approximations are suggested byâand adapted toâthe structure of the data-driven iterative solver and result in no significant loss of solution accuracy. We assess the performance of the ANN algorithm with respect to material data set size with the aid of a 3D elasticity test case. We show that computations on a single processor with up to one billion material data points are feasible within a few seconds execution time with a speed up of more than 10ⶠwith respect to exact k-d trees
Model-Free Data-Driven Inelasticity
We extend the Data-Driven formulation of problems in elasticity of
Kirchdoerfer and Ortiz (2016) to inelasticity. This extension differs
fundamentally from Data-Driven problems in elasticity in that the material data
set evolves in time as a consequence of the history dependence of the material.
We investigate three representational paradigms for the evolving material data
sets: i) materials with memory, i.e., conditioning the material data set to the
past history of deformation; ii) differential materials, i.e., conditioning the
material data set to short histories of stress and strain; and iii) history
variables, i.e., conditioning the material data set to ad hoc variables
encoding partial information about the history of stress and strain. We also
consider combinations of the three paradigms thereof and investigate their
ability to represent the evolving data sets of different classes of inelastic
materials, including viscoelasticity, viscoplasticity and plasticity. We
present selected numerical examples that demonstrate the range and scope of
Data-Driven inelasticity and the numerical performance of implementations
thereof.Comment: Minor revisions: affiliations, acknowledgment
Gradient-extended brittle damage modeling
An elastic-brittle anisotropic model is presented based on the work by Fassin et al. (2019a). After discussing the local model equations and the incorporation of crack-closure, the gradient extension using the micromorphic approach according to Forest (2009) is briefly summarized. In order to run unit cell simulations on the microlevel, relevant material parameters have to be identified. Therefore, the energy dissipation provides a differential equation with a linear and quadratic term for the damage variable. Finally, the isotropic damage model is used to show numerical examples with variation of fracture toughness and volume fraction of pores
Model-free data-driven computational mechanics enhanced by tensor voting
The data-driven computing paradigm initially introduced by Kirchdoerfer and Ortiz (2016) is extended by incorporating locally linear tangent spaces into the data set. These tangent spaces are constructed by means of the tensor voting method introduced by Mordohai and Medioni (2010) which improves the learning of the underlying structure of a data set. Tensor voting is an instance-based machine learning technique which accumulates votes from the nearest neighbors to build up second-order tensors encoding tangents and normals to the underlying data structure. The here proposed second-order data-driven paradigm is a plug-in method for distance-minimizing as well as entropy-maximizing data-driven schemes. Like its predecessor (Kirchdoerfer and Ortiz, 2016), the resulting method aims to minimize a suitably defined free energy over phase space subject to compatibility and equilibrium constraints. The methodâs implementation is straightforward and numerically efficient since the data structure analysis is performed in an offline step. Selected numerical examples are presented that establish the higher-order convergence properties of the data-driven solvers enhanced by tensor voting for ideal and noisy data sets