• Corpus ID: 239049623

DeepBND: a Machine Learning approach to enhance Multiscale Solid Mechanics

  title={DeepBND: a Machine Learning approach to enhance Multiscale Solid Mechanics},
  author={Felipe F. Rocha and Simone Deparis and Pablo Antolin and Annalisa Buffa},
Effective properties of materials with random heterogeneous structures are typically determined by homogenising the mechanical quantity of interest in a window of observation. The entire problem setting encompasses the solution of a local PDE and some averaging formula for the quantity of interest in such domain. There are relatively standard methods in the literature to completely determine the formulation except for two choices: i) the local domain itself and the ii) boundary conditions… 


Data driven approximation of parametrized PDEs by Reduced Basis and Neural Networks
This work proposes to accomplish the approximation of partial differential equations with a data-driven approach based on the reduced basis method and machine learning with a neural network embedding a reduced basis solver as exotic activation function in the last layer.
Material spatial randomness: From statistical to representative volume element☆
Abstract The material spatial randomness forces one to re-examine various basic concepts of continuum solid mechanics. In this paper we focus on the Representative Volume Element (RVE) that is
Convergence and error analysis of FE-HMM/FE2 for energetically consistent micro-coupling conditions in linear elastic solids
Abstract A cornerstone of numerical homogenization is the equivalence of the microscopic and the macroscopic energy densities, which is referred to as Hill–Mandel condition. Among these coupling
The local microscale problem in the multiscale modeling of strongly heterogeneous media: Effects of boundary conditions and cell size
This problem is systematically investigated in the present paper in the context of modeling strongly heterogeneous media, and a mixed Dirichlet-Neumann boundary condition that is often used in porous medium modeling is discussed.
Variational Foundations and Generalized Unified Theory of RVE-Based Multiscale Models
A unified variational theory is proposed for a general class of multiscale models based on the concept of Representative Volume Element. The entire theory lies on three fundamental principles: (1)
Aspects of Computational Homogenization at Finite Deformations: A Unifying Review From Reuss' to Voigt's Bound
The objective of this contribution is to present a unifying review on strain-driven computational homogenization at finite strains, thereby elaborating on computational aspects of the finite element
Multi-scale modelling of arterial tissue: Linking networks of fibres to continua
Abstract In this work we develop a multi-scale model to characterise the large scale constitutive behaviour of a material featuring a small scale fibrous architecture. The Method of Multi-scale
The heterogeneous multiscale finite element method for the homogenization of linear elastic solids and a comparison with the FE2 method
Abstract The Heterogeneous Multiscale Finite Element Method (FE-HMM) is a two-scale FEM based on asymptotic homogenization for solving multiscale partial differential equations. It was introduced in
A multilevel finite element method (FE2) to describe the response of highly non-linear structures using generalized continua
A general method called FE2 has been introduced which consists in describing the behavior of heterogeneous structures using a multiscale finite element model. Instead of trying to build differential
A Selection of Benchmark Problems in Solid Mechanics and Applied Mathematics
In this contribution we provide benchmark problems in the field of computational solid mechanics. In detail, we address classical fields as elasticity, incompressibility, material interfaces, thin