5 papers
Compression of Polyconvex Envelopes of Isotropic Functions via Monotonic Input Convex Neural Networks
Timo Neumeier, Julian Salmon
This work presents a novel neural-network compression approach for polyconvex envelopes of isotropic functions. The approach relies on a classical sufficient criterion for polyconv…
Neural Network Enhanced Polyconvexification of Isotropic Energy Densities in Computational Mechanics
Loïc Balazi, Timo Neumeier, Malte A. Peter +1
We present a neural network approach for fast evaluation of parameter-dependent polyconvex envelopes, which are crucial in computational mechanics. Our method uses a neural network…
Hierarchical Rank-One Sequence Convexification for the Relaxation of Variational Problems with Microstructures
Maximilian Köhler, Timo Neumeier, Malte. A. Peter +2
This paper presents an efficient algorithm for the approximation of the rank-one convex hull in the context of nonlinear solid mechanics. It is based on hierarchical rank-one seque…
Computational polyconvexification of isotropic functions
Timo Neumeier, Malte A. Peter, Daniel Peterseim +1
Based on the characterization of the polyconvex envelope of isotropic functions by their signed singular value representations, we propose a simple algorithm for the numerical appr…
Multidimensional rank-one convexification of incremental damage models at finite strains
Daniel Balzani, Maximilian Köhler, Timo Neumeier +2
This paper presents computationally feasible rank-one relaxation algorithms for the efficient simulation of a time-incremental damage model with nonconvex incremental stress potent…