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In this paper, the finite volume method is developed to analyze coupled dynamic problems of nonlinear thermoelasticity. The major focus is given to the description of martensitic phase transformations essential in the modelling of shape…
This paper presents a homogenization framework for elastomeric metamaterials exhibiting long-range correlated fluctuation fields. Based on full-scale numerical simulations on a class of such materials, an ansatz is proposed that allows to…
This work is concerned with the micro-architecture of multi-layer material that globally exhibits desired mechanical properties, for instance a negative apparent Poisson ratio. We use inverse homogenization, the level set method, and the…
This work presents a matrix-free finite element solver for finite-strain elasticity adopting an $hp$-multigrid preconditioner. Compared to classical algorithms relying on a global sparse matrix, matrix-free solution strategies significantly…
Ab initio atomic relaxations often take large numbers of steps and long times to converge. An atomic relaxation method based on on-the-flight force learning and a corresponding new curved line minimization algorithm is presented to…
Stochastic optimization algorithms update models with cheap per-iteration costs sequentially, which makes them amenable for large-scale data analysis. Such algorithms have been widely studied for structured sparse models where the sparsity…
The failure of heterogeneous materials with microstructures is a complex process of damage nucleation, growth and localisation. This process spans multiple length scales and is challenging to simulate numerically due to its high…
In this paper, we present a Constraint Energy Minimizing Generalized Multiscale Finite Element Method (CEM-GMsFEM) for parabolic equations with multiscale coefficients, arising from applications in porous media. We will present the…
Computational experiments are exploited in finding a well-designed processing path to optimize material structures for desired properties. This requires understanding the interplay between the processing-(micro)structure-property linkages…
A multiscale asymptotic homogenization method for periodic microstructured materials in presence of thermoelasticity with periodic spatially dependent one relaxation time is introduced. The asymptotic expansions of the micro-displacement…
We establish a time-stepping learning algorithm and apply it to predict the solution of the partial differential equation of motion in micromagnetism as a dynamical system depending on the external field as parameter. The data-driven…
A class of algorithms for the solution of discrete material optimization problems in electromagnetic applications is discussed. The idea behind the algorithm is similar to that of the sequential programming. However, in each major iteration…
In the setting of continuum elasticity martensitic phase transformations are characterized by a non-convex free energy density function that possesses multiple wells in strain space and includes higher-order gradient terms for…
This work presents an efficient algorithm for generating statistically representative microstructures of particulate composites in periodic representative volume elements. The Swelling and Random Migration (SRM) algorithm combines…
We propose a new approach for controlling the characteristics of certain mesh faces during optimization of high-order curved meshes. The practical goals are tangential relaxation along initially aligned curved boundaries and internal…
In this work, we have developed a multiscale computational algorithm to couple finite element method with an open source molecular dynamics code --- the Large scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) --- to perform…
A supervised machine learning (ML) based computational methodology for the design of particulate multifunctional composite materials with desired thermal conductivity (TC) is presented. The design variables are physical descriptors of the…
The Reynolds equation, combined with the Elrod algorithm for including the effect of cavitation, resembles a nonlinear convection-diffusion-reaction (CDR) equation. Its solution by finite elements is prone to oscillations in…
Understanding material surfaces and interfaces is vital in applications like catalysis or electronics. By combining energies from electronic structure with statistical mechanics, ab initio simulations can in principle predict the structure…
Nature-inspired stochastic metamaterials with disordered and multiscale architectures have shown great promise towards extraordinary functionalities, including high mechanical resilience, stress modulation and biased stiffness…