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The mathematical formulation of constitutive models to describe the path-dependent, i.e., inelastic, behavior of materials is a challenging task and has been a focus in mechanics research for several decades. There have been increased…
In the present work, a hyperelastic constitutive model based on neural networks is proposed which fulfills all common constitutive conditions by construction, and in particular, is applicable to compressible material behavior. Using…
The major challenge in determining a hyperelastic model for a given material is the choice of invariants and the selection how the strain energy function depends functionally on these invariants. Here we introduce a new data-driven…
Anisotropy in the mechanical response of materials with microstructure is common and yet is difficult to assess and model. To construct accurate response models given only stress-strain data, we employ classical representation theory, novel…
Developing robust constitutive models is a fundamental and longstanding problem for accelerating the simulation of complicated physics. Machine learning provides promising tools to construct constitutive models based on various calibration…
We propose a neural network framework to preclude the need to define or observe incompletely or inaccurately defined states of a material in order to describe its response. The neural network design is based on the classical Coleman-Gurtin…
In solid mechanics, Data-driven approaches are widely considered as the new paradigm that can overcome the classic problems of constitutive models such as limiting hypothesis, complexity, and high dependence on training data. However,…
Model-free data-driven computational mechanics replaces phenomenological constitutive functions by numerical simulations based on data sets of representative samples in stress-strain space. The distance of strain and stress pairs from the…
Data-driven methods have changed the way we understand and model materials. However, while providing unmatched flexibility, these methods have limitations such as reduced capacity to extrapolate, overfitting, and violation of physics…
We develop a new neural network architecture that strictly enforces constitutive constraints such as polyconvexity, frame-indifference, and the symmetry of the stress and material stiffness. Additionally, we show that the accuracy of the…
We apply physics-augmented neural network (PANN) constitutive models to experimental uniaxial tensile data of rubber-like materials whose behavior depends on manufacturing parameters. For this, we conduct experimental investigations on a 3D…
We study large deformations of hyperelastic membranes using a purely two-dimensional formulation derived from basic balance principles within a modern geometric setting, ensuring a framework that is independent of an underlying…
We present a data-driven framework for the multiscale modeling of anisotropic finite strain elasticity based on physics-augmented neural networks (PANNs). Our approach allows the efficient simulation of materials with complex underlying…
Machine learning approaches informed by physics have offered new insights into the discovery of constitutive models from data, helping overcome some limitations of traditional constitutive modelling while reducing the cost of otherwise…
Modeling the full-range deformation behaviors of materials under complex loading and materials conditions is a significant challenge for constitutive relations (CRs) modeling. We propose a general encoder-decoder deep learning framework…
Data-driven turbulence modeling studies have reached such a stage that the fundamental framework is basically settled, but several essential issues remain that strongly affect the performance, including accuracy, smoothness, and…
In a finite element analysis, using a large number of grids is important to obtain accurate results, but is a resource-consuming task. Aiming to real-time simulation and optimization, it is desired to obtain fine grid analysis results…
A novel data-driven constitutive modeling approach is proposed, which combines the physics-informed nature of modeling based on continuum thermodynamics with the benefits of machine learning. This approach is demonstrated on…
This paper explores the application of tensor networks (TNs) to the simulation of material deformations within the framework of linear elasticity. Material simulations are essential computational tools extensively used in both academic…
Wrinkling is the phenomenon of out-of-plane deformation patterns in thin walled structures, as a result of a local compressive (internal) loads in combination with a large membrane stiffness and a small but non-zero bending stiffness.…