Related papers: Rediscovering Hyperelasticity by Deep Symbolic Reg…
The Mullins effect represents a softening phenomenon observed in rubber-like materials and soft biological tissues. It is usually accompanied by many other inelastic effects like for example residual strain and induced anisotropy. In spite…
In this paper, we present a new procedure to automatically generate interpretable hyperelastic material models. This approach is based on symbolic regression which represents an evolutionary algorithm searching for a mathematical model in…
We introduce a data-driven framework to automatically identify interpretable and physically meaningful hyperelastic constitutive models from sparse data. Leveraging symbolic regression, an algorithm based on genetic programming, our…
We present an experimental approach to discriminate hyper-elastic models describing the mechanical behavior of rubber-like materials. An evaluation of the displacement field obtained by digital image correlation allows us to evaluate the…
Identifying governing equations for a dynamical system is a topic of critical interest across an array of disciplines, from mathematics to engineering to biology. Machine learning -- specifically deep learning -- techniques have shown their…
We present an experimental approach to discriminate models describing the mechanical behavior of polymeric materials. A biaxial loading condition is obtained in a multiaxial testing machine. An evaluation of the displacement field obtained…
In this paper we introduce a novel approach to obtain the stored energy density of rubber-like materials directly from experimental data. The model is structure-based, in which the only assumption is the existence of an isotropic…
Many natural materials exhibit highly complex, nonlinear, anisotropic, and heterogeneous mechanical properties. Recently, it has been demonstrated that data-driven strain energy functions possess the flexibility to capture the behavior of…
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…
In this work, we develop Gaussian process regression (GPR) models of hyperelastic material behavior. First, we consider the direct approach of modeling the components of the Cauchy stress tensor as a function of the components of the Finger…
Symbolic regression is emerging as a promising machine learning method for learning succinct underlying interpretable mathematical expressions directly from data. Whereas it has been traditionally tackled with genetic programming, it has…
The mechanical behaviour of isotropic and incompressible vulcanized natural rubbers (NR's) and that of quasi-incompressible carbon black filled vulcanized natural rubbers (NR 70) are considered both theoretically and experimentally. Based…
Machine learning models have become firmly established across all scientific fields. Extracting features from data and making inferences based on them with neural network models often yields high accuracy; however, this approach has several…
Superhard materials with good fracture toughness have found wide industrial applications, which necessitates the development of accurate hardness and fracture toughness models for efficient materials design. Although several macroscopic…
Discovering the underlying mathematical expressions describing a dataset is a core challenge for artificial intelligence. This is the problem of $\textit{symbolic regression}$. Despite recent advances in training neural networks to solve…
Symbolic regression is a machine learning technique that can learn the governing formulas of data and thus has the potential to transform scientific discovery. However, symbolic regression is still limited in the complexity and…
Stress-strain curves, or more generally, stress functions, are an extremely important characterization of a material's mechanical properties. However, stress functions are often difficult to derive and are narrowly tailored to a specific…
We propose a novel deep symbolic regression approach to enhance the robustness and interpretability of data-driven mathematical expression discovery. Our work is aligned with the popular DSR framework which focuses on learning a…
Accurately modeling the friction torque in robotic joints has long been challenging due to the request for a robust mathematical description. Traditional model-based approaches are often labor-intensive, requiring extensive experiments and…
Symbolic regression (SR) aims to discover concise closed-form mathematical equations from data, a task fundamental to scientific discovery. However, the problem is highly challenging because closed-form equations lie in a complex…