Related papers: Learning nonlocal constitutive models with neural …

Accurate constitutive models of soft materials are crucial for understanding their mechanical behavior and ensuring reliable predictions in the design process. To this end, scientific machine learning research has produced flexible and…

Modeling nonlinear spatiotemporal dynamical systems has primarily relied on partial differential equations (PDEs). However, the explicit formulation of PDEs for many underexplored processes, such as climate systems, biochemical reaction and…

Modeling the traffic dynamics is essential for understanding and predicting the traffic spatiotemporal evolution. However, deriving the partial differential equation (PDE) models that capture these dynamics is challenging due to their…

Driven by the need to accelerate numerical simulations, the use of machine learning techniques is rapidly growing in the field of computational solid mechanics. Their application is especially advantageous in concurrent multiscale finite…

Constitutive modeling lies at the core of mechanics, allowing us to map strains onto stresses for a material in a given mechanical setting. Historically, researchers relied on phenomenological modeling where simple mathematical…

Neural network modules conditioned by known priors can be effectively trained and combined to represent systems with nonlinear dynamics. This work explores a novel formulation for data-efficient learning of deep control-oriented nonlinear…

For more than 100 years, chemical, physical, and material scientists have proposed competing constitutive models to best characterize the behavior of natural and man-made materials in response to mechanical loading. Now, computer science…

We propose a novel approach to model viscoelasticity materials using neural networks, which capture rate-dependent and nonlinear constitutive relations. However, inputs and outputs of the neural networks are not directly observable, and…

Data-driven models based on deep learning algorithms intend to overcome the limitations of traditional constitutive modelling by directly learning from data. However, the need for extensive data that collate the full state of the material…

Embeddings provide low-dimensional representations that organize complex function spaces and support generalization. They provide a geometric representation that supports efficient retrieval, comparison, and generalization. In this work we…

Accurately modeling the mechanical behavior of materials is crucial for numerous engineering applications. The quality of these models depends directly on the accuracy of the constitutive law that defines the stress-strain relation.…

Microstructural evolution is a key aspect of understanding and exploiting the structure-property-performance relation of materials. Modeling microstructure evolution usually relies on coarse-grained simulations with evolution principles…

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…

Constitutive modelling is crucial for engineering design and simulations to accurately describe material behavior. However, traditional phenomenological models often struggle to capture the complexities of real materials under varying…

We study a class of nonlocal, energy-driven dynamical models that govern the motion of closed, embedded curves from both an energetic and dynamical perspective. Our energetic results provide a variety of ways to understand physically…

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…

The calibration of solid constitutive models with full-field experimental data is a long-standing challenge, especially in materials which undergo large deformation. In this paper, we propose a physics-informed deep-learning framework for…

We present a computational technique for modeling the evolution of dynamical systems in a reduced basis, with a focus on the challenging problem of modeling partially-observed partial differential equations (PDEs) on high-dimensional…

A nonlocal subgrid-scale stress (SGS) model is developed based on the convolution neural network (CNN), a powerful supervised data-driven approach. The CNN is an ideal approach to naturally consider nonlocal spatial information in…

Elasticity images map biomechanical properties of soft tissues to aid in the detection and diagnosis of pathological states. In particular, quasi-static ultrasonic (US) elastography techniques use force-displacement measurements acquired…