Related papers: Constitutive Manifold Neural Networks

Machine learning has revolutionized the high-dimensional representations for molecular properties such as potential energy. However, there are scarce machine learning models targeting tensorial properties, which are rotationally covariant.…

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…

Machine learning models can be used to predict physical quantities like homogenized elasticity stiffness tensors, which must always be symmetric positive definite (SPD) based on conservation arguments. Two datasets of homogenized elasticity…

Spatial symmetries and invariances play an important role in the behaviour of materials and should be respected in the description and modelling of material properties. The focus here is the class of physically symmetric and positive…

Plastic anisotropy in metals remains challenging to model. This is partly because conventional phenomenological yield criteria struggle to combine a highly descriptive, flexible representation with constraints, such as convexity, dictated…

For multilayer materials in thin substrate systems, interfacial failure is one of the most challenges. The traction-separation relations (TSR) quantitatively describe the mechanical behavior of a material interface undergoing openings,…

Establishing correspondence between shapes is a fundamental problem in geometry processing, arising in a wide variety of applications. The problem is especially difficult in the setting of non-isometric deformations, as well as in the…

Biological soft tissues exhibit substantial inter-subject variability, making the automation of constitutive material modeling essential for patient-specific analysis and design. Such materials are not only highly nonlinear but also display…

Constitutive models play a crucial role in materials science as they describe the behavior of the materials in mathematical forms. Over the last few decades, the rapid development of manufacturing technologies have led to the discovery of…

Effective thermal conductivity is an important property of composites for different thermal management applications. Although physics-based methods, such as effective medium theory and solving partial differential equation, dominate the…

The representation theory of tensor functions is essential to constitutive modeling of materials including both mechanical and physical behaviors. Generally, material symmetry is incorporated in the tensor functions through a structural or…

Connectomics has emerged as a powerful tool in neuroimaging and has spurred recent advancements in statistical and machine learning methods for connectivity data. Despite connectomes inhabiting a matrix manifold, most analytical frameworks…

We present a novel framework for the probabilistic modelling of random fourth order material tensor fields, with a focus on tensors that are physically symmetric and positive definite (SPD), of which the elasticity tensor is a prime…

We propose tensorial neural networks (TNNs), a generalization of existing neural networks by extending tensor operations on low order operands to those on high order ones. The problem of parameter learning is challenging, as it corresponds…

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…

Data-driven constitutive modeling is an emerging field in computational solid mechanics with the prospect of significantly relieving the computational costs of hierarchical computational methods. Traditionally, these surrogates have been…

We present the Cholesky-factored symmetric positive definite neural network (SPD-NN) for modeling constitutive relations in dynamical equations. Instead of directly predicting the stress, the SPD-NN trains a neural network to predict the…

Divergence-free symmetric tensors (DFSTs) are fundamental in continuum mechanics, encoding conservation laws such as mass and momentum conservation. We introduce Riemann Tensor Neural Networks (RTNNs), a novel neural architecture that…

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…

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…