Related papers: Advances in polyconvex anisotropic hyperelasticity
We investigate representations of Coxeter groups into $\mathrm{GL}(n,\mathbb{R})$ as geometric reflection groups which are convex cocompact in the projective space $\mathbb{P}(\mathbb{R}^n)$. We characterize which Coxeter groups admit such…
A fundamental theorem of Laman characterises when a bar-joint framework realised generically in the Euclidean plane admits a non-trivial continuous deformation of its vertices. This has recently been extended in two ways. Firstly to…
Experiments have reached a monumental capacity for designing and synthesizing microscopic particles for self-assembly, making it possible to precisely control particle concentrations, shapes, and interactions. However, more physical insight…
We propose a decomposition of constitutive relations into crack-driving and persistent portions, specifically designed for materials with anisotropic/orthotropic behavior in the phase field approach to fracture to account for the…
Two new approaches to solving first-order quasilinear elliptic systems of PDEs in many dimensions are proposed. The first method is based on an analysis of multimode solutions expressible in terms of Riemann invariants, based on links…
We take the fundamental group of the complement of the branch curve of a generic projection induced from canonical embedding of a surface. This group is stable on connected components of moduli spaces of surfaces. Since for many classes of…
Mechanical densification of granular bodies is a process in which a loose material becomes increasingly cohesive as the applied pressure increases. A constitutive description of this process faces the formidable problem that granular and…
We extend the incremental potential contact (IPC) model for contacting elastodynamics to resolve systems composed of codimensional DOFs in arbitrary combination. This enables a unified, interpenetration-free, robust, and stable simulation…
We address a three-dimensional model capable of describing coupled damage and plastic effects in solids at finite strains. Formulated within the variational setting of {\it generalized standard materials}, the constitutive model results…
Classically, the constitutive behavior of materials is described either phenomenologically, or by homogenization approaches. Phenomenological approaches are computationally very efficient, but are limited for complex non-linear and…
We present a methodology for designing a generalized dual potential, or pseudo potential, for inelastic Constitutive Artificial Neural Networks (iCANNs). This potential, expressed in terms of stress invariants, inherently satisfies…
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…
The existence of the theory of `twisted cotangent bundles' (symplectic groupoids) allows to study classical mechanical systems which are generalized in the sense that their configurations form a Poisson manifold. It is natural to study from…
This paper introduces a novel approach that combines Proper Orthogonal Decomposition (POD) with Thermodynamics-based Artificial Neural Networks (TANN) to capture the macroscopic behavior of complex inelastic systems and derive macroelements…
Symmetry packaging is the phenomenon whereby, upon particle creation, all the internal quantum numbers (IQNs) become locked into a single irreducible representation (irrep) block of the gauge group, as required by locality and gauge…
In the paper we consider convex cones in infinite-dimensional real vector spaces which are endowed with no topology. The main purpose is to study an internal geometric structure of convex cones and to obtain an analytical description of…
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…
Effective and accurate characterization and quantification of complex microstructure of a heterogeneous material and its evolution under external stimuli are very challenging, yet crucial to achieving reliable material performance…
This paper reports a novel result: with proper robot models on matrix Lie groups, one can formulate the kinodynamic motion planning problem for rigid body systems as \emph{exact} polynomial optimization problems that can be relaxed as…
Incorporating known symmetries in data into machine learning models has consistently improved predictive accuracy, robustness, and generalization. However, achieving exact invariance to specific symmetries typically requires designing…