Related papers: An iterative nonlocal residual constitutive model …
A consistent stress-driven nonlocal integral model for nonisothermal structural analysis of elastic nano- and microbeams is proposed. Most nonlocal models of literature are strain-driven and it was shown that such approaches can lead toward…
Engineering problems frequently require solution of governing equations with spatially-varying discontinuous coefficients. Even for linear elliptic problems, mapping large ensembles of coefficient fields to solutions can become a major…
Within the framework of linear elasticity we assume the availability of internal full-field measurements of the continuum deformations of a non-homogeneous isotropic solid. The aim is the quantitative reconstruction of the associated…
Classically, the mechanical response of materials is described through constitutive models, often in the form of constrained ordinary differential equations. These models have a very limited number of parameters, yet, they are extremely…
The purpose of this research is to describe an efficient iterative method suitable for obtaining high accuracy solutions to high frequency time-harmonic scattering problems. The method allows for both refinement of local polynomial degree…
We consider Riesz' fractional gradient and a truncated version of it. The equations of nonlocal nonlinear elasticity based on those gradients are known. We perform a formal linearization and arrive at the equations of linear elasticity…
We review the theoretical bounds on the effective properties of linear elastic inhomogeneous solids (including composite materials) in the presence of constituents having non-positive-definite elastic moduli (so-called negative-stiffness…
Filled rubber-like materials are widely used in engineering applications and are well known to exhibit the Mullins effect. In this work, an established local constitutive model from the literature is extended to a non-local setting to…
We introduce an iterative method to solve problems in small-strain non-linear elasticity, termed ``Phase-Space Iterations'' (PSIs). The method is inspired by recent work in data-driven computational mechanics, which reformulated the classic…
A dual-continuum model can offer a practical approach to understanding first-order behaviours of poromechanically coupled multiscale systems. To close the governing equations, constitutive equations with models to calculate effective…
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…
We analyze one-dimensional discrete and quasi-continuous linear chains of $N>>1$ equidistant and identical mass points with periodic boundary conditions and generalized nonlocal interparticle interactions in the harmonic approximation. We…
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…
Commonly used linear and nonlinear constitutive material models in deformation simulation contain many simplifications and only cover a tiny part of possible material behavior. In this work we propose a framework for learning customized…
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…
Curved beams are basic structural components of Nano-Electro-Mechanical-Sistems (NEMS) whose design requires appropriate modelling of scale effects. In the present paper, the size-dependent static behaviour of curved elastic nano-beams is…
For monodomain nematic elastomers, we construct generalised elastic-nematic constitutive models combining purely elastic and neoclassical-type strain-energy densities. Inspired by recent developments in stochastic elasticity, we extend…
In this work, we extend the existing framework of inelastic constitutive artificial neural networks (iCANNs) by incorporating plasticity to increase their applicability to model more complex material behavior. The proposed approach ensures…
Recent advances in physics-augmented neural networks have enabled thermodynamically consistent data-driven constitutive modeling of complex inelastic materials. Most existing approaches, however, implicitly adopt a specific thermodynamic…
The size-dependent bending behavior of nano-beams is investigated by the modified nonlocal strain gradient elasticity theory. According to this model, the bending moment is expressed by integral convolutions of elastic flexural curvature…