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In this paper, we develop a framework for solving inverse deformation problems using the FEniCS Project finite element software. We validate our approach with experimental imaging data acquired from a soft silicone beam under gravity. In…
The phase field fracture method has emerged as a promising computational tool for modelling a variety of problems including, since recently, hydrogen embrittlement and stress corrosion cracking. In this work, we demonstrate the potential of…
The implementation of finite element methods (FEMs) for nonlocal models with a finite range of interaction poses challenges not faced in the partial differential equations (PDEs) setting. For example, one has to deal with weak forms…
Lightweight, single-use explosion containment structures provide an effective solution for neutralizing rogue explosives, combining affordability with ease of transport. This paper introduces a three-stage simulation framework that captures…
A framework for simulation of dynamics of mechanical aggregates has been developed. This framework enables us to build model of aggregate from models of its parts. Framework is a part of universal framework for science and engineering.
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…
Animal cells are both encapsulated and subdivided by lipid bilayer membranes. Beyond just acting as boundaries, these membranes' shapes influence the function of cells and their compartments. Physically, membranes are two-dimensional fluids…
This paper presents a novel particle method to compute strongly coupled incompressible fluid and rigid bodies. The method adopts a velocity-based formulation and utilizes the linear complementarity problem for the incompressibility…
We consider the problem of shaping the transient step response of nonlinear systems to satisfy a class of integral constraints. Such constraints are inherent in hybrid energy systems consisting of energy sources and storage elements. While…
Residual stresses may appear in elastic bodies due to the formation of misfits in the micro-structure, driven by plastic deformations, thermal or growth processes. They are especially widespread in living matter, resulting from the dynamic…
This paper presents a shape-theoretic framework for dynamical analysis of nonlinear dynamical systems which appear frequently in several video-based inference tasks. Traditional approaches to dynamical modeling have included linear and…
The formulation of rheological constitutive equations -- models that relate internal stresses and deformations in complex fluids -- is a critical step in the engineering of systems involving soft materials. While data-driven models provide…
Multiphysics incompressible fluid dynamics simulations play a crucial role in understanding intricate behaviors of many complex engineering systems that involve interactions between solids, fluids, and various phases like liquid and gas.…
This study introduces the concept of finite element network analysis (FENA) which is a physics-informed, machine-learning-based, computational framework for the simulation of complex physical systems. The framework leverages the extreme…
The cytoskeleton -- a collection of polymeric filaments, molecular motors, and crosslinkers -- is a foundational example of active matter, and in the cell assembles into organelles that guide basic biological functions. Simulation of…
We propose and explore a new, general-purpose method for the implicit time integration of elastica. Key to our approach is the use of a mixed variational principle. In turn its finite element discretization leads to an efficient alternating…
Materials exhibit geometric structures across mesoscopic to microscopic scales, influencing macroscale properties such as appearance, mechanical strength, and thermal behavior. Capturing and modeling these multiscale structures is…
This work presents a modeling framework to represent the thermomechanical behavior of complex materials based on micromechanical dynamics. The framework is applied to nuclear fuel rod elements composed of Zircaloy-2 cladding tubes and…
Disordered network materials abound in both nature and synthetic situations while rigorous analysis of their nonlinear mechanical behaviors still is very challenging. The purpose of this paper is to connect the mathematical framework of…
We present a theory for the elasticity of cross-linked stiff polymer networks. Stiff polymers, unlike their flexible counterparts, are highly anisotropic elastic objects. Similar to mechanical beams stiff polymers easily deform in bending,…