相关论文: A new shape optimization approach for fracture pro…

Simulations of fluid flow in naturally fractured rocks have implications for several subsurface applications, including energy storage and extraction, and waste storage. We are interested in flow in discrete fracture networks, which…

Fracture growth in a material is strongly influenced by the presence of inhomogeneities, which deviate crack trajectories from rectilinearity and deeply affect failure. Increasing crack tortuosity is connected to enhancement of fracture…

We optimize a selection of eigenvalues of the Laplace operator with Dirichlet or Neumann boundary conditions by adjusting the shape of the domain on which the eigenvalue problem is considered. Here, a phase-field function is used to…

We introduce a phenomenological continuum model for mode III dynamic fracture that is based on the phase-field methodology used extensively to model interfacial pattern formation. We couple a scalar field, which distinguishes between…

In this work we present the mathematical models for single-phase flow in fractured porous media. An overview of the most common approaches is considered, which includes continuous fracture models and discrete fracture models. For the…

In the present work we introduce a novel graded-material design based on phase-field and topology optimization. The main novelty of this work comes from the introduction of an additional phase-field variable in the classical single-material…

We develop mathematical models for shape design and topology optimization in structural contact problems involving friction between elastic and rigid bodies. The governing mechanical constraint is a nonlinear, non-smooth, and non-convex…

We present a multi-resolution approach for constructing model-based simulations of hydraulic fracturing, wherein flow through porous media is coupled with fluid-driven fracture. The approach consists of a hybrid scheme that couples a…

We investigate fracture toughness of architected interfaces and their ability to maintain structural integrity and provide stable damage propagation conditions beyond the failure load. We propose theoretical and numerical frameworks to…

Fracture is a ubiquitous phenomenon in most composite engineering structures, and is often the responsible mechanism for catastrophic failure. Over the past several decades, many approaches have emerged to model and predict crack failure.…

In this chapter, we investigate recently proposed nonlinear conjugate gradient (NCG) methods for shape optimization problems. We briefly introduce the methods as well as the corresponding theoretical background and investigate their…

The present work is devoted to approximation of the statistical moments of the unknown solution of a class of elliptic transmission problems in $\mathbb R^3$ with randomly perturbed interfaces. Within this model, the diffusion coefficient…

In shape optimisation it is desirable to obtain deformations of a given mesh without negative impact on the mesh quality. We propose a new algorithm using least square formulations of the Cauchy-Riemann equations. Our method allows to…

This study evaluates four widely used fracture simulation methods, comparing their computational expenses and implementation complexities within the Finite Element (FE) framework when employed on heterogeneous solids. Fracture methods…

This paper proposes topology optimization for considering shielding and penetrating features. Based on the fictitious physical model, which is a useful approach to control geometric features, the proposed method analyzes fictitious…

We present a new phase field framework for modelling fracture and fatigue in Shape Memory Alloys (SMAs). The constitutive model captures the superelastic behaviour of SMAs and damage is driven by the elastic and transformation strain energy…

In this work, we develop a framework based on piecewize B\'ezier curves to plane shapes deformation and we apply it to shape optimization problems. We describe a general setting and some general result to reduce the study of a shape…

The phase-field method is reviewed from the general perspective of converting a free boundary problem into a set of coupled partial differential equations. Its main advantage is that it avoids front tracking by using phase fields to locate…

In this work, we describe our contribution to the Purdue-SANDIA-LLNL \emph{Damage Mechanics Challenge}. The phase field fracture model is adopted to blindly estimate the failure characteristics of the challenge test, an unconventional…

Numerical simulations of flow and transport in porous media usually rely on hybrid-dimensional models, i.e., the fracture is considered as objects of a lower dimension compared to the embedding matrix. Such models are usually combined with…