A multiscale high-cycle fatigue-damage model for the stiffness degradation of fiber-reinforced materials based on a mixed variational framework

Under fatigue-loading, short-fiber reinforced thermoplastic materials typically show a progressive degradation of the stiffness tensor. The stiffness degradation prior to failure is of primary interest from an engineering perspective, as it determines when fatigue cracks nucleate. Efficient modeling of this fatigue stage allows the engineer to monitor the fatigue-process prior to failure and design criteria which ensure a safe application of the component under investigation. We propose a multiscale model for the stiffness degradation in thermoplastic materials based on resolving the fiber microstructure. For a start, we propose a specific fatigue-damage model for the matrix, and the degradation of the thermoplastic composite arises from a rigorous homogenization procedure. The fatigue-damage model for the matrix is rather special, as its convex nature precludes localization, permits a well-defined upscaling, and is thus well-adapted to model the phase of stable stiffness degradation under fatigue loading. We demonstrate the capabilities of the full-field model by comparing the predictions on fully resolved fiber microstructures to experimental data. Furthermore, we introduce an associated model-order reduction strategy to enable component-scale simulations of the local stiffness degradation under fatigue loading. With model-order reduction in mind and upon implicit discretization in time, we transform the minimization of the incremental potential into an equivalent mixed formulation, which combines two rather attractive features. More precisely, upon order reduction, this mixed formulation permits precomputing all necessary quantities in advance, yet, retains its well-posedness in the process. We study the characteristics of the model-order reduction technique, and demonstrate its capabilities on component scale. Compared to similar approaches, the proposed model leads to improvements in runtime by more than an order of magnitude

Computationally Efficient Concurrent Multiscale Framework for the Nonlinear Analysis of Composite Structures

This paper presents a computationally efficient concurrent multiscale platform to undertake the nonlinear analysis of composite structures. The framework exploits refined 1D models developed within the scheme of the Carrera Unified Formulation (CUF), a generalized hierarchical formulation that generates refined structural theories via a variable kinematic description. CUF operates at the macro and microscale, and the macroscale interfaces with a nonlinear micromechanical toolbox. The computational efficiency derives from the ability of the CUF to obtain accurate 3D-like stress fields with a reduced computational cost. The nonlinearity is at the matrix level within the microscale, and its effect scales up to the macroscale through homogenization. The macro tangent matrix adopts a perturbation-based method to have meliorated performances. The numerical results demonstrate that the framework requires some $50$ of the computational time and $10$ of memory usage of traditional 3D finite elements (FE). Very detailed local effects at the microscale are detectable, and there are no restrictions concerning the complexity of the geometry. The present paper is a companion of a linked work dealing with linear material implementations

Computationally Efficient Concurrent Multiscale Framework for the Linear Analysis of Composite Structures

This paper presents a novel multiscale framework based on higher-order one-dimensional finite element models. The refined finite element models (FE) originate from the Carrera Unified Formulation (CUF), a novel and efficient methodology to develop higher-order structural theories hierarchically via a variable kinematic approach. The concurrent multiscale framework consists of a macroscale model to describe the structural level components interfaced with efficient CUF micromechanical models. Such micromechanical models can take into account the detailed architecture of the microstructure with high fidelity. The framework derives its efficiency from the capability of CUF models to detect accurate 3D-like stress fields at reduced computational costs. This paper also shows the ability of the framework to interface with different classes of representative volume elements (RVE) and the benefits of parallel implementations. The numerical cases focus on composite and sandwich structures and demonstrate the high-fidelity and feasibility of the proposed framework. The efficiency of the framework stems from comparisons with the analysis time and memory requirement against traditional multiscale implementations. The present paper is a companion of a linked work dealing with nonlinear material implementations

Computationally-efficient multiscale models for progressive failure and damage analysis of composites

L'abstract è presente nell'allegato / the abstract is in the attachmen

Computationally-efficient multiscale models for progressive failure and damage analysis of composites

A class of computationally-efficient tools to undertake progressive failure and damage analysis of composites across scales is presented. The framework is based on a class of refined one-dimensional (1D) theories referred to as the Carrera Unified Formulation (CUF), a generalized hierarchical formulation that generates a class of refined structural theories through variable kinematic description. 1D CUF models can provide accurate 3D-like stress fields at a reduced computational cost, e.g., approximately one to two orders of magnitude of degrees of freedom less as compared to standard 3D brick elements. The effectiveness of 1D CUF models to undertake physically nonlinear simulation is demonstrated through a class of problems with varying constitutive models. The virtual testing platform consists of a variety of computational tools such as failure index evaluations using component-wise modeling approaches (CUF-CW), CUF-CW micromechanics, concurrent multiscale framework, interface, and impact modeling. Failure index evaluation of a class of composite structures underlines the paramount importance of the accurate stress resolutions. Within the micromechanical framework, the Component-Wise approach (CW) is utilized to represent various components of the RVE. The crack band theory is implemented to capture the damage propagation within the constituents of composite materials and the pre-peak nonlinearity within the matrix constituents is modeled using the $J_2$ von-Mises theory. A novel concurrent multiscale framework is developed for nonlinear analysis of fiber-reinforced composites. The two-scale framework consists of a macro-scale model to describe the structural level components, e.g, open-hole specimens, coupons, using CUF-LW models and a sub-scale micro-structural model encompassed with a representative volume element (RVE). The two scales are interfaced through the exchange of strain, stress and stiffness tensors at every integration point in the macro-scale model. Explicit finite element computations at the lower scale are efficiently handled by the CUF-CW micromechanics tool. The macro tangent computation based on perturbation method which leads to meliorated performances. A novel numerical framework to simulate progressive delamination in laminated structures based on component-wise models is presented. A class of higher-order cohesive elements along with a mixed-mode cohesive constitutive law are integrated within the CUF-CW framework to simulate interfacial cohesive mechanics between various components of the structure. A global dissipation energy-based arc -length method to trace the complex equilibrium path exhibited by delamination problem. The capabilities of the framework are further extended through the introduction of contact kinematics to handle impact problems. A combination of the above tools is used to obtain an accurate material response of the structure in the non-linear regime, from the structural level i.e. macro-scale to the material constituent level i.e. the micro-scale, in a computationally efficient manner, providing a suitable virtual testing environment for the progressive damage analysis of composite structures. The accuracy and efficiency of the proposed computational platform are assessed via comparison against the traditional approaches as well as experimental results found in the literature

Learning constitutive models from microstructural simulations via a non-intrusive reduced basis method

In order to optimally design materials, it is crucial to understand the structure-property relations in the material by analyzing the effect of microstructure parameters on the macroscopic properties. In computational homogenization, the microstructure is thus explicitly modeled inside the macrostructure, leading to a coupled two-scale formulation. Unfortunately, the high computational costs of such multiscale simulations often render the solution of design, optimization, or inverse problems infeasible. To address this issue, we propose in this work a non-intrusive reduced basis method to construct inexpensive surrogates for parametrized microscale problems; the method is specifically well-suited for multiscale simulations since the coupled simulation is decoupled into two independent problems: (1) solving the microscopic problem for different (loading or material) parameters and learning a surrogate model from the data; and (2) solving the macroscopic problem with the learned material model. The proposed method has three key features. First, the microscopic stress field can be fully recovered. Second, the method is able to accurately predict the stress field for a wide range of material parameters; furthermore, the derivatives of the effective stress with respect to the material parameters are available and can be readily utilized in solving optimization problems. Finally, it is more data efficient, i.e. requiring less training data, as compared to directly performing a regression on the effective stress. For the microstructures in the two test problems considered, the mean approximation error of the effective stress is as low as 0.1% despite using a relatively small training dataset. Embedded into the macroscopic problem, the reduced order model leads to an online speed up of approximately three orders of magnitude while maintaining a high accuracy as compared to the FE$^2$ solver