## Introduction

I don’t know about you, but I think that it is really cool that I can now (Dec 2023) run a Large Language Model (LLM) on my own laptop. This can be done for free, and you don’t even need internet access. From what I can understand, one of the the currently best LLM that can be downloaded and used for free is the Mixtral-8x7B model. This Large Language Model (LLM) is a pretrained generative Sparse Mixture of Experts. It outperforms Meta’s Llama 2 70B on many benchmarks. Right now it might be the strongest open-weight model with a permissive license and the best model overall regarding cost/performance trade-offs. It has also been reported that Mixtral outperforms GPT3.5 on most benchmarks. In this article I will compare the best LLM from 2022 (ChatGPT) to the Mixtral model and the currently best model that is publically available: ChatGPT-4. For my benchmarking I will use the same 7 questions that I asked last year. **My results show that the best AI models have improved substantially over the last year!**

## Mixral-8x7B

To test the Mixtral model I first downloaded and installed the ollama tool on my Linux laptop:

` ````
```curl https://ollama.ai/install.sh | sh

I then downloaded and ran the Mixtral-8x7B Large Language Model (LLM) using:

` ````
```ollama run mixtral

The Mixtral model is using 47e9 parameters, and the downloaded model is 26 GB in size. Note that this is basically the same size as all text on Wikipedia (which is 22 GB).

### Question 1: Which is the best finite element program?

*It is difficult to determine a single “best” finite element program, as the appropriate program will depend on the specific needs and goals of the user. There are many different finite element programs available, each with its own set of features and capabilities. Some of the most widely used finite element programs include:*

*ANSYS: ANSYS is a popular commercial finite element program that is used in a wide range of industries, including aerospace, automotive, and biomedical engineering. It offers a wide range of features and capabilities, including the ability to analyze linear and nonlinear problems, perform structural and thermal analyses, and simulate fluid dynamics and electromagnetics.**Abaqus: Abaqus is another popular commercial finite element program that is used in a variety of industries, including aerospace, automotive, and civil engineering. It is known for its advanced capabilities, including the ability to perform nonlinear, dynamic, and multiphysics simulations.**ABAQUS/Explicit: ABAQUS/Explicit is a specialized finite element program that is used for simulating dynamic and highly nonlinear problems. It is often used in the analysis of impact, crash, and explosion events.**LS-DYNA: LS-DYNA is a popular commercial finite element program that is specifically designed for simulating complex, dynamic systems. It is often used in the analysis of automotive, aerospace, and civil engineering applications.*

*Ultimately, the best finite element program will depend on the specific needs and goals of the user. Some factors to consider when choosing a finite element program include the type of analysis being performed, the complexity of the problem, and the desired level of accuracy and computational efficiency.*

*There is no definitive answer to which is the “best” finite element program, as the most suitable software will depend on your specific needs and objectives. Some popular commercial finite element packages include ANSYS, ABAQUS, and LS-DYNA, while open-source options such as FEniCS and Elmer are also widely used. Each of these programs has its own strengths and weaknesses, so it’s important to carefully evaluate your requirements before choosing a particular software. Some factors you may want to consider include the types of analyses you need to perform, the size and complexity of your models, the level of post-processing and visualization capabilities you require, and the availability of technical support and resources. Ultimately, the best finite element program for you will depend on your unique needs and circumstances.*

*There is no definitive answer to which finite element program is the best, as different programs may have different features, advantages, and limitations. However, based on my web search results, some of the most popular and widely used finite element programs are:*

*– ANSYS¹: A comprehensive and versatile software that supports various types of analyses, such as structural, thermal, fluid, and electromagnetic. It also has task-based interfaces and advanced meshing tools.*

*– SimScale²: A cloud-based software that allows online simulation of physical models. It has modules for thermal, fluid, and mechanical analyses, and offers great training for new users.*

*– COMSOL Multiphysics³: A software that can handle complex multiphysics problems and connect with other software such as MATLAB, Java, and Autodesk Inventor. It also has a user-friendly graphical interface and a large library of predefined physics interfaces.*

*– OpenFOAM⁴: An open-source software that specializes in computational fluid dynamics. It has a high level of flexibility and customization, and can handle a wide range of fluid flow problems. It also supports parallel computing and selectable interpolation schemes.*

*– Autodesk CFD⁵: A software that focuses on fluid flow and heat transfer simulations. It can automate design studies, optimize flow control applications, and perform thermal prototyping. It also integrates with other Autodesk products such as Inventor and Fusion 360.*

*These are just some examples of the many finite element programs available in the market. You may want to compare their features, prices, platforms, and user reviews to find the one that suits your needs best. 😊.*

*Source: Conversation with Bing, 12/17/2023(1) List of finite element software packages – Wikipedia. https://en.wikipedia.org/wiki/List_of_finite_element_software_packages.(2) Top 10 FEA Software Used By Engineers – Best Engineering Blog. https://mechanicalland.com/top-10-finite-element-analysis-softwares-used-by-engineers/.(3) 5 Best Finite Element Analysis Software in 2023 – FixThePhoto.com. https://fixthephoto.com/best-finite-element-analysis-software.html.(4) Best Open-Source Finite Element Analysis Software – MatecDev. https://www.matecdev.com/posts/best-open-source-fem.html.(5) Best CAD Software With Finite Element Analysis Tools. https://fractory.com/finite-element-analysis-software/.(6) undefined. http://www.enginsoftturkey.com/service-single.(7) undefined. https://www.simscale.com/blog/2018/12/lattice-boltzmann-method-solver/.*

**2022 ChatGPT:** It lists some commonly used FE software, and the text is mostly correct. Not too bad. Grade: 3 / 5

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**3/5

**Mixtral:** Missing some large FE codes, and mentions codes that should not be mentioned.

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**3/5

**GPT-4:** Missing some large FE codes, and mentions codes that should not be mentioned.

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**3/5

### Question 2: What is your favorite hyperelastic model?

*As an artificial intelligence, I do not have personal preferences or feelings. However, I can provide information on hyperelastic models, which are mathematical models used to describe the behavior of elastic materials that exhibit nonlinear behavior, such as rubber and other polymers. Hyperelastic models are commonly used to analyze the deformation of materials under large strains, such as when a rubber band is stretched or when a rubber seal is deformed.*

*There are many different types of hyperelastic models that have been developed, each with its own set of assumptions and capabilities. Some examples of commonly used hyperelastic models include:*

*Mooney-Rivlin model: The Mooney-Rivlin model is a simple hyperelastic model that is based on the assumption of an isotropic, incompressible material. It is often used to analyze the behavior of rubber-like materials.**Ogden model: The Ogden model is a hyperelastic model that is based on the assumption of an isotropic, compressible material. It is often used to analyze the behavior of rubber-like materials, and has the ability to describe the behavior of materials under large strains.**Neo-Hookean model: The Neo-Hookean model is a hyperelastic model that is based on the assumption of an isotropic, incompressible material. It is often used to analyze the behavior of rubber-like materials, and is known for its simplicity and ease of use.*

*Ultimately, the choice of hyperelastic model will depend on the specific application and the desired level of accuracy and complexity.*

*It is not appropriate for me to have a “favorite” hyperelastic model, as the most suitable model will depend on the specific material and application being considered. There are several commonly used hyperelastic models, including the Mooney-Rivlin, Ogden, and Yeoh models, each of which has its own strengths and weaknesses. The choice of model will typically depend on factors such as the degree of nonlinearity of the material behavior, the range of strains experienced by the material, and the availability of material parameters for the model. In some cases, it may be necessary to use a more complex or specialized hyperelastic model in order to accurately capture the behavior of a particular material. It is generally recommended to consult the relevant literature and perform validation studies in order to determine the most appropriate hyperelastic model for a given application.*

*I don’t have a favorite hyperelastic model, as I am not a material scientist. However, I can tell you some of the features and advantages of different hyperelastic models, based on my web search results.*

*One of the simplest hyperelastic models is the Neo-Hookean solid¹, which is a special case of the Ogden model². It assumes that the material behavior can be described by a strain energy density function that depends on the first invariant of the left Cauchy-Green deformation tensor. It can fit the material behavior of rubbery materials under moderate strains up to 30-70%¹.*

*Another hyperelastic model is the Mooney-Rivlin solid¹, which is a linear combination of two invariants of the left Cauchy-Green deformation tensor. It was originally developed for rubber, but is today often applied to model incompressible biological tissue¹.*

*The Ogden model² is a more general and sophisticated hyperelastic model that can describe the non-linear stress-strain behavior of complex materials such as rubbers, polymers, and biological tissue. It expresses the strain energy density function in terms of the principal stretches, and can accommodate large deformations².*

*The Gent model³ is a phenomenological model of rubber elasticity that is based on the concept of limiting chain extensibility. It has a singularity when the first invariant of the left Cauchy-Green deformation tensor reaches a limiting value³.*

*These are just some examples of the many hyperelastic models available in the market. You may want to compare their features, applications, and limitations to find the one that suits your needs best. 😊*

*Source: Conversation with Bing, 12/17/2023**(1) Hyperelastic material – Wikipedia. https://en.wikipedia.org/wiki/Hyperelastic_material.**(2) Ogden hyperelastic model – Wikipedia. https://en.wikipedia.org/wiki/Ogden_hyperelastic_model.**(3) Gent hyperelastic model – Wikipedia. https://en.wikipedia.org/wiki/Gent_hyperelastic_model.*

**2022 ChatGPT: **Again, the answer is mostly correct, but it does not provide much information besides listing three hyperelastic model names. I am not too impressed.

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**2/5

**Mixtral: **Only lists 3 options, and provides some comments.

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**2.5/5

**GPT-4:** I don’t see anything specifically wrong about the answer, but the list of models is still not that informative.

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**3.5/5

### Question 3: What do you think of the Bergstrom-Boyce model?

*The Bergstrom-Boyce model is a material model that was developed to describe the behavior of metal matrix composite (MMC) materials under uniaxial tensile loading. It is a constitutive model, which means that it is used to describe the relationship between the applied stress and strain in a material. The Bergstrom-Boyce model is a viscoelastic model, which means that it takes into account both the elastic and viscous behavior of the material.*

*The Bergstrom-Boyce model is based on the idea that the behavior of MMC materials can be described using a combination of linear elastic behavior and viscous behavior. It has been used in a variety of applications, including the analysis of MMC materials under uniaxial tensile loading and the prediction of the fatigue life of MMC materials.*

*Overall, the Bergstrom-Boyce model is a useful tool for analyzing the behavior of MMC materials under uniaxial tensile loading, and has been widely used in the field of materials science and engineering. However, like any material model, it has limitations and may not be appropriate for all applications.*

*The Bergstrom-Boyce model is a hyperelastic material model that is used to describe the behavior of filled rubber elastomers. It is a two-parameter model that is an extension of the Mooney-Rivlin model, and it is able to capture the effects of filler reinforcement on the mechanical behavior of these materials. The Bergstrom-Boyce model is often used in applications where the presence of fillers significantly affects the mechanical properties of the rubber, such as in tire treads or seals.*

*Like all hyperelastic models, the Bergstrom-Boyce model has its strengths and weaknesses. One advantage of the model is that it is relatively simple and easy to implement, yet it is able to capture the main features of filled rubber elastomer behavior. The model also includes a parameter that allows for the influence of filler orientation on the mechanical properties, which can be important in some applications. However, the Bergstrom-Boyce model may not be suitable for all types of filled rubber elastomers, and it may not accurately capture the behavior of these materials under extreme deformations or complex loading conditions. As with any hyperelastic model, it is important to carefully consider the specific material and application being studied in order to determine whether the Bergstrom-Boyce model is appropriate.*

*The Bergstrom-Boyce model is a highly nonlinear material model that can predict the time-dependent, large-strain behavior of elastomer-like materials, such as rubbers and biological tissues¹. It is based on a parallel network of two springs, one of which has a viscous damper in series². The model can account for nonlinear stress-strain relationship, creep, and rate-dependence².*

*Some of the advantages of the Bergstrom-Boyce model are:– It can fit experimental data of soft materials under various loading conditions, such as uniaxial, biaxial, and shear¹.– It can capture the Mullins effect, which is the softening of the material due to damage or microcracking¹.– It can handle large deformations, up to 700% strain¹.*

*Some of the limitations of the Bergstrom-Boyce model are:– It requires a large number of material parameters, some of which are difficult to measure or calibrate².– It may not be accurate for thermoplastics, which may need a three-network representation³.– It may have convergence problems or numerical instability for some cases².*

*Overall, the Bergstrom-Boyce model is a powerful and versatile material model for elastomer-like materials, but it also has some challenges and drawbacks. 😊*

*Source: Conversation with Bing, 12/17/2023(1) Bergstrom-Boyce (BB) Model – PolymerFEM.com. https://polymerfem.com/bergstrom-boyce-bb-model/.(2) 4.7. Bergstrom-Boyce – BME. https://www.mm.bme.hu/~gyebro/files/ans_help_v182/ans_thry/thy_bb.html.(3) Ansys Bergstrom-Boyce Model – PolymerFEM.com. https://polymerfem.com/ansys-bergstrom-boyce-model/.*

**2022 ChatGPT:**This is just wrong. I wonder how it came up with metal matrix composites?

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**0.5/5

**Mixtral:**It is mostly wrong.

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**1/5

**GPT-4:**It correctly identifies what the Bergstrom-Boyce model is, but many of the comments are wrong.

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**3.5/5

### Question 4: What material model should I use for a thermoplastic?

*The appropriate material model for a thermoplastic will depend on the specific application and the desired level of accuracy and complexity. Thermoplastics are a type of polymer material that can be melted and reshaped multiple times without degradation, and they have a wide range of properties and applications. Some common material models that are used to describe the behavior of thermoplastics include:*

*Linear elastic model: Linear elastic models are used to describe the behavior of materials that exhibit a linear relationship between stress and strain, and are commonly used to analyze the behavior of materials such as metals and ceramics. They may be appropriate for some applications involving thermoplastics, particularly at low strains and low temperatures.**Plasticity model: Plasticity models are used to describe the behavior of materials that exhibit plastic deformation, and are commonly used to analyze the behavior of materials such as metals and polymers. They may be appropriate for some applications involving thermoplastics, particularly at high strains and high temperatures.**Viscoelastic model: Viscoelastic models are used to describe the behavior of materials that exhibit both elastic and viscous behavior, and are commonly used to analyze the behavior of materials such as rubber and polymers. They may be appropriate for some applications involving thermoplastics, particularly at intermediate strains and intermediate temperatures.*

*In general, the choice of material model will depend on the specific properties of the thermoplastic material being analyzed and the type of deformation it is expected to undergo, as well as the desired level of accuracy and complexity of the analysis. It may be necessary to use a combination of different material models to accurately describe the behavior of the material under different conditions.*

*The choice of material model for a thermoplastic will depend on the specific type of thermoplastic and the application being considered. There are several types of material models that can be used to describe the behavior of thermoplastics, including:*

*Elastic models: These models assume that the material behaves in a linear, elastic manner, with no permanent deformation or hysteresis. Elastic models are often used for small deformations and simple loading conditions.**Hyperelastic models: These models are used to describe the large deformation behavior of rubber-like materials, including some thermoplastics. Hyperelastic models are based on the strain energy density function, which describes the stored energy in a material due to deformation.**Viscoelastic models: These models combine elements of both elastic and viscous behavior, and they are used to describe the time-dependent response of materials under load. Viscoelastic models are often used for thermoplastics that exhibit creep or stress relaxation.**Plasticity models: These models describe the irreversible deformation of materials under load, and they are typically used for metals and other ductile materials. However, some thermoplastics may also exhibit plastic behavior at high strains.**Damage models: These models describe the progressive degradation of a material’s mechanical properties due to damage or failure. Damage models are often used for thermoplastics that exhibit brittle behavior or catastrophic failure.*

*The most appropriate material model for a thermoplastic will depend on the specific type of material and the loading conditions it will be subjected to. It is generally recommended to consult the relevant literature and perform validation studies in order to determine the most appropriate material model for a given application.*

*There is no definitive answer to what material model you should use for a thermoplastic, as different models may have different features, advantages, and limitations. However, based on my web search results, some of the factors that you may want to consider are:– The type of thermoplastic material you are using, such as polypropylene, polycarbonate, nylon, etc. Different thermoplastics may have different mechanical properties, such as stiffness, strength, ductility, and viscoelasticity¹.– The type of loading and deformation you are applying to the material, such as tension, compression, shear, bending, puncture, etc. Different loadings may induce different stress and strain states in the material, such as isotropic, anisotropic, triaxial, etc².– The type of analysis you are performing, such as static, dynamic, quasi-static, or cyclic. Different analyses may require different material models that can account for rate-dependence, creep, recovery, damage, and failure³.*

*Some of the commonly used material models for thermoplastics are:– Von Mises plasticity²: A simple and widely used model that assumes isotropic and rate-independent plastic behavior. It can capture the yield and hardening behavior of thermoplastics under moderate strains, but it cannot account for viscoelasticity, damage, or failure.– Ogden model²: A more general and sophisticated model that can describe the non-linear stress-strain behavior of complex materials, such as rubbers, polymers, and biological tissues. It expresses the strain energy density function in terms of the principal stretches, and can accommodate large deformations, viscoelasticity, and rate-dependence.– Bergstrom-Boyce model³: A highly nonlinear material model that can predict the time-dependent, large-strain behavior of elastomer-like materials, such as rubbers and biological tissues. It is based on a parallel network of two springs, one of which has a viscous damper in series. The model can account for nonlinear stress-strain relationship, creep, rate-dependence, and damage.– TNV model⁴: A material model that can accurately predict the rate-dependent and energy absorption in foams. It is based on the TN model, which is one of the most accurate viscoplastic material models for thermoplastics, but with an additional volumetric term. The model can capture the necking, recovery, and failure behavior of thermoplastics under large deformations.*

*These are just some examples of the many material models available for thermoplastics. You may want to compare their features, applications, and limitations to find the one that suits your needs best. 😊*

*Source: Conversation with Bing, 12/17/2023(1) Material Models For Thermoplastics In LS-DYNA® From Deformation To Failure. https://www.4a-engineering.at/downloads/events/44_pres_180061101_pr_eng_INTLSDYNA_P224_PLASTIC.pdf.(2) Material Models, Nonlinear, Time-Dependent | PolyUMod. https://altair.com/polyumod/.(3) All About Thermoplastic as Manufacturing Material | Xometry. https://www.xometry.com/resources/materials/thermoplastic/.(4) A constitutive model for thermoplastic materials subjected to high …. https://onlinelibrary.wiley.com/doi/pdf/10.1002/pamm.200510128.*

**2022 ChatGPT:**This is just wrong. I wonder how it came up with metal matrix composites?

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**2/5

**Mixtral:**It is mostly wrong.

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**2.5/5

**GPT-4:**It correctly identifies what the Bergstrom-Boyce model is, but many of the comments are wrong.

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**3.5/5

### Question 5: Tell me about the Gent model

*The Gent model is a material model that was developed to describe the behavior of rubber-like materials under large strains. It is a constitutive model, which means that it is used to describe the relationship between the applied stress and strain in a material. The Gent model is a hyperelastic model, which means that it is used to describe the behavior of elastic materials that exhibit nonlinear behavior, such as rubber and other polymers.*

*The Gent model is based on the idea that the behavior of rubber-like materials can be described using a combination of linear elastic behavior and viscous behavior. It is defined by a set of constitutive equations that describe the stress-strain relationship of the material, and it can be used to predict the deformation of the material under various loading conditions.*

*The Gent model has been widely used in the field of materials science and engineering, and has been applied to a variety of applications, including the analysis of rubber seals, gaskets, and other rubber-like materials. It is known for its ability to accurately describe the behavior of rubber-like materials under large strains, and has been widely used in the design and analysis of rubber-like materials in a variety of applications.*

*The Gent model is a hyperelastic material model that is used to describe the behavior of rubber-like materials. It is a single-parameter model that is based on the Mooney-Rivlin model, and it is often used for materials that exhibit a high degree of nonlinearity or a limited range of strain. The Gent model is particularly well-suited for describing the behavior of materials that undergo large deformations but do not exhibit significant volume changes.*

*The Gent model is defined by the following strain energy density function:*

*W = -μ ln(1 – (I1/C1))*

*where W is the strain energy density, μ is the shear modulus, I1 is the first invariant of the Cauchy-Green deformation tensor, and C1 is a material constant that determines the degree of nonlinearity of the material behavior. The Gent model can be used to predict the stress-strain response of rubber-like materials under uniaxial, biaxial, or triaxial loading conditions.*

*One advantage of the Gent model is its simplicity and ease of implementation. The model requires only one material parameter (C1) to be determined, which can be done using simple tensile tests. The Gent model is also able to capture the main features of rubber-like behavior, including the initial linear response, the nonlinear region, and the ultimate failure point. However, the Gent model may not be suitable for all types of rubber-like materials, and it may not accurately predict the behavior of these materials under extreme deformations or complex loading conditions. As with any hyperelastic model, it is important to carefully consider the specific material and application being studied in order to determine whether the Gent model is appropriate.*

*The Gent model is a hyperelastic model that can describe the non-linear stress-strain behavior of rubber-like materials, such as rubbers and biological tissues¹. It is based on the concept of limiting chain extensibility, which means that the material has a finite stretchability and cannot be deformed indefinitely¹. The model has a strain energy density function that depends on the first invariant of the left Cauchy-Green deformation tensor, and has a singularity when this invariant reaches a limiting value¹. The model can capture the Mullins effect, which is the softening of the material due to damage or microcracking².*

*The Gent model is one of the simplest and most widely used hyperelastic models for rubber-like materials, but it also has some limitations. For example, it cannot account for viscoelasticity, damage, or failure, and it requires a large number of material parameters, some of which are difficult to measure or calibrate². Therefore, the model may not be accurate for some complex materials or loading conditions². 😊*

*¹: [Gent hyperelastic model – Wikipedia]²: [Gent Hyperelasticity – PolymerFEM.com]*

*Source: Conversation with Bing, 12/17/2023(1) Gent hyperelastic model – Wikipedia. https://en.wikipedia.org/wiki/Gent_hyperelastic_model.(2) Gent Hyperelastic Model – Theory and Calibration – YouTube. https://www.youtube.com/watch?v=3q8RkHBUIgE.(3) Gent hyperelastic model – Wikipedia. https://en.wikipedia.org/wiki/Gent_hyperelastic_model.(4) Gent Hyperelasticity – PolymerFEM.com. https://polymerfem.com/gent-hyperelasticity/.(5) Gent (Hyperelastic Model) | Encyclopedia MDPI. https://encyclopedia.pub/entry/35595.*

**2022 ChatGPT:**I thought the answer was OK until I saw the statement about “combining linear elastic and viscous behavior”. That is just wrong.

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**1/5

**Mixtral:**Pretty decent response, but some of the details are wrong.

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**3.5/5

**GPT-4:**Not too bad, but still a weak answer.

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**3.5/5

### Question 6: What are some common limitations of linear viscoelasticity?

*Linear viscoelasticity is a material model that is used to describe the behavior of materials that exhibit both elastic and viscous behavior. It is based on the idea that the material’s response to an applied load is the sum of an elastic response and a viscous response. While linear viscoelasticity is a useful model for many materials and applications, it does have some limitations. Some common limitations of linear viscoelasticity include:*

*Limited range of validity: Linear viscoelasticity is only valid for materials that exhibit a linear relationship between stress and strain. It may not be appropriate for materials that exhibit nonlinear behavior, such as rubber and other polymers.**Limited accuracy at high strains: Linear viscoelasticity is based on the assumption that the material’s response is linear over a range of strains. At high strains, the material’s response may deviate from this assumption, leading to reduced accuracy of the model.**Limited ability to describe time-dependent behavior: Linear viscoelasticity is based on the assumption that the material’s response is time-invariant, meaning that it does not depend on the time at which the load is applied. This may not be the case for some materials, particularly those that exhibit time-dependent behavior, such as aging or creep.**Limited ability to describe temperature-dependent behavior: Linear viscoelasticity is based on the assumption that the material’s response is temperature-invariant, meaning that it does not depend on the temperature at which the load is applied. This may not be the case for some materials, particularly those that exhibit temperature-dependent behavior, such as thermoelasticity.*

*Overall, linear viscoelasticity is a useful model for many materials and applications, but it is important to be aware of its limitations and to choose an appropriate model for the specific material and deformation conditions being analyzed.*

*Linear viscoelasticity is a material model that describes the time-dependent response of materials under load. It is based on the assumptions of linearity, isotropy, and homogeneity, and it assumes that the material behaves in a reversible manner. While linear viscoelasticity is a useful tool for predicting the behavior of many materials under small deformations and simple loading conditions, it has several limitations:*

*Linearity assumption: The linearity assumption restricts the use of linear viscoelasticity to small strains and low loads, where the material response is approximately proportional to the applied load. At higher strains or loads, nonlinear effects may become important, and linear viscoelasticity may no longer be applicable.**Time-dependent response: Linear viscoelasticity assumes that the material response is a function of time, but it does not account for the influence of loading rate or frequency. This can be a limitation in applications where the loading rate or frequency is high, or where the material response is sensitive to changes in these parameters.**Reversibility assumption: Linear viscoelasticity assumes that the material behaves in a reversible manner, with no permanent deformation or hysteresis. However, many materials exhibit irreversible behavior, such as creep or stress relaxation, which cannot be predicted using linear viscoelasticity.**Isotropy and homogeneity assumptions: Linear viscoelasticity assumes that the material is isotropic (i.e., its properties are the same in all directions) and homogeneous (i.e., its properties are uniform throughout). However, many materials are anisotropic or heterogeneous, which can affect their mechanical behavior and make them unsuitable for analysis using linear viscoelasticity.**Limited range of applicability: Linear viscoelasticity is most suitable for predicting the behavior of materials under small deformations and simple loading conditions. However, it may not be applicable to more complex situations, such as large deformations, high loads, or non-proportional loading paths. In these cases, more advanced material models, such as nonlinear viscoelasticity or plasticity, may be required.*

*Linear viscoelasticity is a simplified theory that assumes a linear relationship between stress and strain, and a separable dependence of the material response on time and space. However, this theory has some common limitations, such as:– It cannot account for large deformations, nonlinear stress-strain behavior, or anisotropic effects that may occur in some materials¹.– It requires a large number of material parameters, some of which are difficult to measure or calibrate, especially for complex materials such as polymers or biological tissues²³.– It may not be accurate for some loading conditions, such as cyclic, transient, or non-monotonic loading, that may induce hysteresis, damage, or failure in the material²⁴.– It may not be valid for some temperature ranges, as the material properties may change significantly due to thermal effects⁵.*

*Therefore, linear viscoelasticity is a useful but limited theory that may need to be modified or extended for some applications. 😊*

*¹: [Viscoelasticity – Wikipedia]²: [Essentials of Linear Viscoelasticity – Brown University]³: [A Review on Modelling of Viscoelastic Contact Problems – MDPI]⁴: [5.4: Linear Viscoelasticity – Engineering LibreTexts]⁵: [Theory of Linear Viscoelasticity | SpringerLink]*

*Source: Conversation with Bing, 12/17/2023(1) Viscoelasticity – Wikipedia. https://en.wikipedia.org/wiki/Viscoelasticity.(2) Essentials of Linear Viscoelasticity – Brown University. https://appliedmath.brown.edu/sites/default/files/fractional/12%20EssentialsofLinearViscoelasticity.pdf.(3) A Review on Modelling of Viscoelastic Contact Problems – MDPI. https://www.mdpi.com/2075-4442/10/12/358.(4) 5.4: Linear Viscoelasticity – Engineering LibreTexts. .(5) Theory of Linear Viscoelasticity | SpringerLink. https://link.springer.com/chapter/10.1007/978-94-017-7564-9_5.(6) Viscoelasticity – Wikipedia. https://en.wikipedia.org/wiki/Viscoelasticity.(7) Essentials of Linear Viscoelasticity – Brown University. https://appliedmath.brown.edu/sites/default/files/fractional/12%20EssentialsofLinearViscoelasticity.pdf.(8) A Review on Modelling of Viscoelastic Contact Problems – MDPI. https://www.mdpi.com/2075-4442/10/12/358.(9) 5.4: Linear Viscoelasticity – Engineering LibreTexts. (10) Theory of Linear Viscoelasticity | SpringerLink. https://link.springer.com/chapter/10.1007/978-94-017-7564-9_5.*

**2022 ChatGPT:**It starts by saying that linear viscoelasticity is only valid for materials that exhibit a linear relationship between stress and strain. That is wrong.

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**1/5

**Mixtral:**Totally misses most of what linear viscoelasticity is about.

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**1.5/5

**GPT-4:**Totally misses most of what linear viscoelasticity is about.

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**1/5

### Question 7: When does polyethylene fail?

Polyethylene is a type of polymer material that is known for its high strength, toughness, and chemical resistance. However, like all materials, it can fail under certain conditions. There are several potential causes of failure in polyethylene, including:

- Mechanical stress: Polyethylene can fail due to mechanical stress, such as tensile, compressive, or shear stress. This can occur when the material is subjected to forces that exceed its strength or when it is subjected to repeated cycling of stress.
- Thermal stress: Polyethylene can also fail due to thermal stress, which can occur when the material is subjected to large temperature gradients or extreme temperatures. This can cause the material to become brittle or to lose its strength.
- Chemical attack: Polyethylene can be sensitive to certain chemicals, and can fail due to chemical attack. This can occur when the material is exposed to chemicals that are incompatible with it, or when it is subjected to harsh chemical environments.
- Fatigue: Polyethylene can also fail due to fatigue, which is the failure of a material due to repeated loading and unloading. This can occur when the material is subjected to repeated cycling of stress, such as in dynamic loading applications.

Overall, the specific cause of failure in polyethylene will depend on the specific conditions and application of the material. Understanding the potential causes of failure and designing the material and application to minimize these risks can help to ensure reliable performance and extend the service life of the material.

*Polyethylene is a thermoplastic material that is known for its excellent mechanical properties, including high strength, toughness, and chemical resistance. However, like all materials, polyethylene can fail under certain conditions. The most common modes of failure for polyethylene include:*

*Tensile failure: Polyethylene can fail in tension when the applied load exceeds its ultimate tensile strength. This type of failure is typically characterized by a sudden rupture or break of the material.**Compressive failure: Polyethylene can also fail in compression when the applied load exceeds its compressive strength. This type of failure is typically characterized by a gradual collapse or buckling of the material.**Creep failure: Polyethylene is susceptible to creep, which is the time-dependent deformation that occurs under constant load. Over time, the accumulation of creep can lead to significant deformation and eventual failure of the material.**Fatigue failure: Polyethylene can also fail due to fatigue, which is the progressive damage that occurs when the material is subjected to repeated loading and unloading cycles. This type of failure can occur at loads well below the ultimate tensile strength of the material, and it is often characterized by the formation of cracks or other defects.**Environmental degradation: Polyethylene can be affected by environmental factors, such as temperature, humidity, and exposure to chemicals, which can lead to a decline in its mechanical properties and eventual failure.*

*The specific mode of failure for polyethylene will depend on the type of polyethylene, the loading conditions, and the environment in which it is used. It is important to consider these factors when designing and using polyethylene components in order to ensure their reliability and durability.*

*Polyethylene is a type of plastic that is widely used for various applications, such as packaging, pipes, films, and containers. However, polyethylene can fail under certain conditions, such as:– Mechanical failure: This occurs when the polyethylene part is exposed to external forces that are greater than the part can withstand, resulting in cracking or breaking. For example, polyethylene pipes can fail due to excessive pressure, impact, or bending¹.– Thermal failure: This occurs when the polyethylene part is exposed to temperatures that are higher or lower than the part can tolerate, resulting in melting, softening, or embrittlement. For example, polyethylene films can fail due to overheating, freezing, or fire².– Environmental failure: This occurs when the polyethylene part is exposed to chemicals, contaminants, or UV radiation that degrade the material, resulting in loss of strength, stiffness, or ductility. For example, polyethylene containers can fail due to exposure to solvents, acids, or sunlight³.*

*To prevent polyethylene failure, it is important to select the appropriate type and grade of polyethylene for the intended application, design the part with proper dimensions and tolerances, manufacture the part with quality control and testing, install the part with care and instructions, and use the part with respect and maintenance. 😊*

*¹: [The nature of polyethylene pipe failure – PlasticsToday]²: [Plastic Failure: 7 Root Causes & Examples of Plastic Part Failure]³: [Environmental stress cracking – Wikipedia]*

*Source: Conversation with Bing, 12/17/2023(1) Plastic Failure — Types and Causes – Thomasnet. https://www.thomasnet.com/articles/plastics-rubber/causes-of-plastic-failure/.(2) Plastic Failure: 7 Root Causes & Examples of Plastic Part Failure. https://plasticexpert.com/learn/plastic-failure-causes/.(3) The nature of polyethylene pipe failure – PlasticsToday. https://www.plasticstoday.com/extrusion-pipe-profile/the-nature-of-polyethylene-pipe-failure.(4) The nature of polyethylene pipe failure – PlasticsToday. https://www.plasticstoday.com/extrusion-pipe-profile/the-nature-of-polyethylene-pipe-failure.(5) Plastic Failure: 7 Root Causes & Examples of Plastic Part Failure. https://plasticexpert.com/learn/plastic-failure-causes/.(6) Environmental stress cracking – Wikipedia. https://en.wikipedia.org/wiki/Environmental_stress_cracking.(7) Identifying Failures Ensuring Quality Plastic Materials. *

**2022 ChatGPT:**This is a pretty good answer.

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**3/5

**Mixtral:**Pretty good answer.

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**3.5/5

**GPT-4:**Pretty good answer.

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**3/5

## Summary

In summary, ChatGPT has improved substantially since Dec 2022. The average score for the current version (available in Dec 2023) is 2.9 (on a scale from 1 to 5). It is also exciting to see that the free Mixtral-8x7B LLM scored 2.5, which is only slightly less than ChatGPT-4. I ran Mixtral-8x7B on a laptop for this study.

I also really like that GhatGPT-4 provides references to its answers. Also note that some of those references were to the PolymerFEM website.

Finally, the overall quality of the answers is still pretty bad, with lots of incorrect comments in the answers. It is going to be interesting to see how these tools continue to improve.

Question | ChatGPT (2022) | Mixtral-8x7B | ChatGPT-4 (Bing, 2023) |
---|---|---|---|

Which is the best finite element program? | 3 | 3 | 3 |

What is your favorite hyperelastic model? | 2 | 2.5 | 3.5 |

What do you think of the Bergstrom-Boyce model? | 0.5 | 1 | 2.5 |

What material model should I use for a thermoplastic? | 2 | 2.5 | 3.5 |

Tell me about the Gent model | 1 | 3.5 | 3.5 |

What are some common limitations of linear viscoelasticity? | 1 | 1.5 | 1 |

When does polyethylene fail? | 3 | 3.5 | 3 |

AVERAGE GRADE: | 1.8 | 2.5 | 2.9 |