Sheldon's unique intellect sets him apart from the other characters on The Big Bang Theory, and makes him harder to relate to. However, his relationship with Amy changes him over the course of the show, making him less obnoxious and more tolerable. By the end, he evolves into someone relatively relatable, in a relationship that sometimes imitates those in reality.
There isn't much any real relationship can have in common with a sitcom one, but there are elements of Amy and Sheldon's affair of the heart that the audience can identify with. Between the bazingas and complex science references, the show slips in some realistic moments and storylines about the couple that makes them more relatable than others.
They Work Together To Achieve A Goal
One of the best things about Amy and Sheldon's relationship is the way they work together, especially academically. Considering the way Sheldon is condescending when it comes to academics and not wanting to share credit, it's nice to see him act differently with Amy. Their work together on super-asymmetry even earns them a Nobel Prize—one of the best career achievements on The Big Bang Theory.
Not every couple may win a Nobel Prize but they can definitely relate to working with their partner to achieve a certain goal. It can be anything as small as figuring out how to cut down on monthly expenses or something bigger, like buying a new house. Whatever the goal, Amy and Sheldon's partnership perfectly mirrors the way couples work together to achieve it.
They Have Scheduled Date Nights
As part of their relationship agreement, the couple has designated date nights when they either go to a restaurant or hang out in one of their apartments. Those nights are strictly enforced and when Sheldon goes away in "The Status Quo Combustion," Amy insists that he has to make up for all the dates he missed upon his return.
This is a realistic aspect of their relationship—minus the relationship agreement. With so many commitments like work and family, couples sometimes have to actively schedule time with each other and date nights to keep the romance alive. Although it might not involve something as fun as the relationship agreement Amy and Sheldon have, the principle is the same.
The Break Up Because Of Feeling Undervalued
After a sweet kiss in Sheldon's apartment in the episode, "The Commitment Determination," Amy comments on that date night being their fifth anniversary. Instead of building on that, Sheldon asks her if he should watch the new Flash TV show. This upsets Amy as she realizes that Sheldon takes her for granted, despite how patient she's been with him, and they break up shortly after.
One of the many reasons couples break up in real life is because one of them feels unappreciated by the other like Amy feels. With good communication of the issue, some are able to fix the problem. For Amy and Sheldon, things weren't so easy to fix because at first, he didn't even see what was wrong and kept blaming her for overreacting.
They Help Each Other Navigate Social Interactions
A running gag throughout the show is Sheldon's trouble navigating social interactions. Leonard and Penny usually help him with those and so does Amy once they're in a relationship. Unlike Leonard and Penny, who are often frustrated by him, Amy is a little more patient and kind when she corrects and advises him.
From social interactions to life in general, couples usually rely on each other to navigate both. Amy understands Sheldon's troubles because she was socially awkward for a while too but improved thanks to her friendship with Penny. That's why she's the best person to help him understand when he's wrong and tell him how to fix it. One good example is when she points out that he hurt and offended their friends just before their Nobel Prize ceremony.
They Hide Their Feelings From Each Other
Penny and Leonard's love story drags on through the seasons but Sheldon and Amy have them beat when it comes to the slow progression of their relationship. Before they officially start dating, Sheldon repeatedly specifies that Amy is a girl who's his friend, but not his girlfriend. When someone else shows interest in her, Sheldon eventually admits to Amy that he wants her to be his girlfriend.
It's not uncommon for people to hide or deny their true feelings about each other. Like Sheldon, it might be because they're afraid to take the relationship to the next level or they're worried about ruining a good friendship in case the other person doesn't feel the same way.
They Try Moving In Together To See How It Goes
After a pipe bursts in Amy's apartment, she and Sheldon take it as an opportunity to try living together for a while in Penny's apartment. Their experiment initially has a five-week end date but eventually, their living arrangement becomes permanent.
In reality, moving in together is a step that couples take when they feel that they're ready to take their relationship to another level. The way Amy and Sheldon learn to adjust to living together and accomodating their individual habits and preferences are all things that real couples can identify with too.
They Share A Common Interest
Out of all the couples and pairings on The Big Bang Theory, Amy and Sheldon have the most in common. Apart from their social awkwardness, they're both passionate about science even if their fields of interest are different.
It might not be neuroscience and theoretical physics but a lot of couples share some common interests too. Amy and Sheldon's shared interest in science allows them to understand each other and that's something real couples can relate to. From inside jokes to spirited conversations, a shared interest can help a couple bond and strengthen their relationship as it did for Sheldon and Amy.
They Take Care Of Each Other When They're Sick Or Emotional
When Amy falls sick in "The Fish Guts Displacement," Sheldon nurses her back to health. Similarly, when he's stressing about not being able to identify people's emotions on his own, she lets him open up to her without judgment and comforts him after. There are plenty more times like these throughout the series when the two of them take care of each other.
Just as Amy and Sheldon turn to each other in moments of sickness or emotional turmoil, so do couples in real life. A person's significant other is usually the person who knows them best and how to comfort them or help them feel better again.
They Talk To Each Other About Their Troubles
When either Sheldon or Amy have something troubling them, they turn to each other for comfort or advice. One example is in season 9 episode, "The Empathy Optimization" when Sheldon complains that his friends are upset with him because he was mean to them when he was sick—which he feels wasn't wrong.
In most relationships, one partner is the other's go-to in times of trouble. Just as Amy and Sheldon advise and comfort each other, couples in reality also help each other with whatever problems they're facing. In this case, Amy tells him to apologize to his friends and even makes him practice saying it genuinely so they can be in good books again.
They Have Intimacy Issues
When Sheldon and Amy first meet, they share the same aversion to intimate relations. With time, both of them warm up to the idea and get comfortable with being intimate together.
This is an aspect of a relationship that's common even in reality. Some couples take time getting to a stage where they're comfortable being intimate with each other. In such cases, they might take it slow like Sheldon and Amy do until both of them feel ready.