You may also have diarrhea or a fever. It is sometimes called stomach flu, but it is not the flu. Germs like viruses and bacteria can cause it. You can catch it from someone else who has it, or you can get it from food poisoning. Food poisoning can happen if you eat foods that contain harmful germs.
The circular muscle located at the entrance and exit to the stomach is called the sphincter. So for this question, you are talking about two distinct sphincters. This anatomical structure is able to open, and contract or close as needed.
First one is the Upper Oesophageal Sphincter, which allows entry of a food bolus into the oesophagus. Then the Lower Oesophageal Sphincter (also known as cardia, or cardiac sphincter), found at the entrance to the stomach. This stops reflux of food back up the oesophagus. Next is the pyloric sphincter, which allows stomach contents into the duodenum (small intestine) for further digestion. Then the ilio-caecal valve, which isn't a sphincter, but mediates movement of small intestine contents into the large intestine (caecum).